Keynote Lectures ICCSE1

Earlier developed ideas on gradient and stochastic mechanics are used to model the mechanical behavior of composites materials and structures across the scale spectrum. The interaction of deterministic strain gradients and random internal stresses is considered and the implications on macroscopic stress-strain curves and observed size effects are discussed. The proposed framework is general enough to account for various types of composite materials ranging from metal matrix and polymeric ones to concrete and biological tissues. Some remarks on FE implementations are also given.

The present study introduces a rigorous higher-order polynomial in the thickness coordinate to develop a theory with thickness and shear deformations for doubly curved, laminated composite shells. In this theory, the nonlinear terms in all the kinematic parameters are kept. By applying the conditions of zero transverse normal and shear stresses at the top and bottom surfaces of shells, a third-order thickness and shear deformation theory with six kinematic parameters is derived. This is a particularly interesting result since the developed theory presents a single additional parameter to describe the thickness deformation with respect to the popular Reddy’s third-order shear deformation theory, which has five parameters. The accuracy of the proposed six-parameter theory is tested for static and dynamic benchmark cases. Results are also very satisfactorily compared to those obtained with a more sophisticated and computationally onerous nine-parameter theory. The considered cases are isotropic and cross-ply laminated circular cylindrical shells under radial forces and pressure, and nonlinear forced vibrations of a cross-ply laminated shell under harmonic radial excitation.

The generalized introduction of lightweight composites in the automotive and aerospace industries, while leading to significant weight reductions and associated fuel savings, poses a serious problem of low acoustic performance when these structures are subjected to mechanical or acoustic excitation. This work addresses the issue of vibration and noise reduction in laminated sandwich plates using piezoelectric patches with passive shunted damping. A finite element implementation of a laminated sandwich plate with viscoelastic core and surface bonded piezoelectric patches is used to obtain the frequency response of the panels. The sound transmission characteristics of the panels are evaluated by computing their radiated sound power using the Rayleigh integral method. Resistor and inductor shunt damping circuits are used to add damping to the sandwich panels. The optimal location of the surface-bonded piezoelectric patches is then obtained, along with the resistor and inductor circuits optimal resistance and inductance values, using direct multisearch optimization to minimize added weight, number of patches, and noise radiation, for each one of the vibration modes of the panel. Trade-off Pareto fronts and the respective optimal patch configurations are obtained and compared with those presented previously by the authors. Comparisons are also established between the obtained optimal circuits for each mode and the ones obtained directly by tuning the electrical resonances to the mechanical ones.

The talk shares a ground-breaking approach which consists in the integration of materials modelling and knowledge-based systems with business process for decision making. The proposed concept moves towards a new paradigm of composite material design and and process by developing and implementing an integrated multi-disciplinary, multi-model and multi-field approach together with its software implementation for efficient and cost effective material and process design. In this approach, the interoperability, information management of materials models and data are used to connect composite materials modelling with industry standard business process models, BPMN 2.0, resulting in a more consistent material by design approach.

The detection of failure onset and progression in composites requires the proper modeling of various mechanical behaviors at various scales. Furthermore, the necessity of virtual models of large structures and the nonlinear nature of failure demand computational efficiency without accuracy penalties. Over the last years, a set of modeling strategies based on refined structural theories has been developed via the Carrera Unified Formulation (CUF). Such developments range from Equivalent Single Layer (ESL) and Layer-Wise (LW) models for the macro- and mesoscale to the component-wise modeling of microscale. The computational efficiency and accuracy stem from the use of 1D or 2D models, node-dependent kinematics (NDK) and global-local strategies providing the complete 3D stress state necessary to capture failure in critical locations such as free-edges. The coupling with well-known models for micromechanics, progressive failure (including non-local methodologies based on peridynamics) and multiscale analyses led to promising outcomes with multifold reductions of computational times.

Functional composite materials are widely used in many industries including even in medical fields showing excellent performance. The most attractive attribute of fibrous composites is tailorable properties which contributes to provide affirmative environment for bone healing. Bone healing process is fully affected by mechanical environment of the fracture site and the type and level of mechanical stimuli control cell and tissue development and finally determine bone healing status. Therefore, fibrous composite prostheses can provide most appropriate mechanical environment for a certain type of bone fracture and moreover, bio-degradable fibrous composites optimize prostheses stiffness during healing period and get rid of the second operation for removing them after complete healing. To design optimal composite prostheses cell and tissue development during healing period under bio-mechanical condition. The relationship between the developing pathway of cells or tissues and mechanical stimuli is well defined by various Mechano-regulation theories and until now, deviatoric strains for solid tissues and flow velocity of body fluid in the callus are known as the crucial factors to control bone healing. We refined the bone healing simulation technique with biphasic (deviatoric strain and fluid flow) Mechano-regulation algorithm by considering cell’s whole life and callus volume changes under mechanical environment. During the callus volume increases biologic process of bone healing and the involved cell phenotypes in the callus are qualitatively explained and the developing pathway of cells and tissues according to the mechanical stimuli is quantitatively estimated. This simulation technique is able to contribute the optimal design of composite prostheses for a certain type of fracture in terms of fracture type customized prosthesis design technology.

