A three-dimensional computational multiscale micromorphic analysis of porous materials in linear elasticity

We present an extension of a multiscale micromorphic theory to three-dimensional problems for porous materials, where a clear scale separation is not given. Following the multiscale micromorphic framework of Biswas and Poh (J Mech Phys Solids 102:187–208, 2017), macroscopic governing equations of a micromorphic continuum are derived from a classical continuum on the microscale by means of a kinematic field decomposition. The macro–microenergy equivalence is guaranteed via the Hill–Mandel condition. For linear elasticity problems, generalized elasticity tensors are determined via several RVE computations once and for all, avoiding concurrent RVE computations for an online structural analysis. A three-dimensional implementation is revealed in detail. A comparative study with direct numerical simulations and first-order multiscale computations shows that the computational multiscale micromorphic method has sufficient accuracy and computational efficiency, thus providing a powerful tool for design and practical engineering applications of porous materials.