A deep learning energy method for hyperelasticity and viscoelasticity
This provides a faster, data-free alternative for simulating material deformation in engineering and physics, though it appears incremental as it builds on existing deep learning and energy methods.
The authors tackled solving partial differential equations for hyperelastic and viscoelastic materials by merging potential energy formulation with deep learning, resulting in a meshfree method that accurately captures 3D mechanical responses without needing training data from classical methods like FEM, enabling instant predictions after training.
The potential energy formulation and deep learning are merged to solve partial differential equations governing the deformation in hyperelastic and viscoelastic materials. The presented deep energy method (DEM) is self-contained and meshfree. It can accurately capture the three-dimensional (3D) mechanical response without requiring any time-consuming training data generation by classical numerical methods such as the finite element method. Once the model is appropriately trained, the response can be attained almost instantly at any point in the physical domain, given its spatial coordinates. Therefore, the deep energy method is potentially a promising standalone method for solving partial differential equations describing the mechanical deformation of materials or structural systems and other physical phenomena.