Micromorphic homogenization of a porous medium: elastic behavior and quasi-brittle damage

Today it is well known that the classical Cauchy continuum theory is insufficient to describe the deformation behavior of solids if gradients occur over distances which are comparable to the microstructure of the material. This becomes crucial e.g., for small specimens or during localization of deformation induced by material degradation (damage). Higher-order continuum approaches like micromorphic theories are established to address such problems. However, such theories require the formulation of respective constitutive laws, which account for the microstructural interactions. Especially in damage mechanics such laws are mostly formulated in a purely heuristic way, which leads to physical and numerical problems. In the present contribution, the fully micromorphic constitutive law for a porous medium is obtained in closed form by homogenization based on the minimal boundary conditions concept. It is shown that this model describes size effects of porous media like foams adequately. The model is extended toward quasi-brittle damage overcoming the physical and numerical limitations of purely heuristic approaches.