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.

表示非线性断裂力学中单调增加的状态变量的耗散应变能可用于开发弧长约束方程，用于跟踪能量耗散路径而不是结构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局裂纹元素方法（GCEM）的框架中实施该方法。借助于裂纹的开口和牵引力，即通过位移的跳跃和裂纹的两个表面之间的内聚力，来提取耗散的能量。弧长约束方程的刚度因子在求解过程中通过Sherman-Morrison公式获得。进行了几个数值测试。结果证明了该方法的鲁棒性。它捕获了全局和局部峰值载荷以及具有多个裂缝的受力结构的力-位移响应的所有折回部分。