Evolving Density

Bison computes the current density throughout the finite element mesh. Conservation of mass requires (1) where and are the current and original mass densities, and and are the current and original volumes.

The deformation gradient is defined as (2) where is the identity tensor and is the displacement vector. The determinant of the deformation gradient is a measure of volume change: (3) This allows (4) This calculation is done at each integration point throughout the finite element mesh.