Construction of first and second order grade anisotropic continuum media for 3D porous and textile composite structures
Résumé
This paper aims at developing homogeneous, anisotropic strain-gradient continuum models as substitutes of 3D heterogeneous porous or composite materials and structures. We construct effective first and second order grade continuum models equivalent to such inhomogeneous structures. This in turn leads to the construction of a strain-gradient continuum with effective mechanical properties at the first and second order, accounting for the impact of the underlying microstructure on the overall effective mechanical response of the effective continuum. The effective properties are obtained based on the response of the representative volume element or unit cell of the initial structure under prescribed boundary conditions. Mixed boundary conditions comprising both traction and displacement boundary conditions are applied on the structure boundaries to identify the equivalent 3D strain gradient elasticity. The first and second order mechanical constants of the effective strain-gradient continuum are deduced by an equivalent strain energy method. We perform this study computationally using a finite element approach. The present methodology is exemplified in certain applications, considering sequentially three-dimensional random porous polymer scaffolds, composite reinforced by inclusions, and woven composites, including layered composites and 3D through-thickness orthogonal interlocks.