Estratégia multiescala para descrição micromórfica do contínuo a partir do contínuo clássico

Abstract

The macroscopic behavior of materials is a function of the structure they exhibit at the microscopic level. The phenomenological approach adopted in the classical continuum theory does not consider the individual behavior of the microstructure constituents, but rather deals with the e ective macroscopic properties. Due to the lack of microstructural parameters, this theory does not adequately describe materials with complex microstructure or when the structural dimensions are comparatively small with respect to its microstructure. In this sense, numerous so-called generalized continuum theories were developed, incorporating the microstructural behavior of the material medium. These theories fall into two groups: (a) those that consider higher order displacement gradients and (b) those that add kinematic degrees of freedom to material particles. The micromorphic continuum theory, in which each material particle is endowed with nine additional kinematic degrees of freedom, represents the most general case of this second group. This theory is suited to analysis of materials with arbitrarily deforming microstructure. The heuristic construction of the micromorphic continuum based on thermodynamic considerations (or at the principle of virtual work) is well-established. However, the identi cation of corresponding constitutive laws and the determination of the large number of constitutive parameters limit the practical application of such theory. In this sense, this work proposes a multiscale formulation for obtaining the macroscopic micromorphic constitutive relations through the solution of boundary value problems at the microscale according to the classical continuum theory. The INSANE system (INteractive Structural ANalysis Environment), a free software developed at the Department of Structural Engineering of the Engineering School of the Federal University of Minas Gerais, is used in the implementation.