Elastoplastic Constitutive Models using Machine Learning and the Finite Volume Method

Numerical simulation is playing an increasingly prominent role in industrial manufacturing, providing an effective means to analyse and optimise processes alongside traditional experimental approaches. These simulations couple physical laws with constitutive models that represent material behaviour. However, in metal forming, simulation accuracy is often limited by the ability of constitutive models to capture the path-dependent relationship between stress and strain. Developing such models is challenging, as they often involve assumptions and parameters that lack clear physical interpretation or are difficult to measure. This thesis proposes a methodology for constructing elastoplastic constitutive models directly from full-field strain and global force data, eliminating the need for a priori assumptions about the model form or parameters. This is achieved by replacing traditional constitutive laws with machine learning-based models trained directly on measured data. The objectives of the thesis are achieved through the following novel contributions: i) the design of a new algorithm, One-Step SelfSim, which enables the training of history-dependent, machine learning-based material models using measured strain fields and global forces, based on simulations with known applied loads; ii) the application of the finite volume method within an inverse modelling framework to formulate material models, representing a departure from the finite element method commonly used in related studies; and iii) the development of an efficient framework for integrating Python code into the C++-based OpenFOAM environment without translation or overhead, termed pybind11foam, along with a higher-level toolbox named pythonpal4foam. The proposed methodology is demonstrated through a series of 2-D elasticity and elastoplasticity test cases using synthetic strain data. The simulations are conducted in OpenFOAM, with machine learning-based material models implemented in Python and coupled via pythonpal4foam. This framework contributes to the growing field of machine learning-enhanced physics simulation and opens avenues for designing products and processes in manufacturing with improved precision and efficiency.