Two‐scale computational homogenization of calcified hydrogels

Abstract

The development of new type of hydrogels featuring enhanced properties is a recent topic and of particular interest for a wide range of industrial applications, especially in biomedical sector. The present contribution focuses on the mutliscale modeling of hydrogels that are treated by the enzymatic mineralization and thus enriched with calcium phosphate. More specifically, the calcium phosphate forms spherical or honeycomb structures in the hydrogel matrix, which significantly improves effective material properties such as stiffness and strength. The chosen multiscale finite element method (FEM) homogenization strategy uses the Hill–Mandel macrohomogeneity condition for bridging two scales: the macroscopic boundary value problem (BVP) simulates the specimen behavior, whereas the microscopic BVP investigates the representative volume element (RVE) depicting the heterogeneous multiphase microstructure. The approach proposed uses the Ogden model to simulate the hydrogel and the neo‐Hooke model for the calcium phosphate phase. It varies the RVE type and the macroscopic tests in order to study the influence of the microstructure on the effective behavior and uses experimental data to determine missing microscopic material parameters. Chosen numerical examples demonstrate the applicability of the numerical tool for the estimation of the optimal microscopic arrangement of phases.