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Cracking elements method with a dissipation-based arc-length approach

机译：用耗散的弧长方法开裂元素方法

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摘要

The dissipated strain energy, representing a monotonically increasing state variable in nonlinear fracture mechanics, can be used to develop an arc-length constraint equation for tracking the energy dissipation path instead of the elastic unloading path of the response of a structure. This was the motivation for the development of a dissipation-based arc-length method, followed by its implementation in the framework of the recently proposed Global Cracking Elements Method (GCEM). The dissipated energy is extracted with the help of the crack openings and tractions, i.e. by means of the displacement jumps and the cohesive forces between the two surfaces of a crack. The stiffness factor of the arc-length constraint equation is obtained in the solution process by means of the Sherman-Morrison formula. Several numerical tests are performed. The results demonstrate the robustness of the proposed method. It captures both global and local peak loads and all snap-back parts of the force-displacement responses of loaded structures with multiple cracks.
机译：代表非线性断裂力学中的单调增加状态变量的耗散应变能量可用于开发用于跟踪能量耗散路径的弧长约束方程，而不是结构的响应的弹性卸载路径。这是开发基于耗散的弧长方法的动机，然后在最近提出的全球开裂元素方法（GCEM）的框架中实现。在裂缝开口和牵引力的帮助下，即借助于位移跳跃和裂缝的两个表面之间的粘性力来提取散热能量。通过Sherman-Morrison公式在解决方案过程中获得弧长约束方程的刚度因子。执行几个数值测试。结果证明了该方法的稳健性。它捕获了具有多个裂缝的加载结构的力 - 位移响应的全局和局部峰值载荷和所有动力排量响应。

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