Composite sandwich panels, combining fibre-reinforced polymer (FRP) face sheets (and webs) and lightweight cores, are being increasingly considered for civil engineering structural applications, namely as building floors or roofs. This is due to their advantages over conventional materials, such as lightness, high mechanical properties, thermal insulation, ease of assembly and durability. On the other hand, there is a major concern about the use of composite sandwich panels in buildings due to the polymeric nature of the constituent materials: their behaviour under fire exposure. This keynote lecture presents experimental and numerical investigations recently carried out at the University of Lisbon (in the scope of the FireFloor and EasyFloor projects) about the fire behaviour of composite sandwich panels for building applications. The experiments comprised mechanical tests at elevated temperature of the constituent materials – FRP laminates and different polymeric foam cores (polyurethane, polyethylene terephthalate) as well as balsa wood – and fire resistance tests on sandwich panels simultaneously subjected to four-point bending and the ISO 834 fire curve. These tests allowed assessing the thermal and mechanical responses of unprotected sandwich panels and panels comprising different fire protection systems. Alongside the experimental programme, thermal and thermo-mechanical finite element (FE) models were developed to simulate the thermal and structural responses of the sandwich panels under fire exposure. In a first stage, 1D thermal FE models were developed using Matlab and used to determine the thermo-physical properties of the constituent materials, based on an inverse-analysis and an optimization routine. In a second stage, using the temperature-dependent thermo-physical and mechanical properties of the constituent materials as input, 2D (uncoupled) thermo-mechanical FE models, implemented in Abaqus, were used to simulate the responses of the sandwich panels under fire exposure. This keynote lecture summarizes the main findings from these investigations and discusses the feasibility of using composite sandwich panels in buildings regarding the fire hazard.

In the last three decades, the lattice Boltzmann method (LBM) has been extensively adopted to perform numerical simulations of the flow of viscous fluids governed by the incompressible Navier-Stokes equations. In short, the computational domain is represented by a Cartesian lattice that is kept fixed during the whole simulation. Here, the fluid is idealized as collections (also known as distributions or populations) of particles colliding and streaming along the links of the lattice. These collections carry with them information about the flow physics, as density and momentum. If compared to more classical approaches based on finite volumes/differences, the LBM possesses some very unique game-changing features. Among the others, the possibility to easily impose arbitrarily-shaped boundary conditions, the simplicity of its algorithm, and the intrinsic suitability to be parallelized have promoted its phenomenal popularity. Interestingly, the LBM has proved to be able to simulate phenomena beyond those obeying the incompressible Navier-Stokes equations. Indeed, magnetohydrodynamics flows, multi-component flows with interface tracking, heat transfer and supersonic flows are just few examples of the very rich and broad variety of advection-convection-diffusion physical processes that can be tackled. In 1992, Ponce Dawson et al. showed that the LBM can be successfully employed to recover the solutions of another class of equations: the reaction-diffusion (RD) ones. When dealing with RD equations, a significant advantage comes from the fact that the LBM does not involve the evaluation of second order spatial derivatives in the Laplacian operator. Therefore, the involved computational cost is drastically reduced to approximately a half of standard finite differences procedures . It is compelling to note that RD processes are ubiquitous in nature. One of the most common is the change in space and time of the concentration of one or more chemical substances. However, the system can also describe dynamical processes of non-chemical nature. Examples are found in biology, geology and physics and ecology. Other applications of the RD equations include ecological invasions, predator-prey systems, spread of epidemics , wound healing and tumor growth. Regarding the latter, here we develop an original LBM-based numerical framework to predict tumor growth. It includes three basic processes: cell proliferation, motility and death. These three processes depend on (i) the local concentration of nutrients, (ii) the local concentration of cancer cells and (iii) the imposition of a radiotherapy. The problem is governed by two RD equations, one for the transport of nutrients and one for the dynamics of cells. Therefore, we introduced and solve two LB equations possessing all the aforementioned game-changing features. The resultant LB model shows intelligible theoretical derivations, it is very concise and easy to be implemented. Moreover, it is able to: • simulate the space-and-time evolution of tumors with different proliferation and nutrients consumption rates; • account for the beneficial effect of the radiotherapy; • qualitatively reproduce finger-like tumor patterns; • qualitatively reproduce tumor shapes with border irregularity. An example of the evolution of a tumor computed by our proposed LB scheme is sketched in Figure 1. References Succi S. The lattice Boltzmann equation: for fluid dynamics and beyond. Oxford University Press, 2001. Ponce Dawson S., S. Chen, and G. D. Doolen. "Lattice Boltzmann computations for reaction-diffusion equations." The Journal of chemical physics 98.2 (1993): 1514-1523. Marié S., Ricot D., and Sagaut P. "Comparison between lattice Boltzmann method and Navier–Stokes high order schemes for computational aeroacoustics." Journal of Computational Physics 228.4 (2009): 1056-1070. De Rosis A. "Modeling epidemics by the lattice Boltzmann method." Physical Review E 102.2 (2020): 023301.

