Generalised Mori-Tanaka Scheme to Model Anisotropic Damage Using Numerical Eshelby Tensor

Abstract

This work presents a new micromechanical model to describe the 3-D elastic and damaged behaviour of randomly oriented fibre composite. The damage mechanisms are described by the progressive introduction of oriented microcracks in a random discontinuous fibre composite. In this work, the homogenisation is performed using a Mori-Tanaka scheme. Whereas, symmetry is not obtained in estimates of the overall stiffness for multiphase systems with heterogeneity of different shapes or orientations. For this reason, in this work two levels of homogenisation are considered. The Mori-Tanaka method is applied on the matrix with microcracks to give an equivalent damaged matrix, which can be anisotropic. The Mori-Tanaka scheme is used for the second time to homogenise fibres embedded in the new equivalent damage matrix. Generally, this new matrix is anisotropic and for this case no explicit formula for the Eshelby tensor ( S) has been obtained. Thus, it is necessary to compute numerically the components of this fourth order tensor. Moreover damage mechanisms can be modelled using statistical considerations. The damage onset and growth can appear in the matrix, fibres or interface. Hence, overall damaged behaviour can be modelled and predicted as well as the microscopic damage accumulation process.