Principal Investigator Kenneth Kamrin
Solid constitutive laws are naturally descibed in Lagrangian frame, where local deformation measurements are most easily accessible. Even so, there is a desire from some communities for methods that can capture the essential physics of general solid deformation but in an Eulerian framework, which can be discretized and simulated as a finite-difference scheme. This work presents such an alternative, by way of a surrogate quantity called the reference map. The reference map is a vector field that appropriately reflects the deformation history, and evolves under an explicit update law on the grid. Finite-difference of the reference map can be used to approximate the deformation gradient, which is key to solid response. This field is in direct analogy to the roll the velocity field plays in simulating fluid stress on a fixed computational grid.