We discuss few examples of beam-lattice metamaterials which show attractive mechanical properties concerning their enriched buckling. The first one concerns a beam-lattice with sliders and the nonlinear solution is discussed in analytic way and, finally, extended to the case of uniform in-plane tension. This case shows the possibility multiple eigen-modes with higher order of multiplicity [1]. The instability under tension was also discussed using nonlinear micropolar elasticity [2]. The presented examples show interesting new examples of instabilities under tension as well as peculiarities related to additional kinematical degrees of freedom. The simple discrete model analysis is complemented by FEA using various finite elements developed for six-parameter shell model. Finally, we consider pantographic beams. Here the nonlinear solution is traced out numerically on the base of a Hencky’s model and an algorithm based on Riks’ arc-length scheme. Some concluding remarks draw possible future developments and challenges.

This talk is aimed at presenting the mechanical response and the wave dynamics of highly nonlinear lattice materials, and at discussing how such systems can be employed for the computational design of novel mechanical metamaterials. The focus is on lattices with tensegrity architecture and their multifaceted mechanical behavior. Tensegrity concepts are ubiquitous in nature and appear, e.g., in every cell, in the microstructure of the spider silk, and in the arrangement of bones and tendons for control of locomotion. The talk will highlight how it is possible to employ the geometrically nonlinear response of tensegrity units to create complex global systems (the metamaterials) with unprecedented mechanical properties, for applications in structural engineering, sound focusing and impact protection.

The aim of this work is to develop advanced numerical theories and methods for composite materials and structures, not only in the framework of classical computational mechanics (CCM), but also in the framework of data-driven computational mechanics (DDCM). In terms of CCM, we established a macro-micro-integrated numerical scheme by developing a series of new robust and efficient model reduction techniques and accurate multi-scale methods. In terms of DDCM, we proposed a new concept of “material twin” and Structural-Genome-Driven computing, and established a data-driven scheme from constitutive data collection to material-structure-integrated analysis.

In civil, mechanical, and aerospace engineering, structural dynamics is viewed as a discipline concerned with the analysis and characterization of the vibratory response of structures. Key elements of the response are the amplitude, phase, and damping ratio, which are quantities that vary with the excitation frequency. In this work, we extend the notion of damping engineering in structural dynamics to the realm of materials engineering by intrinsically introducing locally resonating substructures within, or attached to, the material domain itself−which is viewed as an extended medium without defined external boundaries. This essentially yields a locally resonant elastic metamaterial, except here it is viewed from the perspective of its dissipation characteristics rather than its subwavelength effective properties or band gaps, as widely done in the literature. We provide a theory, validated by experiments, for substructurally synthesizing the dissipation under the conditions of free-wave motion, i.e., waves not constrained to a prescribed driving frequency. We use an extended elastic beam with attached pillars as an example of a metamaterial. When compared to an identical infinite beam with no attached substructures, we show that within certain frequency ranges the metamaterial exhibits either enhanced or reduced dissipation−which we refer to as positive and negative metadamping, respectively. These regimes are rigorously identified and characterized using the metamaterial’s band structure and wavenumber-dependent dissipation diagram, thus opening up a new paradigm for dissipation engineering without addition or subtraction of damped material. This concept impacts applications that require a combination of high stiffness and high damping or, conversely, applications that benefit from a reduction in loss without the need to change the backbone constituent material.

