Multiscale numerical strategy for micromorphic description of quasi-brittle media from classical elastic damage models at the microscale

Abstract

The formulation of the micromorphic continuum theory and its finite element approach are well-established, however, the physical interpretation and determination of the large number of constitutive parameters of this theory limit its practical application. In this sense, this paper presents a multiscale numerical strategy to obtain a macroscopic micromorphic description of the continuum from a proposed solution to the boundary value problems at the microscale governed by the classical continuum theory. Consequently, the micromorphic analysis is performed adopting well-known material parameters. To obtain the macroscopic micromorphic material response based on classical constitutive parameters, an approach which employs a cubic displacement ansatz is derived from a micromorphic homogenization framework proposed in the literature. To illustrate the capacity of the strategy to reproduce a micromorphic description adopting classical material parameters, the approach is implemented in an finite element code to demonstrate that the method overcomes the spurious mesh dependency of classical models of quasi-brittle damage due to regularization effects in localization problems achieved with generalized continuum models.