Constitutive Multiscale Modeling of Heat Diffusion Reaction Problems

Abstract

This article describes a homogenization procedure based on Multiscale analysis. Such homogenization techniques are important for computer-modeling of heterogeneous materials when the heterogeneities measures allows us to have separation of scales. Multiscale analysis is a reliable technique to understand material responses in where the micro structure is mainly characterized by heterogeneities. The described Multiscale procedure relies on a unified variational basis: (i) Kinematic Admissibility, where the micro-macro kinematics are established and properly linked, (ii) Duality, where the force and stress like physical quantities are characterized, and (iii) Principle of Multiscale Virtual Power, where the homogenization rules are established. For academic purposes a one dimensional numeric implementation is done. We compare the constitutive modeling laws for heat transfer phenomenon, when considering Multiscale analysis and neglecting it.