Development of Data-driven Constitutive Models: Applications in the Fi- nite Element Simulation of Hyperelastic Materials

Resumo

When subjected to large deformations, hyperelastic materials present a highly nonlinear behaviour, which 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 nonexistent. In this work, surrogate models, able to describe the constitutive behaviour of different materials, were developed and were then incorporated into Abaqus, using a user defined material, 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 hyperelastic materials. The proposed approach can be a viable alternative, avoiding the need to express a given material constitutive equation directly.