Micromechanics of inelastic composites with misaligned inclusions: Numerical treatment of orientation Original Research Article

This paper is concerned with the micromechanics of multi-phase fiber- or inclusion-reinforced inelastic composites with a special emphasis on the numerical treatment of misaligned orientation. Mean-field homogenization of these composites involves volume and orientation averaging. The latter usually needs average orientation measures known as the second- and fourth-rank orientation tensors a and A, respectively. Usually the only orientation data available is a and a first issue is to reconstruct A using closure approximations. We propose a new weighted regularization method which deals with orientations which are strictly neither 1D, 2D nor 3D and ensures a smooth transition between the 3 cases. A second issue is that there are situations where the inclusions’ orientation distribution function (ODF) is needed for homogenization but is unavailable. The ODF is recovered using a and A and numerically computed at a number of discrete orientations. A third issue is the actual computation of orientation averaging integrals. An efficient algorithm approximates the integrals with sums over a finite number of orientations. Orientation and volume averaging concepts are applied to the mean-field homogenization of two classes of multi-phase composites: linear thermo-elastic and rate-independent inelastic. In the latter case, an incremental formulation is proposed which enables the simulation of unloading, cyclic and otherwise non-proportional loadings. Implicit time-discretization and consistent tangent operators are employed. The procedures and the corresponding algorithms were implemented in the [DIGIMAT version 1.4, 2004. Linear and nonlinear multi-scale material modeling software, e-Xstream engineering SA (), Louvain-la-Neuve, Belgium.] software and several numerical simulations show their accuracy and efficiency.