Keynote Lectures

The interpenetrating composites (IPCs) are built up of a ceramic skeleton and metallic matrix, which fills the ceramic foam under pressure and high temperature. The specific examples of IPCs analysed in the paper are made of the ceramic skeleton - SiC or Al2O3 - which is a brittle material, whereas the matrix is created by AlSi12 alloy – elasto-plastic material. Both phases of IPCs are crushable and their degradations under the loading are subjected to two different damaging processes. The ceramic foams are brittle throughout the loading process, but the AlSi12 alloy is brittle during the elastic phase; then, its behaviour becomes viscous-plastic. The presentation concerns the experimental testing and simulations of the impact and fragmentation of metal matrix composite - AlSi12/(SiC or Al2O3). The microstructure of the composite is complex and consists of a metallic phase (85%), ceramic skeleton, porosity, and a system of imperfect interfaces. The presented data-driven micromechanical numerical model is based on micro-CT scanning of composite material to get information about the internal structure and the assessment of local thermo-mechanical properties done by Alemnis observations under SEM at nanoscale or microscale using nano- or microindetation technique. The description of the dynamic response of IPCs by impact is investigated in a few scenarios. The exemplary scenario is realised by imposing the initial conditions on the sample that hits a hard elastic barrier. The second one corresponds to SHPB experiments. The last one is the hitting of an elastic impactor against the sample. The influence of the impact velocities and material parameters of the phases on the failure modes is observed. Previously, analyses of the modes of loading application on the micromechanical failure of metal matrix composite were analysed in [1, 2]. An analysis of the empty SiC scaffolds is presented in [3]. The proposed finite element model of the AlSi12/SiC composite behaviour describing gradual degradation under impact loading was tested for different impact scenarios. In all cases, the damage growth in the composite is very realistic. These results conclude that the proposed finite element model is very effective. Acknowledgement The results presented in this paper were obtained within the framework of research grant No. 2019/33/B/ST8/01263 financed by the National Science Centre, Poland. Numerical analyses: PLGRID facilities - ICM UW Warsaw, CI TASK in Gdańsk, CYFRONET, Kraków and LUMI in Kajaani (Finland). References [1] Postek, E. and Sadowski, T. Distributed microcracking process of WC/Co cermet under dynamic impulse compressive loading. Compos. Struct. (2018) 194: 494-508. [2] Postek, E. and Sadowski, T. Qualitative comparison of dynamic compressive pressure load and impact of WC/Co composite. Int. J. Refract. Hard. Met. (2018) 77: 68-81. [3] Postek, E., Sadowski, T. and Bieniaś, J. Simulation of impact and fragmentation of SiC skeleton, Phys. Letters (2021) 24:578-587.

