On general imperfect interfaces with spatially non-constant displacement jumps

Abstract A novel constitutive framework suitable for material interfaces undergoing large deformations is presented. In contrast to previous works, it accounts for spatially non-constant displacement jumps in the Helmholtz energy by employing their gradient along the interface. This first-order generalization encompasses classic cohesive zone models and surface elasticity theory as special cases. Based on a unifying variational ansatz, all balance laws are derived in a natural manner. Balance of angular momentum is enforced pointwise by designing energies that are material frame indifferent. It is shown that for quadratic energies already existing interface models can predict the same features as the novel framework. However, for higher-order energies, this analogy is lost and the generalized, gradient-based framework indeed allows to capture additional effects. An exemplary experiment highlights such effects for a 3d-printed specimen with a soft interface.