### Context

This is a physical simulation environment. The physical simulation is built based on the Material Point Method. The objective of this problem is to fill in a code block so that the result from executing the code matches the ground-truth result.

The code block defines the full constitutive behavior of the simulated material through two separate classes:
1. **PlasticityModel**: defines the deformation gradient correction model. This class contains two functions that divide the code into a continuous part that defines the differentiable parameters and a discrete part that defines the symbolic deformation gradient correction model. The input to the symbolic deformation gradient correction model is the deformation gradient, and the output is the corrected deformation gradient. 
2. **ElasticityModel**: defines the constitutive law that maps corrected deformation gradient to stress. This class contains two functions that divide the code into a continuous part that defines the differentiable parameters and a discrete part that defines the symbolic constitutive law. The input to the symbolic constitutive law is the corrected deformation gradient, and the output is the Kirchhoff stress tensor.

The simulation applies the `PlasticityModel` first to correct the deformation gradient, then passes this corrected deformation gradient into the `ElasticityModel` to compute the stress.

States that capture the physical dynamics of the system and metrics that measure the difference from the ground-truth result are included in the feedback section.