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.

提出了一种适用于经历大变形的材料界面的新型本构框架。与之前的工作相比，它通过沿界面使用梯度来解释亥姆霍兹能量中空间非恒定位移跳跃。这种一阶概括包括作为特殊情况的经典内聚区模型和表面弹性理论。基于统一的变分 ansatz，所有的平衡定律都是以自然的方式推导出来的。角动量的平衡是通过设计与物质框架无关的能量来逐点执行的。结果表明，对于二次能量，现有的界面模型可以预测与新框架相同的特征。然而，对于更高阶的能量，这个类比就失去了，概括了，基于梯度的框架确实允许捕捉额外的效果。一个示例性实验突出了具有软界面的 3d 打印样本的这种效果。