The main aim of this work to report current stage of the advances in the generalized stochastic perturbation method as well as their perspectives in the context of structural and solid mechanics applications. It is a modern extension of the traditional perturbation method, used in applied science and engineering in both deterministic and stochastic context. It is well known that this method is based upon the general order Taylor expansion of the given uncertainty sources about their expected values appearing in fundamental equations of structural problem. The additional expansions substituted in static or dynamic equilibrium equations of the increasing order enable for analytical derivation or numerical determination of basic probabilistic characteristics of the structural response. Stochastic perturbation technique has been initially formulated in its first as well as second order versions, where the first two statistics of structural responses were determined and then it has been extended towards the nth order approach, where one may efficiently determine up to the fourth order statistics. Most frequently this method has been implemented in conjunction with the Finite Element Method as the Stochastic Finite Element Method although some applications for the Boundary Element Method , Finite Volume Method as well as Finite Difference Method are also available. According to the very recent literature this implementation may be done in two different ways – using the Direct Differentiation Method (DDM) and, alternatively, thanks to the Response Function Method (RFM), where structural responses algebraic forms are predicted using some polynomial bases. The first one needs availability of the FEM open computer code to rearrange and to solve up to the given order equilibrium equation. The RFM needs some series of the FEM solutions obtained for varying values of the given uncertainty source and further Least Squares Method based polynomial fittings of various precision. There is no doubt that stochastic perturbation method is very attractive for civil engineers – it is relatively easy programmable, especially in the second order second moment formulation necessary to meet the standards of Eurocode 0 and necessity of the reliability index determination. Perturbation based formulas does not demand deep understanding neither of probability theory and nor of computational statistics complexities and the relevant algorithms and programs may be installed and programmed on medium laptop with high efficiency and low computational effort. Despite of a generalization of this method until some higher order guarantying a priori desired accuracy of computations and its various computer implementations, it has some inherent limitations and these undoubtedly are (i) linearization procedure for higher order moments derivation, where one assumes that expectation equals to its mean value, which remarkably simplifies higher order formulas derivation, (ii) very complex structure of analytical expressions for higher order moments of the structural response under consideration, (iii) input uncertainty PDF character, which practically is limited to the Gaussian distribution (with no truncation), (iv) difficulties in computer programming while using the DDM approach, (v) algebraic complexity while analyzing increasing number of correlated or not uncertainty sources in the model (even if all of them are Gaussian), (vi) spatial and temporal uncertainties cannot be simply linked in a single model, so that stochastic processes modelling or time-dependent reliability analysis are rather challenging problems in this context, (vii) very long and extremely hard for verification analytical formulas describing higher order probabilistic moments (i.e. of the 3rd and 4th order), (viii) low and controversial accuracy of the output probabilistic characteristics for relatively large input uncertainty (when for instance standard deviation equals to a half of the expected value of more), (ix) disputable accuracy when engineering problems under consideration are highly nonlinear or even coupled, (x) unknown efficiency when truncation of the input uncertainty (to nonnegative values only, for instance) is of remarkable importance, (xi) questionable role of the perturbation parameter, whose value arbitrarily taken as 1 may significantly affect both convergence and precision of this method. Finally, one needs to notice that engineering software based on the FEM programs does not offer any extension towards this method implementation and even does not allow for probabilistic response and reliability index computations. In the view of these limitations statistical Monte-Carlo simulations is frequently preferred together with polynomial chaos, spectral, kriging, filtering or fuzzy techniques as well as some semi-analytical probabilistic methods also. This classical method does not need any access to the source code of the FEM solver and may be used as the grid computing tool excluding permanent and long employment of the personal computer. However, it is known that some of these limitations have been recently eliminated by an application of the computer algebra software and its analytical tools. Linearization procedure has been replaced with the iterative strategy, where expected value of the given structural response is substituted to the expansion adjacent to variance, and they both are used next for calculation of both the third and the fourth central probabilistic moments. This procedure brings remarkably higher precision and better theoretical convergence to the exact solutions as well as better numerical precision illustrated in this paper. Application of the computer algebra software created the opportunity to derive automatically perturbation-based formulas by the computer program itself and validation of the entire uncertainty analysis is done a posteriori using Monte-Carlo or semi-analytical reference solutions. Then, even the hundredth or thousandth order expansions can be taken into account, so that an issue of numerical precision practically plays marginal role. The same concerns perturbation parameter, which can be the second independent input variable close to the input uncertainty. The additional MAPLE applications created in this area include (i) time-dependent analytical reliability analysis including stochastic corrosion of the steel plate girder in various environments, (ii) stochastic vibrations of two-span beam with uncertain damping, (iii) DDM tenth order stochastic solver for elastostatic problem, (iv) visualization tool to compare Monte-Carlo scheme, semi-analytical method and stochastic perturbation technique of the given order for a given uncertainty range and external data exported from some FEM analysis. Some extension towards implementation of the iterative generalized stochastic perturbation technique towards symmetric but non-Gaussian distribution has been also recently completed. On the other hand, an effect of the truncation related to the input Gaussian parameter has been recently studied in the same research group. It should be underlined that now a library of engineering problems solved with the use of generalized perturbation technique is very huge and include some flagship large scale ABAQUS FEM models like telecommunication towers, steel structural elements with and without openings, plated structures with the corrugated webs, particle-reinforced anisotropic composites with and without interface defects; many real engineering problems have been solved with the use of the system ROBOT also. So that, it is seen that the generalized stochastic perturbation technique despite of many years of extensive theoretical and numerical studies and despite of many criticism still has big scientific capacity with a huge number of opened research issues and wide field of engineering applications, not only in civil but also in mechanical, aeronautical, biomedical or chemical engineering and also in agriculture, physics or in environmental engineering. Civil engineering applications will include nonlinear elastic or inelastic applications as well as spatial cross-correlations.

The present work concerns the numerical prediction and experimental validation of the sound transmission of wooden windows in the low frequency range. The considered window is composed of many substructures including double glazing with fluid cavity, pieces of wood, rubber, etc. In this context, a reduced order model applied to a finite element formulation of the fluid- structure coupled system is developed to solve the considered multiphysics problem at a lower cost. In order to evaluate the numerical sound transmission loss factor, the structure is excited by a diffuse field on the emitting side and the Rayleigh integral method is applied in order to calculate its radiated sound power. The numerical model of the window is calibrated with an Experimental Modal Analysis. Finally, numerical results of the sound transmission are compared to experimental ones for different kind of windows.

Filament winding is one of the major manufacturing methods for polymeric composite structures and its productions have become the key components of the power unit and the fuel system. The conventional filament winding process cannot simultaneously achieve the manufacturability and the desired mechanical properties and significantly confines the structural performance improvement of filament-wound structures. One of the key solutions to this limitation is the exploration of a novel winding pattern with more degrees of freedom, which is able to fully utilize the laminate strength of the overwrap while satisfying the requirements for the winding process. Accordingly, the objective of this research is to investigate a new non-geodesic pattern based on variable slippage coefficients along the fiber paths, and to obtain the optimal winding parameters of this new pattern. The mathematical model, mechanical model and the optimization model will be established for the designed non-geodesic pattern. The design methods that integrate the winding pattern, the windability and the structural performance, will be systematically outlined. The effects of the slippage coefficient distribution on the non-geodesic pattern and the resulting vessel performance will be revealed. The advantage of using the present non-geodesic pattern will also be clarified. The results show that the structural performance can be improved by 20%-30% using the present method and a variety of non-symmetrical bodies can be fully overwrapped using the present non-geodesics. The resulting winding patterns simultaneously satisfy the windability and fully utilize the laminate strength. This research is of great scientific and application significance for effectively improving the mechanical performance of filament-wound composite structures.

