The lattice discrete particle model (LDPM) has been proven to be one of the most appealing computational tools to simulate fracture in quasi-brittle materials. Despite tremendous advancements in the definition and implementation of the method, solution strategies are still limited to dynamic algorithms, resulting in prohibitive computational costs and challenges related to solution accuracy for quasi-static conditions. This study presents a novel static solver for LDPM, introducing fundamental innovation: (1) LDPM constitutive laws are modified to provide continuous response through all possible strain/stress states; (2) an adaptive arc-length method is proposed in combination with a criterion to select the sign of the iterative load factor; (3) an adaptive limit-unloading–reloading path switch algorithm is proposed to restrict oscillations in the global stiffness matrix. Extensive validation of the proposed approach is presented. Numerical results demonstrate that the static solver exhibits satisfactory convergence rates, significantly outperforming available dynamic solutions in computational efficiency.

中文翻译：

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晶格离散粒子模型的高效静态求解器


晶格离散粒子模型（LDPM）已被证明是模拟准脆性材料断裂最有吸引力的计算工具之一。尽管该方法的定义和实现取得了巨大进步，但求解策略仍然仅限于动态算法，导致计算成本过高，并且在准静态条件下求解精度面临挑战。本研究提出了一种新颖的 LDPM 静态求解器，引入了根本性创新：（1）修改 LDPM 本构定律，以在所有可能的应变/应力状态下提供连续响应； (2)结合迭代载荷因子符号选择准则，提出了自适应弧长法； (3)提出了一种自适应限制卸载-重载路径切换算法来限制全局刚度矩阵的振荡。对所提出的方法进行了广泛的验证。数值结果表明，静态求解器具有令人满意的收敛速度，在计算效率方面明显优于可用的动态解。