  The deep energy method (DEM) has been used to solve the elastic deformation
of structures with linear elasticity, hyperelasticity, and strain-gradient
elasticity material models based on the principle of minimum potential energy.
In this work, we extend DEM to elastoplasticity problems involving path
dependence and irreversibility. A loss function inspired by the discrete
variational formulation of plasticity is proposed. The radial return algorithm
is coupled with DEM to update the plastic internal state variables without
violating the Kuhn-Tucker consistency conditions. Finite element shape
functions and their gradients are used to approximate the spatial gradients of
the DEM-predicted displacements, and Gauss quadrature is used to integrate the
loss function. Four numerical examples are presented to demonstrate the use of
the framework, such as generating stress-strain curves in cyclic loading,
material heterogeneity, performance comparison with other physics-informed
methods, and simulation/inference on unstructured meshes. In all cases, the DEM
solution shows decent accuracy compared to the reference solution obtained from
the finite element method. The current DEM model marks the first time that
energy-based physics-informed neural networks are extended to plasticity, and
offers promising potential to effectively solve elastoplasticity problems from
scratch using deep neural networks.