We discuss propagation of surface and interfacial waves in elastic and viscoelastic media possessing surface stresses and surface energy. Nowadays mechanics of media with surface stresses found various applications at small scales as well as at macroscales. The discussed class of models describes of coupled deformations of solids with thin coatings or interface layers. In particular, surface stresses could be responsible for size-effects observed at the nanoscale. With the lecture we discuss a series of boundary-value problems for antiplane motions, see [1-7] for details. These problems illustrate the influence of surface stresses. For example, antiplane surface waves exist in an elastic half-space only if one takes into account surface kinetic energy and surface strain energy in addition to classic constitutive equations in the bulk. Here we discussed the propagation of antiplane waves in an elastic half-space, in an elastic strip perfectly or non-perfectly attached to a half-space. Transverse waves are also studied in an elastic cylinder. Dispersion curves were obtained and analysed. In particular, it was shown that surface waves related to surface stresses propagate with lower speed than others. Finally, viscosity effects were analysed. We demonstrated that even small dissipation essentially changes the behaviour of dispersion curves and the decay with the depth. This is more pronounced for relatively large values of a wave frequency. This work has been supported by the project ``Metamaterials design and synthesis with applications to infrastructure engineering'' funded by the MUR Progetti di Ricerca di Rilevante Interesse Nazionale (PRIN) Bando 2022 - grant 20228CPHN5, Italy. 1. Eremeyev, V.A., Rosi, G. and Naili, S., 2016. Surface/interfacial anti-plane waves in solids with surface energy. Mechanics Research Communications, 74, 8-13. 2. Eremeyev, V.A., Rosi, G. and Naili, S., 2019. Comparison of anti-plane surface waves in strain-gradient materials and materials with surface stresses. Mathematics and mechanics of solids, 24(8), p 2526-2535. 3. Eremeyev, V.A. and Sharma, B.L., 2019. Anti-plane surface waves in media with surface structure: Discrete vs. continuum model. International Journal of Engineering Science, 143, 33-38. 4. Eremeyev, V.A., Rosi, G. and Naili, S., 2020. Transverse surface waves on a cylindrical surface with coating. International Journal of Engineering Science, 147, 103188. 5. Mikhasev, G.I., Botogova, M.G. and Eremeyev, V.A., 2022. Anti-plane waves in an elastic thin strip with surface energy. Philosophical Transactions of the Royal Society A, 380(2231), 20210373. 6. Mikhasev, G., Erbaş, B. and Eremeyev, V.A., 2023. Anti-plane shear waves in an elastic strip rigidly attached to an elastic half-space. International Journal of Engineering Science, 184, 103809. 7. Eremeyev, V.A., 2024. Surface finite viscoelasticity and surface anti-plane waves. International Journal of Engineering Science, 196, 104029.

Fiber Reinforced Cementitious Matrix FRCM composites represent a relatively new strengthening technology suitable especially for the reinforcement of masonry, that has gained traction in the last two decades in substitution of the more consolidated external retrofitting with FRP (Fiber Reinforced Polymer). The utilization of an inorganic matrix is probably the main difference with FRP, where the fiber is glued to the substrate with a polymeric adhesive. When compared with FRP, it has many advantages, such as a better compatibility with the substrate, vapor permeability, reversibility. The mechanical performance to debonding is obviously lower, but still adequate to obtain a good seismic upgrading of existing masonry. It is used in particular to reinforced arches and double curvature vaults, because of their reversibility. The experimental literature available for FRCM is nowadays quite comprehensive and mainly deals with (i) coupon and (ii) debonding tests, or (iii) experimentation on entire structural elements (shear walls, arches, vaults). On the contrary, the analytical and numerical counterpart appears still patchy. The aim of the keynote speech is therefore to review and classify what already exists in the field of advanced analytical and numerical modelling for FRCM composites applied to brittle substrates, and to investigate the near future possible developments. Some analytical and semi-analytical approaches will be reviewed when applied in a variety of laboratory experimentation, including coupons and shear tests carried out on FRCM bonded to flat and curved substrates. In the study of such examples, attention will focus on different numerically efficient strategies used to predict the global and local behavior of the FRCM components at progressively increased external loads. A particular insight will be provided for (i) the recursive utilization of the elastic solution when sawtooth constitutive laws for matrix and interfaces are assumed and for (ii) multi-dimensional shooting numerical algorithms generalized to systems of ordinary differential equations. Having clear in mind the limits of applicability of the aforementioned approaches, the keynote will then introduce a new simple truss finite element with 16th degrees of freedom. The finite element is a two-node assemblage of three trusses representing matrix and fiber layers. The interfaces between the layers are modeled with shear and normal springs lumped at the nodes, mutually connecting contiguous trusses and the inner matrix to the substrate. The degrees of freedom, 8 per node, are the longitudinal and transversal displacements of the three layers and of the substrate, evaluated at the nodes. The particularly appealing simplicity and the direct possibility of implementation within already existing FE software dedicated to the advanced analysis of masonry, allows to study the behavior of large-scale structures reinforced with FRCM at a fraction of the computational burden required by a heterogeneous discretization of the reinforcing package. The keynote will end with real scale applications, which include reinforced arches, vaults and in- and out-of-plane loaded panels.