Fracture of viscoelastic materials is considered to be a complex phenomenon due to their highly rate sensitive behavior. In this context, we are interested in the quasi-static response of a viscoelastic solid subjected to damage. This paper outlines a new incremental variational based approach and its computational implementation to model damage in viscoelastic solids. The variational formalism allows us to embed the local constitutive equations into a global incremental potential, the minimization of which provides the solution to the mechanical problem. Softening damage models in their local form are known to result in spurious mesh-sensitive results, and hence non-locality (or regularization) has to be introduced to preserve the mathematical relevance of the problem. In the present paper, we consider two different regularization techniques for the viscoelastic damage model : a particular phase-field and a lip-field approach. The model parameters are calibrated to obtain some equivalence between both these approaches. Numerical results are then presented for the bidimensional case and both these approaches compare well. Numerical results also demonstrate the ability of the model to qualitatively represent the typical rate-dependent behaviour of the viscoelastic materials. Besides, the novelty of the present work lies in the use of lip-field approach for the first time in a viscoelastic context.

翻译：粘弹性材料的断裂由于其高度速率敏感性而被视为一种复杂现象。在此背景下，我们关注受损粘弹性固体的准静态响应。本文提出了一种新的基于增量变分的方法及其计算实现，用于模拟粘弹性固体中的损伤。该变分形式允许我们将局部本构方程嵌入到全局增量势中，通过最小化该势能即可获得力学问题的解。已知局部形式的软化损伤模型会导致虚假的网格敏感结果，因此必须引入非局部性（或正则化）以保持问题的数学合理性。在本文中，我们考虑了两种不同的粘弹性损伤模型的正则化技术：特定的相场法和唇场法。模型参数被校准以实现两种方法之间的某种等价性。随后给出了二维情况下的数值结果，两种方法对比良好。数值结果还证明了该模型能够定性表征粘弹性材料典型的速率相关行为。此外，本工作的创新之处在于首次在粘弹性背景下应用了唇场方法。