Overview

Example	Highlight
Poisson equation	\({\color{green}Basics:}\) Poisson’s equation in a unit square domain with Dirichlet and Neumann boundary conditions, as well as a source term.
Linear elasticity	\({\color{green}Basics:}\) Bending of a linear elastic beam due to Dirichlet and Neumann boundary conditions. Second order tetrahedral element (TET10) is used.
Hyperelasticity	\({\color{blue}Nonlinear \space Constitutive \space Law:}\) Deformation of a hyperelastic cube due to Dirichlet boundary conditions.
Plasticity	\({\color{blue}Nonlinear \space Constitutive \space Law:}\) Perfect J2-plasticity model is implemented for small deformation theory.
Compute gradients	\({\color{red}Inverse \space Problem:}\) Sanity check of how automatic differentiation works.
Topology optimization	\({\color{red}Inverse \space Problem:}\) SIMP topology optimization for a 2D beam. Note that sensitivity analysis is done by the program, rather than manual derivation.
Source field identification	\({\color{red}Inverse \space Problem:}\) Gradient of the objective function with respect to the source field term.
Traction force identification	\({\color{red}Inverse \space Problem:}\) Gradient of the objective function with respect to the Neumann boundary condition.
Thermal mechanical control	\({\color{red}Inverse \space Problem:}\) Gradient of the objective function with respect to the Dirichlet boundary condition.
Shape optimization	\({\color{red}Inverse \space Problem:}\) Gradient of the objective function with respect to a stiffness related term.
Structure/material co-design	\({\color{red}Inverse \space Problem:}\) Co-design of structure and material in a plasticity problem.