Micromorphic homogenisation and the application to damage mechanics

Project manager

Dr.-Ing. Geralf Hütter

Motivation

It is well-known and accepted that damage mechanics approaches within the classical framework of simple materials leads to ill-posed boundary value problems and thus, if implemented to FEM, to a pathological mesh sensitivity. This problem is manifested in the missing intrinsic length of classical theories of continuum mechanics.

Today, certain higher order continuum theories are established to overcome this problem in principle. In particular, the micromorphic theory of Eringen and Mindlin and its generalisation to damage mechanics by Forest attract research activities as they firstly retain the modular concept of continuum mechanics of balance equations, kinematic equations and constitutive equations and thermodynamics and secondly can be  implementated in FEM codes in a straightforward way. However, although each of these "ingredients" is known in principle, the formulation of the constitutive relations for a particular material is challenging due to the increased number of generalized measures of stress and deformation in higher-order theories compared to classical continuum mechanics.

Scope

The goal of this project is to develop homogenization method which allow to derive the constitutive laws of micromorphic continua from homogenization of the damage mechanisms at the microscale.

Publications