A virtual power principle for RVE-based multiscale models

P.J. BLANCO; P.J. SÁNCHEZ; E.A. DE SOUZA NETO; R.A. FEIJÓO

Tandil, Buenos Aires

Congreso; V Congreso de Matemática Aplicada, Computacional e Industrial (MACI 2015); 2015

Asociación Argentina de Matemática Aplicada, Computacional e Industrial (ASAMACI)

In this talk a unified variational theory is proposed for a general class of multiscale models based on the concept of Representative Volume Element (RVE). The entire theory lies on three fundamental principles: (i) kinematical admissibility, whereby the macro- and micro-scale kinematics are defined and linked so as to ensure their magnitudes are in some sense preserved in the micro-macro transition; (ii) duality, through which the force- and stress-like quantities are uniquely identified as the dual objects of the adopted kinematical variables; and (iii) the principle of multiscale virtual power, a generalization of the well-known Hill-Mandel principle of macrohomogeneity, from which equilibrium equations and homogenization relations for the force- and stress-like quantities are unequivocally derived by straightforward variational arguments.The overall theory is presented within a clear, logically structured multiscale framework that provides a rational justification of classical formulations and facilitates the rigorous development of new multiscale models in systematic, well-defined steps. In addition, due to its variational basis, the format in which resulting models are presented is naturally well suited for discretization by finite element methods or any other numerical approximation. Multiscale models already published in the literature can be cast straightforwardly inside the proposed general theory including coupled multiphysics, high order strains effects, dynamics, localization of deformations at macro and micro level and material failure, among others. Several of the above applications are also discussed.