In practical applications of optimization, it is common to find problems where it is impossible to use derivative-based methods, either by considering numerical approximations of the derivatives or by using automatic differentiation tools for their calculation. Frequently, function evaluation uses computational simulation, being of black-box type (given a point, the function value is returned and no further information is provided) and/or could be contaminated by numerical noise. This prevents the use of derivative-based techniques, motivating the use of Derivative-Free Optimization (DFO). In this presentation we are focus to DFO algorithm: Direct Search Methods (DSM). A direct search method solves optimization problems without requiring any information about the gradient of the objective function, neither attempting to use or approximate its derivatives. A direct search algorithm evaluates the objective function on a set of points around the current best point, looking for one where the value of the objective function is lower than the value at the current point. In other words, minimization is achieved through an iterative process of function evaluation at finite sets of points, using the results to determine which new points should be evaluated at the next iteration. Rather than a quantitative assessment of the objective function value, it is sufficient to be able to compare any pair of points and decide which point presents a better value for the objective function. In addition, it is common to have multiple objective functions, which need to be simultaneously optimized. In the design phase of a new product, for example, the simultaneously optimized. In the design phase of a new product, for example, the designer does not only want to minimize the production cost, but additionally wishes to maximize both the performance and the safety, minimize the conception time, and maximize the life time of the product. Another different challenge is related to global optimization. Local optimization methods are the best choice for convex or at least unimodal optimization problems. However, when tackling real-world applications, we often get into situations in which objective functions to be optimized are multimodal, nonconvex, nondifferentiable or even discontinuous. Unfortunately, even if derivatives would be available for use, it is hard to prove that a local minimum is a global one. In such settings, many traditional methods are not so helpful, being necessary to find more suitable approach. In the past, users were pleased with a simple improvement in the function value to optimize, considering the initialization provided to the solvers. Nowadays, with the increase of the computational power available, users aspire to global solutions for their problems. Locating and identifying points as global minimizers is, in general, a hard and time- consuming task. An overview of some recent developments in derivative-free optimisation with direct search will be presented. The presentation ends with applications of direct search algorithm to real problems.

The challenge to the pipeline industry is to meet the increased worldwide demand while reducing the cost. Currently, metallic and composite pipelines are the most cost-effective way of transporting water, oil, and gas. Limitations of metallic and composite pipelines are familiar. Corrosion reduces the load-carrying capacity of metallic pipelines, while matrix cracking/abrasion causes the failure of the composite pipelines. Both corrosion and abrasion cause significant losses and decrease the structural integrity of pipelines. This work proposes a corrosion-free hybrid pipe, which will improve the pipeline's pressure capacity and eliminate internal and external corrosion. The internal pressure capacity of hybrid composite/steel/composite pipes was tested according to the ASTM D1599 standard, and the testing results showed significant improvement in the internal pressure capacity compared to the conventional steel pipes. Detailed evaluation for the effect of fiber type on the electrochemical corrosion aspects in different highly corrosive solutions; 0.5 M NaCl, 0.5 M HCl, and 0.5 M H2SO4, was presented. Finally, the corrosion aspects of composite overwrapped steel pipes were evaluated, where the FRP/steel pipes were immersed in a glass container containing the corrosive solutions and monitored for six months and one year. The corrosion condition was qualitatively analyzed using SEM, EDX, and XRD analysis, and results showed an excellent corrosion resistance for the FRP/steel pipes compared to the conventional carbon steel pipes.

The higher order Haar wavelet method (HOHWM), introduced in 2018, has shown improved accuracy and convergence rate in comparison with commonly used Haar wavelet method also, finite difference (FDM) and differential quadrature methods (DQM). However, the problems studied, cover mostly linear and nonlinear ordinary differential equations. Thus, the multidimensional problems can be considered next step in development and application of the HOHWM. Another, not less important issue in development of any numerical method, is the complexity. In more precisely, both numerical and implementation complexities. Current study covers accuracy and complexity analysis of the HOHWM based on case studies: vibration problems of beams & plates, buckling problems of beams & plates, functionally graded structures, nonlinear wave propagation equations, etc. The results obtained for particular problems and/or classes of problems confirm principal improvement of the accuracy and convergence rate with reasonable growth of complexity.

