发表机构
Wuhan University of Technology（武汉理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对准脆性断裂模拟的精度-效率-简洁性权衡，提出镶嵌各向同性弹性弹簧格子模型（IELSM），通过理论判据确定单元可容许性，并利用节点共享与有限元耦合，在保持精度的同时大幅降低计算成本。
AI 中文摘要
准脆性断裂普遍存在于混凝土、岩石、陶瓷、复合材料及砌体结构中，其模拟面临精度、效率与简洁性之间的权衡。经典弹簧格子模型（LSM）通过键断裂捕捉开裂而无需重新网格化，但其单元具有经验性，且仅限于少数具有固定泊松比的可镶嵌形状。我们提出了一种镶嵌各向同性弹性弹簧格子模型（IELSM），将连续体离散为带有轴向弹簧和体积约束的多边形单元，在任意多边形镶嵌上实现各向同性弹性。宏观各向同性可归结为控制方程，其可解性为单元可容许性提供了理论判据，证明了传统可镶嵌单元并推广至任意正N边形和凹形单元。利用与有限元边界插值的兼容性，IELSM通过直接节点共享进行组装，无需界面单元或运动学约束。与各向同性损伤模型耦合后，纯弯曲试验和四个断裂基准测试表明，该耦合保持了位移精度，得到的裂纹路径和荷载-位移曲线与实验一致且优于标准有限元法，并且对网格细化不敏感。IELSM也可仅限制在易损伤区域，其余部分通过节点共享由有限元建模。对于基准测试，与全域IELSM相比，这使节点减少41.2%-80.9%，CPU时间减少34.2%-85.2%。该框架将IELSM单元构建从经验试错推进到理论确定，并将耦合简化为节点共享，为复杂准脆性断裂分析提供了一条均衡的路径。
英文摘要
Quasi-brittle fracture is prevalent in concrete, rock, ceramics, composites, and masonry, and its simulation faces a trade-off among accuracy, efficiency, and simplicity. The classical Lattice Spring Model (LSM) captures cracking via bond breakage without remeshing, but its elements are empirical and limited to a few tessellable shapes with fixed Poisson's ratios. We propose a tessellated Isotropic Elastic Lattice Spring Model (IELSM) that discretizes continua into polygonal elements with axial springs and a volumetric constraint, achieving isotropic elasticity on arbitrary polygonal tessellations. Macroscopic isotropy reduces to governing equations whose solvability gives a theoretical criterion for element admissibility, proving conventional tessellable elements and extending to arbitrary regular N-gons and concave elements. Exploiting boundary interpolation compatibility with finite elements, IELSM is assembled by direct node sharing, without interface elements or kinematic constraints. Coupled with an isotropic damage model, a pure bending test and four fracture benchmarks show that the coupling preserves displacement accuracy, yields crack paths and load-displacement curves agreeing with experiments and outperforming standard FEM, and is insensitive to mesh refinement. IELSM can also be restricted to damage-prone regions, with the remainder modeled by finite elements via node sharing. For the benchmarks, this reduces nodes by 41.2-80.9% and CPU time by 34.2-85.2% versus full-domain IELSM. The framework advances IELSM element construction from empirical trial and error to theoretical determination and simplifies coupling to node sharing, offering a balanced route for complex quasi-brittle fracture analysis.
