Homogenization of inelastic composites with misaligned inclusions by using the optimal pseudo-grain discretization

A two-stage homogenization for modelling of elastic-plastic functionally graded composites

“…Consequently, each pseudo-grain is a unidirectional, two-phase composite containing the same volume fraction of the reinforcement as the “original” composite. Then, the homogenization is performed in two steps: the goal of the first step is to homogenize each pseudo-grain individually and the second step involves aggregation of the pseudo-grains contributions by weighting by the orientation distribution function ψ (p) (Figure 6) (Ogierman and Kokot, 2017).…”

“…Consequently, when hundreds of pseudo-grains must be applied there is no point in using hybrid M-T/FE approach because a time of the computations may be even far larger than the time of the FE homogenization based on the complex RVE. However, the optimal pseudo-grain method has been recently proposed to reduce the required number of pseudo-grains (Ogierman and Kokot, 2017). In this case, the orientations and weights of the pseudo-grain are optimized in a way to minimize the discrepancy between given fourth-order orientation tensor and fourth-order orientation tensor depending on the pseudo-grain parameters.…”

“…The inconvenience with this approach is that the number of pseudo-grains must be selected to perform optimization, although it is not known “a priori” if it will satisfy the termination condition. One way is to use the number of pseudo-grains that is enough to provide accurate solution for any orientation, Ogierman and Kokot (2017) suggest that nine optimally selected pseudo-grains can provide satisfactory results for any orientation distribution. A different way is to perform a preliminary simulation considering different numbers of the pseudo-grains and evaluate the accuracy, which is then provided.…”

“…The main contribution of the paper in this field is implementation of the hybrid homogenization in the framework of the discrete orientation averaging procedure. In particular, the discrete orientation averaging procedure involving the optimal pseudo-grain discretization technique (Ogierman and Kokot, 2017) was applied to reduce a number of the discrete orientations, which is required to represent the given orientation state. Unlike the extended equivalent inclusion problem (Ogierman, 2019), the proposed approach is based on several simple equivalent inclusion problems consisting of the single inclusion.…”

Inverse Identification of Elastic Properties of Constituents of Discontinuously Reinforced Composites

“…During the solution of optimization problem formulated in such a way it is important to avoid getting stuck in local optimum. It could be achieved by using global optimization methods like the evolutionary algorithm [20,21,22], artificial immune algorithm [23,24] or particle swarm optimization [25,26]. Other advantages of the global optimization methods over the traditional methods are: no need of computing the objective function gradient and low impact of initial values of the project variables on the optimization results.…”