Identification of higher-order continua equivalent to a Cauchy elastic composite

Abstract

A heterogeneous Cauchy elastic material may display micromechanical effects that can be modeled in a homogeneous equivalent material through the introduction of higher-order elastic continua. Asymptotic homogenization techniques provide an elegant and rigorous route to the evaluation of equivalent higher-order materials, but are often of difficult and awkward practical implementation. On the other hand, identification techniques, though relying on simplifying assumptions, are of straightforward use. A novel strategy for the identification of equivalent second-gradient Mindlin solids is proposed in an attempt to combine the accuracy of asymptotic techniques with the simplicity of identification approaches. Following the asymptotic homogenization scheme, the overall behaviour is defined via perturbation functions, which (differently from the asymptotic scheme) are evaluated on a finite domain obtained as the periodic repetition of cells and subject to quadratic displacement boundary conditions. As a consequence, the periodicity of the perturbation function is satisfied only in an approximate sense, nevertheless results from the proposed identification algorithm are shown to be reasonably accurate.

A diffuse interface model for the analysis of propagating bulges in cylindrical balloons

“…This appendix provides details on the elimination of the unknown λ(Z) from the intermediate form (19) of the energy, leading to the final form (20).…”

Determination of metamaterial parameters by means of a homogenization approach based on asymptotic analysis

“…Higher order theories are called generalized mechanics and homogenization in the framework of generalized mechanics is a challenging task endeavored by many scientists, among others by [17,31,40,49,55,71,79]. Mostly, it is agreed that homogenization of an RVE by involving so-called higher gradient terms of the macroscopic field is a natural way to include size effect [14,[41][42][43][44]58].…”

Wave propagation modeling in periodic elasto-thermo-diffusive materials via multifield asymptotic homogenization

“…The application of homogenization methods and multiscale modelings allows avoiding the demanding numerical computation of the whole heterogeneous medium leading to the identification of effective macroscopic properties for the equivalent continuum. In order to study the overall properties of composite materials, numerous homogenization approaches have been provided over the last decades, which can be divided in asymptotic techniques (Sanchez-Palencia, 1974;Bensoussan et al, 1978;Bakhvalov and Panasenko, 1984;Gambin and Kröner, 1989;Allaire, 1992;Bacigalupo, 2014;Fantoni et al, 2017Fantoni et al, , 2018, variational-asymptotic techniques (Smyshlyaev and Cherednichenko, 2000;Peerlings and Fleck, 2004;Bacigalupo and Gambarotta, 2014), and numerous identification approaches including the analytical (Bigoni and Drugan, 2007;Milton and Willis, 2007;Bacca et al, 2013a,b,c;Nassar et al, 2015;Bacigalupo et al, 2018) and computational methods (Forest and Sab, 1998;Ostoja-Starzewski et al, 1999;Feyel and Chaboche, 2000;Kouznetsova et al, 2002;Forest, 2002;Feyel, 2003;Kouznetsova et al, 2004;Lew et al, 2004;Kaczmarczyk et al, 2008;Yuan et al, 2008;Scarpa et al, 2009;Bacigalupo and Gambarotta, 2010;Forest and Trinh, 2011;De Bellis and Addessi, 2011;Addessi et al, 2013;Zäh and Miehe, 2013;Salvadori et al, 2014;Trovalusci et al, 2015). The present study is devoted to provide a multifield asymptotic homogenization technique ...…”