We have formulated a new gradient-damage theory for the deformation and failure of amorphous polymers. Our theory accounts for inelastic deformation and damage due to crazing, and also due to a network-disentanglement mechanism, with the damage eventually culminating in brittle fracture at small levels of stretch for the former mechanism, or ductile fracture at relatively large levels of stretch for the latter mechanism. Our damage theory depends not only on a damage variable but also its gradient, and this helps to regularize the strain-softening behavior during the damage process to avoid mesh-dependency related issues during finite element simulations.

We have numerically implemented our theory in a finite element program, and using this simulation capability we show that the predictions from our theory match (reasonably well) the load–displacement curves – as well as the crack-paths under mixed-mode loading conditions – for polymethylmethacrylate (PMMA) as well as polycarbonate (PC) in several technically relevant geometries reported in the literature. The good correspondence of the results from our numerical simulations and available experimental data indicates that our simulation capability should be of practical utility in the design and analysis of structures made from PMMA and PC under largely tensile dominated stress states, the ones that usually control structural failure.

我们为非晶态聚合物的变形和破坏制定了新的梯度损伤理论。我们的理论解释了由于开裂以及网络解缠结机制造成的非弹性变形和破坏，对于前一种机制，破坏最终会在较小拉伸水平下最终达到脆性断裂，而对于较高拉伸水平则最终会导致延性断裂。后一种机制。我们的损伤理论不仅取决于损伤变量，还取决于其梯度，这有助于规范损伤过程中的应变软化行为，从而避免了有限元模拟过程中与网格相关性相关的问题。

我们已经在有限元程序中以数字方式实现了理论，并且利用这种仿真能力，我们证明了我们理论的预测与载荷-位移曲线以及混合模式载荷条件下的裂纹路径（合理地匹配）相吻合。文献中报道的几种技术相关的几何形状中，聚甲基丙烯酸甲酯（PMMA）和聚碳酸酯（PC）的合成。我们的数值模拟结果与可用的实验数据的良好对应关系表明，我们的模拟能力应在设计和分析主要由拉伸控制的应力状态下（通常控制结构破坏的）PMMA和PC制成的结构中具有实用性。