Many multi-phase alloys of practical relevance display a combination of high yield strength and elongation at failure, stemming from various deformation mechanisms that occur at the material microstructure – namely, slip plasticity and martensitic phase transitions. Well-established examples of such materials include TRIP (transformation-induced plasticity) steels, which undergo mechanically-induced martensitic transformations that play a crucial role in the observed mechanical response. Multiscale models constitute a natural modelling approach due to their ability to capture the relevant fine-scale crystalline features directly. Nevertheless, multiscale models based on the first-order homogenization are only valid if the assumption of scales separation holds true, i.e., if the RVE is smaller than the macroscopic characteristic length, such that the macroscopic deformation may be considered uniform throughout the RVE. This limits the applicability of these models that cannot be employed when the size of the micro-constituents approaches the macroscale characteristic length or when the spatial variation of macroscopic deformations or loadings does not comply with the scale separation principle, which occurs when strain localization emerges. Moreover, these formulations cannot capture size effects from the microstructure. A general second-order formulation for the multiscale description of materials, where more advanced constitutive laws can be employed to describe the microscale behavior, is presented. The variationally consistent, fully second-order homogenization formulation is derived from the Method of Multiscale Virtual Power. A second-order continuum theory is employed to describe both the macro and micro-scale behavior. The finite element solution of the resulting multiscale equilibrium problem is described in detail. Several microstructural representative volume elements are initially considered to study the importance of the size of the RVE together with the size of the constituents under the influence of strain gradients. Application examples are presented using both RVE homogenisation and fully-coupled multiscale analyses, where the models are calibrated using data from micro-pillar experiments performed on the individual phases of a TRIP steel microstructure. Results show that the employed constitutive models successfully capture the experimentally observed effect of the martensite transition in these alloys, causing an initial softening in their overall response, followed by significant hardening once a substantial amount of martensite is formed.

This talk is aimed at presenting an overview of the scaled boundary finite element method and discuss its applications to various problems in engineering. Classified as a semi-analytical method, the scaled boundary finite element method (SBFEM) shares the advantages of the boundary element method (BEM) and finite element method (FEM). Like the BEM, it only requires the boundary to be discretised and like the FEM, it does not require Green’s functions. It involves introducing a new coordinate system: radial-circumferential. This reduces the computational complexity by one dimension. Analytical solutions are sought along the radial direction, whilst, finite element like solutions are obtained in the circumferential direction. This particular feature, makes is the most accurate method to model singularities in homogeneous/heterogenous media. Further, the scaled boundary framework relaxes the meshing constraint that FEM imposes and accommodates elements with arbitrary shapes and sizes, with the only requirement that the elements satisfy star convexity. It also provides a seamless integration with the CAD models. The robustness of the framework will be demonstrated with examples from different problems in engineering.

An overview on the application of the p-version finite element method to analyse modes of vibration, forced response to dynamic excitations and aeroelastic instability of plates and shells is presented. Analysis in the linear and geometrically non-linear regimes of panels in variable stiffness and in multi-scale hybrid composite materials are addressed. The accuracy and the computational cost of the p-version models are examined. Some results are compared to data from experimental modal analysis, where the effect of boundary conditions is considered in detail. The computational features of three types of methods to solve the non-linear equations of motion - direct time domain integration; the harmonic balance method; the shooting method - are discussed. Advantages/disadvantages of using curvilinear fibres and carbon nanotubes to reinforce polymeric matrices of panels that undergo vibrations are debated.

Advanced ceramic composites are used in many strategic essential industries, such as the armaments industry, aviation, automotive, nuclear power, or space exploration. In other areas, they set the path of technological progress in modern applications. As an example are presented Interpenetrating Phase Composites (IPCs) made of ceramic and metallic phases – two very different components. In engineering applications, the advanced composites can be subjected to extreme thermo-dynamics loads, such as the sudden increase of pressure loads and the jump of high temperatures. In the presentation, the gradual degradation process of an IPC skeleton is described. The presentation deals with ceramic foam models that work as a skeleton of Interpenetrating Phase Composites (IPCs) before filling the preforms by plastic material. Two types of ceramic skeleton were made of SiC or Al2O3. An IPC skeleton's gradual degradation process was investigated for: (1) quasi-static loading and (2) impact loading. The results of the quasi-static analysis will serve as a reference to the impact analyses. In the dynamic analysis, the impact of the considered ceramic foams against the rigid surface is performed. The initiation and evolution of gradual degradation of skeleton parts were related to the impact time. The analysis of the IPCs skeleton is performed due to an evaluation of the skeleton’s role in the final product that is the filled IPCs. The hints for the designers of the IPCs are given. Acknowledgment The results presented in this paper were obtained within the framework of research grant 2018/31/B/ST8/00601 financed by the National Science Centre, Poland. The calculations were done using PL-GRID national computational resources at the Academic Computer Centre Cyfronet in Krakow, Poland and the Interdisciplinary Centre for Mathematical and Computational Modeling, University of Warsaw, Poland.

