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Application of material forces in finite element simulations

Presented is a theoretical description and computation method to calculate configurational forces in the context of the finite element method. We take fully 3D-case dynamics and large deformations in hyper-elastic materials into account. The FE implementation and numerical analysis of different structures demonstrates the applicability of the constitutive description. In our derivation, the Lagrangian depends on the deformation gradient and on the position (in the reference configuration) explicitly, which accounts for inhomogeneous materials, e.g. materials with phase boundaries, voids or cracks. In analogue to the local balance of momentum for the material motion problem), where configurational force balance (balance of momentum for the material motion problem), where configurational (or material) forces correspond to the volume forces in the physical space. An FE desription is obtained by formulating the weak form of the configurational force balance. Thus, the configurational forces action on the finite element nodes may be computed as the physical boundary value problem is solved. For the static case and small deformations, the configurational force corresponds to the well known J-Integral in fracture mechanics.