Smart constitutive laws: Inelastic homogenization through machine learning

Abstract Homogenizing the constitutive response of materials with nonlinear and history-dependent behavior at the microscale is particularly challenging. In this case, the only option is generally to homogenize numerically via concurrent multiscale models (CMMs). Unfortunately, these methods are not practical as their computational cost becomes prohibitive for engineering-scale applications. In this work, we develop an alternative formulation to CMMs that leverage state-of-the-art micromechanical modeling and advanced machine learning techniques to develop what we call smart constitutive laws (SCLs). We propose a training scheme for our SCLs that makes them suitable for arbitrary loading histories, making them equivalent to traditional constitutive models. We also show how to implement a SCL into a traditional finite element solver and investigate the response of an engineering-scale component. We compare our results to those obtained via a high fidelity simulation. Our findings indicate that SCLs can dramatically boost the computational efficiency and scalability of computational homogenization for nonlinear and history-dependent materials with arbitrary microstructures, enabling in this way the automatic and systematic generation of microstructurally-informed constitutive laws that can be adopted for the solution of macro-scale complex structures.