Using Galerkin Finite Volume method, a 2D adaptive algorithm is developed for crack propagation simulation of concrete structures under mixed mode loading. The matrix free Finite Volume formulation is applied to implement a crack propagation model in a fully automatic adaptive mesh refinement framework for unstructured meshes. Cohesive cracks are implemented using nonlinear interface elements with bilinear softening constitutive equation. On contrary to existing cohesive crack models where the Newton-Raphson techniques are required to simulate the nonlinear behavior in the fracture process zone, the need for such a computational costly technique is relaxed. The matrix-free Finite Volume formulation method can provide better computational performance than the matrix-base methods. The introduced Method can also relax the problems of the standard Finite Element base methods with high aspect-ratio elements. The present Finite Volume model accurately predicts the crack propagation path and correctly evaluates the load-displacement curve while consumes low computational CPU time.

使用伽辽金有限体积法，开发了一种二维自适应算法，用于混凝土结构在混合模式载荷下的裂纹扩展模拟。无矩阵有限体积公式用于在非结构化网格的全自动自适应网格细化框架中实现裂纹扩展模型。使用具有双线性软化本构方程的非线性界面单元来实现内聚裂纹。与需要 Newton-Raphson 技术来模拟断裂过程区中的非线性行为的现有内聚裂纹模型相反，对这种计算成本高的技术​​的需求有所缓解。与基于矩阵的方法相比，无矩阵的有限体积公式方法可以提供更好的计算性能。引入的方法还可以缓解具有高纵横比元素的标准有限元基方法的问题。目前的有限体积模型准确预测裂纹扩展路径并正确评估载荷-位移曲线，同时消耗较低的计算 CPU 时间。