Cluster based nonuniform transformation field analysis: An efficient homogenization for inelastic heterogeneous materials

In this article, the authors propose an efficient numerical homogenization method, the so‐called cluster based nonuniform transformation field analysis (NTFA), for inelastic heterogeneous material. The method enables to predict the effective properties directly from the local constitutive relations for microstructural phases of heterogeneous material, thus no requiring preliminary assumptions and any derivations for the effective constitutive relation as in the conventional NTFA. Evolution of plastic strain field is expressed by combination of nonuniform plastic strain modes evaluated from the nonlinear finite element analysis for training directions previously given and snapshot proper orthogonal decomposition. Eventually, microscopic stress and strain field are represented by scalar reduced variables and plastic strain modes. A simple maximization of minimum distance is proposed in order to choose uniformly distributed training directions on a unit sphere in the load space. Also, scalar reduced variables are directly determined from the integration of local constitutive relation, where material points are compressed into a number of clusters by clustering scheme. Thus, evolution of reduced variables is evaluated by the integration of local constitutive relation only in clusters. Numerical examples that consider material models followed J2 plasticity and pressure‐dependent non‐associated flow rule show that the current approach may predict the effective properties of inelastic heterogeneous material accurately and efficiently. It should be noted that the current approach can be available for material followed not only associated flow rule but also non‐associated flow one.