Isotropic Polyconvex Hyperelastic Energies and Hulls: A Novel Neural Network Framework Satisfying the Universal Approximation Theorem
Please login to view abstract download link
Incorporating physical principles and mathematical restrictions in artificial neural networks often significantly improves the constitutive modeling of materials and remains an ongoing challenge [1,2]. Since physical principles usually require different constraints, their individ-ual implementations may interfere with each other causing additional scientific challenges. This work introduces a novel neural network for hyperelasticity that rigorously fulfills the different constraints associated with objectivity, polyconvexity and isotropy. Further con-straints such as growth conditions can also be embedded easily. In contrast to previous frameworks, the novel approach fulfills the universal approximation theorem such that any objective, polyconvex and isotropic energy can be approximated in this function space with any desired accuracy. Additionally, the proposed method allows for the approximation of polyconvex hulls. Numerical examples demonstrate the ability of the novel approach to approximate energies that could not be captured by previous neural networks. Likewise, polyconvex hulls of non-polyconvex energies can also only be computed