The mechanical behaviour of composites reinforced with synthetic fibres use to be assumed linear-elastic up to failure. However, the mechanical behaviour of biodegradable composites is different: their elastic response is non-linear, plastic strains can be observed, and strain-rate has a strong influence on their behaviour. Thus, the modelling of biocomposites requires the use viscoplastic constitutive equations. A three branches rheological model is described in this presentation. The seven model parameters have been adjusted by quasi-static tensile tests, while the model has been successfully validated by tensile tests at different strain rates. The constitutive model has proved to be valid for composites reinforced with cotton, flax and jute, allowing a greater understanding of the behaviour of those biocomposites. The existence of a constitutive model for biocomposites can lead to get a better understanding of the mechanical behaviour of these materials and to find future industrial applications. The constitutive equation was implemented in a Finite Element Model to predict the behaviour of biocomposites under low-velocity impacts. An excellent agreement between numerical predictions and experimental tests was found. The results of impacts on flax/PLA plates were compared with carbon/epoxy specimens and two important differences were observed. First, delamination was the main failure mode in carbon/epoxy composites but it was not observed in flax/PLA plates, fibre failure was the main failure mode in biocomposites. Second, the normalized after impact residual strength of flax/PLA plates was higher than that of carbon/epoxy composites. The absence of delamination can explain the better after impact behaviour of flax/PLA biocomposites. The different mechanisms of damage induced in drilling had been studied. Induced damage under different cutting speeds, advances and drill geometries was analysed, noting that in this case delaminations were neither found as failure mode, revealing a good cohesion between fibre and matrix. Is also remarkable the damage reduction with increasing drill feed rate, which is a novelty that can reduce the processing times of these materials in the industry. These results provided by the numerical model were verified by experimental tests on fla/PLA biocomposites. Finally, the buckling behaviour of biocomposites was analysed. The buckling Euler theory based on lineal-elastic behaviour cannot be applied to natural fibre reinforced composites. A modified buckling theory using the modified Ludwick nonlinear elastic model was used to predict the critical load of biocomposites columns. Experimental tests were conducted on flax/PLA columns and the accuracy of the Ludwick model was verified.

Optimization problems where several objectives have to be considered concurrently arise naturally in many applications. Since decision making processes are getting more and more complex, there is a recent trend to consider more and more objectives in such problems, known and many objective optimization problems (MaOPs). For such problems it is not possible any more to compute finite size approximations of the entire solution set. In this presentation, we will present the Pareto Explorer (PE) for the numerical treatment of MaOPs. The PE is a global/local exploration tool that consists of two steps: first, an optimal solution of the given MaOP is selected via a global solver. In a next step, the Pareto landscape around this point is explored around this solution according to the users preferences that can be articulated in decision variable, objective, or weight space. We finally demonstrate the effectiveness of the PE on several MaOPs related to real-world problems.

The synthesis of long and stable carbyne chains inside carbon nanotubes has recently drawn renewed attention to this linear one-dimensional carbon allotrope. Carbyne’s mechanical properties have been predicted to exceed that of carbon nanotubes and graphene, making it a very suitable structural component for many nanoscale applications. While carbyne’s mechanical behavior under tensile loading is superlative, this linear chain of bonded carbon atoms readily buckles due to thermal fluctuations, showing minimal strength under compressive loading. Here we present a detailed study on the enhancement of carbyne’s mechanical properties under compression by confinement in small diameter carbon nanotubes. First, we develop a new classical empirical forcefield based on ab-initio calculations. Molecular dynamics (MD) simulations are then carried, using this forcefield, to determine the mechanical properties of carbyne under tensile loading, namely to assess their dependence on chain length and temperature. The bending rigidity of carbyne and its persistence length are also calculated. After the validation of the new forcefield, MD simulations are employed to study the mechanical behavior of carbyne under compressive loading, when confined inside (5,5), (6,6) (7,7) and (8,8) CNTs. It is found that the mechanical behavior of confined carbyne chains depends on the confinement radius and the chain length, and can be described in three stages. For “tight” confinements, carbyne chains assume a rigid rod behavior, allowing the calculation of compressive mechanical properties and attesting an effective “bracing” effect. For “looser” confinements, a spring like behavior arises which can be modeled by Hooke’s law. In the third stage confined carbyne chains tend to buckle into a large local bend, losing the elastic flexibility that characterizes the previous stage.

Recently, meshless methods have become attractive to model problems in computational mechanics. Peridynamics is a meshless approach that addresses some of the difficulties and limitations associated with mesh-based topology optimization methods. The most significant advantage of peridynamics is its ability to model discontinuities in a relatively simple manner. The minimization of compliance or strain energy was chosen as the objective function under the volume constraint. The filtering scheme was adopted to avoid the checkerboard issues and provide a high stability during optimization. Various problems were solved with and without cracks under different loading, boundary conditions and manufacturing constraints. In order to consider manufacturing constraints, a continuation multi-phase projection scheme is applied on solid and void phases. Using this projection scheme, the designer has control over the solid and void features to achieve a manufacturable optimal topology. It is shown that peridynamics based topology optimization can be an effective tool in finding optimal topologies with manufacturing constraints, which can prevent crack growth in engineering structures.

