Micromechanical Estimates Compared to FE-Based Methods for Modelling the Behaviour of Micro-Cracked Viscoelastic Materials

Abstract

The purpose of this study is to investigate the effective behaviour of a micro-cracked material whose matrix bulk and shear moduli are ruled by a linear viscoelastic Burgers model. The analysis includes a detailed study of randomly oriented and distributed cracks displaying an overall isotropic behaviour, as well as aligned cracks resulting in a transversely isotropic medium. Effective material properties are approximated with the assumption that the homogenized equivalent medium exhibits the characteristics of a Burgers model, leading to the identification of short-term and long-term homogenized modules in the Laplace–Carson space through simplified formulations. The crucial advantage of this analytical technique consists in avoiding calculations of the inverse Laplace–Carson transform. The micromechanical estimates are validated through comparisons with FE numerical simulations on 3D microstructures generated with zero-thickness void cracks of disc shape. Intersections between randomly oriented cracks are accounted for, thereby highlighting a potential percolation phenomenon. The effects of micro-cracks on the material’s behaviour are then studied with the aim of providing high-performance creep models for macrostructure calculations at a moderate computation cost through the application of analytical homogenization techniques.