This study presents the use of the dynamic particle difference method (PDM) to analyze tensile failure in concrete subjected to high loading rates. In general, strong form-based meshfree methods suffer from limitations pertaining to the material modeling of concrete because concrete exhibits both softening and damage behaviors that initiate crack growth under an impact load. These methods are generally based on the direct discretization of the governing equations, such as Navier's equation, which involves second-order differentiation. However, conventional material models are based on the first-order derivatives of displacement. The newly developed dynamic PDM can effectively address the limitations of material modeling using a combination of first-order derivative approximations. This circumvents the requirement for high-order derivative approximations, which are essential in strong formulations, such as the finite difference method and point collocation method. The strain rate effect caused by an extremely high loading speed was successfully modeled by accurately reflecting the energy dissipations that result from the cohesive property of the concrete and brittle cracking. Although the developed method incorporates the elastic constitutive relation, it enables the effective modeling of these nonlinear effects. In addition, it can reduce the computational effort. The proportional damping algorithm simulates the effect of velocity in the equation of motion and the cohesion effect in the concrete material. The damage model and the visibility criterion adequately handle crack initiation and propagation in the concrete member. Furthermore, it is noteworthy that the final discrete forms of the dynamic PDM are similar to the integrands of the weak form in the conventional finite element formulation. We ascertained that the stiffness and mass proportional damping effects are related to the inertia and strain of the material, respectively. It was confirmed that the location and direction of crack propagation in concrete varied with the strain rate. Hence, the accuracy and robustness of the proposed method were successfully verified by simulation, and the strain-rate dependency of concrete fracture was efficiently simulated using the proposed method.

这项研究提出了使用动态颗粒差异法（PDM）来分析高加载速率下混凝土的拉伸破坏。通常，基于强形式的无网格方法会遭受与混凝土材料建模有关的限制，因为混凝土会同时表现出软化和破坏行为，这些行为会在冲击载荷下引发裂纹扩展。这些方法通常基于控制方程的直接离散化，例如涉及二阶微分的Navier方程。但是，常规材料模型基于位移的一阶导数。新开发的动态PDM可以结合使用一阶导数近似来有效解决材料建模的局限性。这就避免了对高阶导数逼近的要求，这在强大的公式中必不可少，例如有限差分法和点配置法。通过精确反映混凝土内聚性和脆性开裂导致的能量耗散，成功地模拟了极高加载速度引起的应变率效应。尽管开发的方法结合了弹性本构关系，但它可以对这些非线性效应进行有效建模。另外，它可以减少计算量。比例阻尼算法模拟了运动方程中的速度效应和混凝土材料的内聚效应。损伤模型和可见性标准足以处理混凝土构件中的裂纹萌生和扩展。此外，值得注意的是，动态PDM的最终离散形式类似于常规有限元公式中的弱形式的整数。我们确定刚度和质量比例阻尼效应分别与材料的惯性和应变有关。可以确定，混凝土中裂纹扩展的位置和方向随应变率而变化。因此，通过仿真成功地验证了该方法的准确性和鲁棒性，并使用该方法有效地模拟了混凝土断裂的应变率依赖性。我们确定刚度和质量比例阻尼效应分别与材料的惯性和应变有关。可以确定，混凝土中裂纹扩展的位置和方向随应变率而变化。因此，通过仿真成功地验证了该方法的准确性和鲁棒性，并使用该方法有效地模拟了混凝土断裂的应变率依赖性。我们确定刚度和质量比例阻尼效应分别与材料的惯性和应变有关。可以确定，混凝土中裂纹扩展的位置和方向随应变率而变化。因此，通过仿真成功地验证了该方法的准确性和鲁棒性，并使用该方法有效地模拟了混凝土断裂的应变率依赖性。