A mixed eulerian-lagrangian displacement model for large-deformation analysis in solid mechanics

A new mixed kinematic description for large-deformation solid mechanics is presented. The novel aspect of the new model is that both the initial and current configurations are treated as unknown. Large-deformation statements of the principles of virtual work and stationary potential energy are formulated with the new description and presented in incremental form suitable for iterative finite element solutions. The well-known total Lagrangian and updated Lagrangian descriptions are shown to be special cases of the mixed formulation. The new description is advantageous in situations where it is difficult to select an appropriate material discretization prior to analysis. Applications to large-deformation frictional contact and fracture mechanics are presented to demonstrate the utility of the new kinematic description.