Nonlinear Elasticity

Nonlinear elasticity studies the deformation of materials under large strains, where the relationship between stress and strain is no longer linear. Current research focuses on developing efficient computational methods, such as physics-informed neural networks (PINNs), neural operators, and meshfree methods, to solve the complex partial differential equations governing these deformations, often for both forward and inverse problems (e.g., material property identification). These advancements are improving the accuracy and speed of simulations across diverse applications, including medical image registration, soft robotics, and material characterization, offering significant improvements over traditional finite element methods in certain contexts. The resulting models are enabling more realistic and computationally efficient simulations of complex systems.