应变梯度相关损伤的间断Galerkin方法：插值、收敛性和二维问题的研究
A discontinuous Galerkin method for strain gradient-dependent damage: Study of interpolations, convergence and two dimensional problems
摘要：
发展了一种应变梯度相关损伤的间断Galerkin方法。这种方法的优势在于，它允许使用$C^0$插值函数的连续理论，涉及高阶导数，而在传统的框架中，至少$C^1$插值是必需的。因此，不连续Galerkin公式为应变梯度相关模型的工程计算提供了重要的潜力。当使用具有低连续度的基函数时，在弱形式中并入的单元边缘处出现跳跃条件。除了制定本身，各种元素类型的方法的收敛性能的详细研究，进行了误差分析，该方法也被证明是在两个维度的工作。
英文摘要：
A discontinuous Galerkin method has been developed for strain gradient-dependent damage. The strength of this method lies in the fact that it allows the use of $C^0$ interpolation functions for continuum theories involving higher-order derivatives, while in a conventional framework at least $C^1$ interpolations are required. The discontinuous Galerkin formulation thereby offers significant potential for engineering computations with strain gradient-dependent models. When using basis functions with a low degree of continuity, jump conditions arise at element edges which are incorporated in the weak form. In addition to the formulation itself, a detailed study of the convergence properties of the method for various element types is presented, an error analysis is undertaken, and the method is also shown to work in two dimensions.
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