Final work : Integration scheme of a continuous formulation based on incremental-secant homogenization

Abstract

The field of micromechanics aims to model the behaviour of the continuum of the materials at microscopical level. This work takes a code for a Mean-Field-Homogenization scheme for composite materials and applies a different derivation with the aim of being able to model the continuous reality; to then use a mathematical discretization and be able to draw the stress-strain curve of a number of two-phase composite materials. This model is based on the limit of the classical MFH system of equations to an infinitesimally small time step. This results in a new strain localization tensor that relates the strains in the matrix and inclusion phases, allowing to modify said system and obtain an improved solution.

Wit this new model, one can obtain results with a similar accuracy with respect to the original in one of its variants, the residual-incremental-secant scheme, with a bigger step size in the stress-strain curve. Therefore, the modification of the code performed could be potentially adapted to obtain faster first-order results with an acceptable accuracy.