Deep learning operator network for plastic deformation with variable loads and material properties

The advent of data-driven and physics-informed neural networks has sparked interest in deep neural networks as universal approximators of solutions in various scientific and engineering communities. However, in most existing approaches, neural networks can only provide solutions for a fixed set of input parameters such as material properties, source terms, loads, boundaries, and initial conditions. For any change of those parameters, re-training is necessary. Classical numerical methods are no different, as a new independent simulation needs to be performed for every new input parameter value. This can be particularly computationally costly in nonlinear material deformation, such as in plasticity, for parametric analysis, optimization, sensitivity analysis and design with variable loads, boundary conditions, and material properties. Unlike classical neural networks, which approximate solution functions, the newly introduced deep learning operator network DeepONet approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to other output spaces' solution functions. We extend the DeepONet formulation to solve the stress distribution in small strain plastic deformation problems with the variable loads, material properties, and random deformation path functions as its parameters. We show that once the proposed framework is adequately trained on high-end computers, it can predict the stress solutions in the entire domain accurately and many orders of magnitude faster than traditional numerical solvers for any combination of input parameters and without any additional training.