Computation of material forces based on a gradient-enhanced mixed variational formulation

Configurational (or material) forces are computed based on a previously derived thermodynamically consistent definition of material forces, in conjunction with a gradient-enhanced constitutive theory. The primary problem solved for is based on a mixed variational formulation. Under the proposed mixed formulation, no nodal smoothing of internal variables for the computation of material forces is required at the post-processing. Results are shown in terms of energetic quantities which stem from the computed material forces. The mesh sensitivity of the latter quantities is examined and compared to respective results based on local constitutive theory in a "standard"displacements-based variational formulation