Time-dependent deformation and damage in viscoelastic materials exhibit distinct characteristics compared to purely brittle or ductile materials, especially under large deformations. These behaviours become even more complex in the presence of pre-cracks. To model this process, we propose an improved non-ordinary state-based peridynamics (NOSB-PD) with implicit adaptive time-stepping (IATS). The proposed formulation encompasses several key aspects, including peridynamic governing equations, improvements to the conventional NOSB-PD, incorporation of a hyper-viscoelastic constitutive model, and an implicit discretization method. The highlights of this study include: (1) Proposing an improved NOSB-PD integrated with a stabilised bond-associated (BA) scheme; (2) Incorporating a hyper-viscoelastic constitutive model combined with a damage model into the framework; (3) Developing a novel IATS method for efficient simulation of time-dependent behaviours; and (4) Exploring the effects of crack patterns and material properties on damage evolution, offering key insights into underlying mechanisms. Then, numerical examples are conducted using the proposed IATS BA-NOSB-PD to simulate hyper-viscoelastic deformation and creep damage. Numerical performance is thoroughly evaluated through benchmark tests, demonstrating that the proposed method effectively simulates creep processes under stepwise loading and unloading conditions. The effects of crack patterns, critical energy release rate, and shear modulus on creep damage are explored in-depth. The results reveal that the propagation and coalescence of multiple cracks take longer compared to a single crack. The influence of crack patterns becomes more pronounced when multiple cracks are present.

中文翻译：

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具有预裂纹的高粘弹性固体中随时间变化的行为和蠕变损伤的近场动力学建模


与纯脆性或延展性材料相比，粘弹性材料中的随时间变化的变形和损伤表现出明显的特性，尤其是在大变形下。在存在预裂纹的情况下，这些行为变得更加复杂。为了模拟这个过程，我们提出了一种改进的非非常态基于状态的近场动力学 （NOSB-PD） 和隐式自适应时间步长 （IATS）。所提出的公式包括几个关键方面，包括近场动力学控制方程、对传统 NOSB-PD 的改进、超粘弹性本构模型的结合以及隐式离散化方法。本研究的亮点包括：（1） 提出一种改进的 NOSB-PD 与稳定债券相关 （BA） 方案相结合;（2） 将超粘弹性本构模型与损伤模型相结合纳入框架;（3） 开发一种新的 IATS 方法，用于有效模拟时间依赖性行为;（4） 探索裂纹模式和材料特性对损伤演变的影响，为潜在机制提供关键见解。然后，使用所提出的 IATS BA-NOSB-PD 进行数值算例，模拟超粘弹性变形和蠕变损伤。通过基准测试对数值性能进行了全面评估，表明所提出的方法有效地模拟了逐步加载和卸载条件下的蠕变过程。深入探讨了裂纹模式、临界能量释放速率和剪切模量对蠕变损伤的影响。结果表明，与单个裂纹相比，多个裂纹的扩展和聚结需要更长的时间。当存在多个裂纹时，裂纹模式的影响会变得更加明显。