A cluster‐based incremental potential approach for reduced order homogenization of bones

Abstract We develop a cluster‐based model order reduction (called C‐pRBMOR) approach for efficient homogenization of bones, compatible with a large variety of generalized standard material (GSM) models. To this end, the pRBMOR approach based on a mixed incremental potential formulation is extended to a clustered version for a significantly improved computational efficiency. The microscopic modeling of bones falls into a mixed incremental class of the GSM framework, originating from two potentials. An offline phase of the C‐pRBMOR approach includes both a clustering analysis spatially decomposing the micro‐domain within an RVE and a space–time decomposition of the microscopic plastic strain fields. A comparative study on two different clustering approaches and two algorithms for mode identification is additionally conducted. For an online analysis, a cluster‐enhanced version of evolution equations for the reduced variables is derived from an effective incremental variational formulation, rendering a very small set of nonlinear equations to be numerically solved. Several numerical examples show the effectiveness of the C‐pRBMOR approach. A striking acceleration rate beyond 10 4 against conventional FE computations and that beyond 10 3 against the original pRBMOR approach are observed.