Journal
APPLIED MATHEMATICAL MODELLING
Volume 109, Issue -, Pages 52-76Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2022.03.036
Keywords
Micromorphic continuum; Multiscale numerical strategy; Classical constitutive parameters; Regularization effects
Funding
- CAPES (Coordenacao de Aperfeicoamento de Pessoal de N?vel Superior)
- FAPEMIG (Fundacao de Amparo Pesquisa do Estado de Minas Gerais)
- CNPq (Conselho Nacional de Desenvolvimento Cientfico e Tecnologico)
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This paper presents a multiscale numerical strategy to obtain a macroscopic micromorphic description of a continuum. The strategy utilizes classical constitutive parameters and a cubic displacement ansatz to achieve the macroscopic micromorphic material response.
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 mi-cromorphic 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 parame-ters, an approach which employs a cubic displacement ansatz is derived from a micro-morphic homogenization framework proposed in the literature. To illustrate the capacity of the strategy to reproduce a micromorphic description adopting classical material pa-rameters, 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 dam-age due to regularization effects in localization problems achieved with generalized con-tinuum models.(c) 2022 Elsevier Inc. All rights reserved.
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