Modeling strain localization with a second gradient model can become problematic at the late stages of softening response, when the second gradient terms become significant compared to the first gradient terms. This is particularly true for mode I crack problems where an unrealistic spreading of the localized zone can be encountered. To deal with these limitations, a novel second gradient interface element for mode I crack propagation problems is introduced. It is shown that the model is able to correctly reproduce all the different phases up to failure; the adherence phase, strain localization, the transition from localized strains to cohesive zones and full crack opening.

在软化响应的后期，当第二个梯度项与第一个梯度项相比变得显着时，使用第二个梯度模型对应变局部化进行建模可能会出现问题。对于可能遇到局部区域不切实际的扩展的模式 I 裂纹问题尤其如此。为了解决这些限制，引入了一种用于模式 I 裂纹扩展问题的新型第二梯度界面单元。结果表明，该模型能够正确再现直至失败的所有不同阶段；粘附阶段，应变局部化，从局部应变到内聚区的转变和完全开裂。