Physics-Based Simulation

Summary

Defining the flow map which transforms continuum bodies from the material space (initial configuration) to the world space (current configuration), we introduced a mathematical description of the change in shapes -- the deformation gradient $\mathbf{F}\in {\mathbb{R}}^{d\times d}$ ($d=2$ or $3$), which is the Jacobian of the flow map with respect to $\mathbf{X}$.

When $\mathbf{F}$ at a certain point on the continuum body is a rotation matrix, it indicates there is no deformation and, consequently, no local elasticity forces should be present. In the next lecture, we will explore how to define more realistic elastic potential energies using the deformation gradient.