Sensitivity to material contrast in homogenization of random particle composites as micropolar continua

Abstract

Several composite materials used in engineering – such as ceramic/metal matrix composites, concrete, masonry-like/geo–materials and innovative meta–materials – have internal micro-structures characterized by a random distribution of inclusions (particles) embedded in a matrix. Their structural response is highly influenced not only by the mechanical properties of components, but also by the shape, size and position of the inclusions. In this work, we adopt a statistically-based micropolar homogenization procedure, to obtain the overall elastic properties of homogeneous micropolar continua able to naturally account for scale and skew–symmetric shear effects. Attention is paid to the sensitivity to material contrast, defined as the mismatch between classical and micropolar constitutive properties of matrix and inclusions. A statistical specifically conceived convergence criterion is adopted which allow us to identify the REV (Representative Volume Element) for any value of material contrast

Fast statistical homogenization procedure (FSHP) for particle random composites using virtual element method

“…The results obtained by adopting the FSHP, inclusive of a combined VEM-FEM methodology, are here compared with the results previously obtained by some of the authors (Trovalusci et al, 2015;Reccia et al, 2018) using a standard commercial FEM code. Several simulations are then performed by modifying the material contrast: the size of the RVE and the effective moduli of various kind of two-phases random composites -either with inclusions stiffer or softer than the matrix -are determined.…”

“…In the case of materials with random microstructure, the lack of periodicity in the particle disposition makes it difficult to perform the homogenization process, with particular reference to the possibility of identifying a Representative Volume Element (RVE) and proper boundary conditions to apply at the REV boundary. Since many years in the literature a variety of approaches aimed at defining and implement the effective properties of non-uniform composite microstructures have been proposed (Kanit et al, 2003;Du and Ostoja-Starzewski, 2006;Ostoja-Starzewski, 2006;Khisaeva and Ostoja-Starzewski, 2006;Gitman et al, 2007;Zeman and Sejnoha, 2007;Ostoja-Starzewski, 2008, 2009;Bouaoune et al, 2016;Ghosh and Kubair, 2016;Kubair et al, 2018), also referred to non-classical continua (Trovalusci et al, 2014(Trovalusci et al, , 2015Reccia et al, 2018). Among these models, we focus our attention on the possiblity of approaching the RVE using finite-size scaling of intermediate control volume elements, named Statistical Volume Elements (SVEs), and proceed to homogenization (e.g.…”

“…This procedure has provided significant results (Trovalusci et al, 2014(Trovalusci et al, , 2015(Trovalusci et al, , 2016, with particular reference to the debated problem of the convergence in the presence of materials with very low (or very high) contrast, defined as the ratio between the elastic moduli of inclusions and matrix (Ostoja-Starzewski, 2006;Ranganathan and Ostoja-Starzewski, 2008;Salmi et al, 2012). The limits of the procedure are essentially ascribable to the huge number of simulations needed to define the RVE size, that compromises the applicability of the method (Reccia et al, 2018).…”

Characterization of hybrid piezoelectric nanogenerators through asymptotic homogenization

“…In order to overcome these drawbacks, multiscale techniques, based on homogenization approaches, are a very valuable tool to gather both a synthetic and thorough description of the complex material behaviour. The investigation of the overall static and dynamic behaviour of periodic elastic composite materials has been performed resorting either to asymptotic approaches (Bakhvalov and Panasenko, 1984;Gambin and Kröner, 1989;Allaire, 1992;Boutin, 1996;Fish and Chen, 2001;Andrianov et al, 2008;Tran et al, 2012;Bacigalupo, 2014), or to variational-asymptotic approaches (Smyshlyaev and Cherednichenko, 2000;Peerlings and Fleck, 2004;Bacigalupo andGambarotta, 2012, 2014), or also to identification techniques, among which computational approaches (Forest and Sab, 1998;Kouznetsova et al, 2004;Kaczmarczyk et al, 2008;Bacigalupo and Gambarotta, 2010;De Bellis and Addessi, 2011;Li et al, 2011;Addessi et al, 2013;Lesičar et al, 2014;Trovalusci et al, 2015;Addessi et al, 2016;Biswas and Poh, 2017;Reccia et al, 2018;Trovalusci et al, 2017) and analytical approaches (Bigoni and Drugan, 2007;Mühlich et al, 2012;Bacca et al, 2013a,b;Bacigalupo and Gambarotta, 2013;Bacigalupo et al, 2017;Hütter, 2017). Generalized homogenization approaches have been proposed to date to handle multi-field problems, ranging from thermo-elastic, thermo-diffusive, to piezoelectric and thermo-piezoelectric problems (Gałka et al, 1996;Pettermann and Suresh, 2000;…”

A micromechanics‐based inverse study for stochastic order reduction of elastic UD fiber reinforced composites analyses

“…When uncertainties are involved, or when the volume element is not several order of magnitude larger than the microscale size, the mesoscale volume element does not respect the statistical representativity and is called statistical or stochastic volume element (SVE). 16 Therefore, the homogenized response depends on the SVE realization, and on the applied boundary conditions as discussed for two-dimensional (2D) particle reinforced composites in the case of elasticity, 17,18 linear micropolar continua, [19][20][21] elastoplasticity, 17 thermoelasticity, or again finite elasticity. 17 For a given type of boundary condition, the homogenized properties of SVE realizations exhibit a distribution whose standard deviation increases when the SVE size becomes closer to the inclusion size.…”