Polytopal elements, including polygonal elements for a two-dimensional case and polyhedral elements for a three-dimensional case, are adopted to mesh material domains with high complexity. In our recent work [1], polytopal composite finite elements (PCEs), which were proposed to model the mechanical behavior of compressible and incompressible materials, could pass the patch test and satisfy the inf-sup stability with high accuracy. The PCEs were constructed with a polynomial projection of compatible strain fields through the least-squares approximation. For incompressible materials, volumetric locking arises when the Poison’s ratio close to being 0.5, leading to the over stiffening of incompressible material elements. The volumetric locking phenomenon occurs when a fully integrated element (e.g., Q4 elements with 4 quadrature points or H8 elements with 8 quadrature points) is employed. One well-known solution to the volumetric locking is to couple pressure unknowns together with displacement unknowns. However, this way requires additional unknowns in the system of linear equations, thus require large storage and cost expensively. Fortunately, PCEs, which were purely based on displacement formulation without the additional unknowns, could overcome the over stiffening to accurately model incompressible materials. The moving morphable bar (MMB) approach [2], which has been proposed for structural optimization recently, has advantages: (1) using a small number of design variables; (2) accurately capturing structural-boundary features; (3) easy control of structural feature sizes; and (4) direct multiscale design of porous structures without material homogenization, connector constraints, and local volume constraints [3]. In this study, we present an efficient computational tool using a combination of PCEs and MMBs to model and design incompressible materials (i.e., rubbers), but it can be extended to other material models. Especially, the presentation emphasizes the direct multiscale design of porous structures (i.e., biology soft tissues) for additive manufacturing techniques. The idea is to project adaptive geometric components (AGCs) onto a fixed mesh of PCEs. The structure is simultaneously optimized at both macro-structural and micro-structural scales by directly optimizing geomety parameters of AGCs. Some numerical examples are investigated to verify the effectiveness of the present approach. References [1] H. Nguyen-Xuan, K.N. Chau, K.N. Chau, Polytopal composite finite elements, Comput. Methods Appl. Mech. Eng. 355 (2019) 405–437. doi:10.1016/j.cma.2019.06.030. [2] V.N. Hoang, G.W. Jang, Topology optimization using moving morphable bars for versatile thickness control, Comput. Methods Appl. Mech. Eng. 317 (2017) 153–173. doi:10.1016/j.cma.2016.12.004. [3] V.-N. Hoang, N.-L. Nguyen, P. Tran, M. Qian, H. Nguyen-Xuan, Adaptive concurrent topology optimization of cellular composites for additive manufacturing, JOM. 72 (2020) 2378–2390. doi:10.1007/s11837-020-04158-9.

Due to their outstanding mechanical properties, graphene and its derivatives such as graphene nanoplatelets (GPLs) have attracted tremendous attention and are well accepted as ideal reinforcing nanofillers in developing new generation lightweight structures that are of prime importance in aerospace, automotive, marine, and defence industries. However, its reinforcing effect has been considerably affected by the poor interfacial strength between graphene and the matrix. It has been demonstrated in a series of recent studies that this challenging issue can be considerably alleviated by using chemically functionalized graphene fillers with mechanically induced wrinkles. By employing molecular dynamics simulations, this talk explores an effective route to improve the interfacial shear strength (ISS) of graphene sheets through the introduction of mechanically induced wrinkles formed by shear/compressive pre-strains to graphene and the chemical modification of graphene using various functional groups. The slide-out tests of a functionalized wrinkled graphene sliding over metal matrix show that such graphene sheet gives rise to larger surface roughness and better bonding which leads to stronger interfacial interactions between graphene and matrix and consequently, significant improvement in ISS. It is also found that shear induced wrinkles are much more effective in enhancing ISS than compression induced ones. Compared with its counterpart functionalized with hydrogen, graphene functionalized with alkyl (methyl, ethyl, propyl, and butyl) offers better interfacial interactions with metal matrix because these functional groups are longer than hydrogen functional group and can be embedded deeper into the matrix.

The talk presents a novel procedure to evaluate mechanical properties of random micro-fibre reinforced composites with consideration of primary pores. Micro-CT experiment is firstly conducted to detect micro-scale morphology of the constituent materials, including size of pores and arrangement of fibres, etc. On this basis, a two-step modelling strategy with consideration of primary pores is proposed. In the first step, equivalent mechanical properties of the pore defects and the micro-fibers are determined based on the experimental results and by the 3D parametric finite volume directly averaging micromechanics (FVDAM). In the second step, the equivalent pores and fibres are embedded into matrix materials to construct a RVE of the random micro-fibre reinforced composite, by which elastic modulus and Poisson’s ratio are calculated. In addition, the 3D parametric FVDAM is further extended to simulate plastic deformation of PEEK matrix under quasi-static tensile loading. The proposed two-step modelling strategy shows a good agreement with the results from experiments and can be used in multiscale modelling of micro-fibre reinforced materials.

Automated Fiber Placement (AFP) technology has revolutionized composites manufacturing and is quickly replacing traditional manual production. Among others, the notable advantage of AFP is that the designer is no more restricted to the use straight fibers, which means it is possible to have steered fiber paths designed for optimizing structural performance. The scope of this work is to identify the manufacturing parameters and associated constraints imposed by these parameters on the mathematical design space and introduce this in an optimization framework to design future aerospace structures (wings, fuselages etc.) for superior mechanical performance. In this talk, the design of a structural panel with a cutout to minizime stress concentration and the design of a skin to maximize buckling loads will be addressed. Furthermore, the effects of manufacturing induced unintended defects on the strength (tensile and compressive) of these strucures will also be addressed through experimentally validated computational models that account for the material microstructure.