The description of a problem involving the existence of an interface or of a strong discontinuity requires to solve partial differential equations on a moving domain, whose evolution is also unknown, leading to severe difficulties, especially when the interface undergoes topological changes. The solution becomes even more complex when the whole problem domain changes, such as in mechanical problems involving large deformations. In this context, the phase-field approach allows to easily reformulate the problem through the use of a continuous field variable mimicking the real physical discontinuity. In the present paper we take advantage of such an approach for the description of damage and failure of highly deformable strain rate-dependent materials, such as the elastomeric ones. By harnessing a statistical physics-based micromechanical model of the polymers chain network characterized by the capability to reorganize the distribution of its chain lengths in time, the behavior of a rate-dependent polymer can be simulated. The adopted physics-based approach, upscaled at the continuum level and combined with a phase-field approach, allows us to describe the damage and fracture occurring in this class of materials in the large deformations regime. Some examples are provided to demonstrate the reliability of the proposed model.

对涉及存在界面或强不连续性的问题的描述需要解决运动域上的偏微分方程，该方程的演化也是未知的，从而导致严重的困难，尤其是当界面经历拓扑变化时。当整个问题域发生变化时，例如在涉及大变形的机械问题中，解决方案将变得更加复杂。在这种情况下，相场方法可以通过使用模拟实际物理不连续性的连续场变量轻松地重新构造问题。在本文中，我们利用这种方法来描述高变形应变率相关材料（例如弹性体材料）的损坏和破坏。通过利用基于统计物理学的聚合物链网络的微机械模型，其特征在于能够及时重组其链长的分布，可以模拟速率相关聚合物的行为。所采用的基于物理的方法，在连续水平上进行了放大，并与相场方法相结合，使我们能够描述在大变形状态下此类材料中发生的破坏和断裂。提供了一些示例来证明所提出模型的可靠性。使我们能够描述在大变形状态下此类材料中发生的损坏和断裂。提供了一些示例来证明所提出模型的可靠性。使我们能够描述在大变形状态下此类材料中发生的损坏和断裂。提供了一些示例来证明所提出模型的可靠性。