On boundary potential energies in deformational and configurational mechanics

Abstract This contribution deals with the implications of boundary potential energies, i.e. in short surface, curve and point potentials, on deformational and configurational mechanics. Within the realm of deformational mechanics the surface/curve potentials are allowed in the most general case to depend on the deformation, the surface/curve deformation gradient and the spatial surface normal/curve tangent and are parametrised in the material placement and the material surface normal/curve tangent. The point potentials depend on the deformation and are parametrised in the material placement. From the configurational mechanics perspective the roles of fields and parametrisations are reversed. By considering variational arguments based on the kinematics of deforming surfaces/curves, in particular the relevant surface/curve stresses and distributed forces contributing to (localized) deformational and configurational force balances at surfaces/curves/points, which extend the common traction boundary conditions, are derived. Thereby, dissipative distributed configurational forces that are energetically conjugate to configurational changes are introduced as definitions. The (localized) force balances at surfaces/curves/points together with the contributing stresses and distributed forces within deformational and configurational mechanics display an intriguing duality. The resulting dissipative configurational tractions at the boundary are exemplified for some illustrative cases of boundary potentials.

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