A unified concept of elastic-viscoplastic Cosserat and micromorphic continua

摘要

The paper is concerned with a unified formulation and treatment of Cosserat, micromorphic, and more general continua. First the classical understanding of Cosserat and micromorphic continua is reviewed and critically examined. It is shown that the strain measures of the micromorphic continuum as suggested by Eringen and co-workers do exhibit shortcomings which become evident when discussing the Euler-Lagrange equations of a corresponding action. Assuming that invariance of the strain measures should be required with respect to the group SO(3) alone and not to that of GL~+(3), new strain measures of the micromorphic continuum and corresponding field equations are derived. A new unified understanding of Cosserat and micromorphic continua is propagated which views the rotation field in case of the Cosserat continuum as a first approximation of a generalized displacement field. The unified treatment allows for a straightforward formulation of finite strain viscoplasticity of such continua. The formulation is based on a multiplicative decomposition of the micro stretch tensor. Furthermore it allows for the application of constitutive laws of the unified type generally formulated for classical continua.