Finite electro-elasticity with physics-augmented neural networks

Abstract

In the present work, a machine learning based constitutive model for electro-mechanically coupled material behavior at finite deformations is proposed. Using different sets of invariants as inputs, an internal energy density is formulated as a convex neural network. In this way, the model fulfills the polyconvexity condition which ensures material stability, as well as thermodynamic consistency, objectivity, material symmetry, and growth conditions. Depending on the considered invariants, this physics-augmented machine learning model can either be applied for compressible or nearly incompressible material behavior, as well as for arbitrary material symmetry classes. The applicability and versatility of the approach is demonstrated by calibrating it on transversely isotropic data generated with an analytical potential, as well as for the effective constitutive modeling of an analytically homogenized, transversely isotropic rank-one laminate composite and a numerically homogenized cubic metamaterial. These examinations show the excellent generalization properties that physics-augmented neural networks offer also for multi-physical material modeling such as nonlinear electro-elasticity.

References in corpus (4)

• NN-EUCLID: deep-learning hyperelasticity without stress data
• Data-driven fracture mechanics
• Solving the wave equation with physics-informed deep learning
• Optimisation of hierarchical dielectric elastomer laminated composites

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• Multiscale topology optimization of functionally graded lattice structures based on physics-augmented neural network material models
• Physics-augmented neural networks for constitutive modeling of hyperelastic geometrically exact beams
• When invariants matter: The role of I1 and I2 in neural network models of incompressible hyperelasticity
• A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strains
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