Development of data-driven constitutive models: Applications in the finite element simulation of hyperelastic materials

When subjected to large deformations, hyperelastic materials, such as polymers and soft tissues, present a highly nonlinear behaviour. This often makes their constitutive description complex and computationally expensive. Surrogate models can replace these traditional and costly models and overcome some computational limitations by learning directly from acquired data. Currently, the usage of surrogate models in commercial finite element (FE) software, such as Abaqus, is non-existent. Therefore, this work advances the current state of the art by developing a methodology to use surrogate models to describe the constitutive behaviour of hyperelastic materials. These models were then incorporated into the FE commercial software, Abaqus, using a user defined material – UMAT, programmed in Fortran Language. Artificial neural networks were trained to predict the isochoric part of the Cauchy stress tensor and the spatial elasticity tensor from the existing data. With the parameters of the trained neural networks, a user defined material was developed. The present method was validated using classical benchmark problems, and the results obtained using the developed constitutive models were compared with the ones obtained with the conventional approach. The correctness of the obtained results highlights the possibility of using data-driven constitutive models to describe the behaviour of incompressible hyperelastic materials. The developed method can be a viable alternative to avoid the need to directly express a given material constitutive equation that is not implemented in the software and show the potential to use this to model materials with experimental data, without the need to derive a material model.