Tessellated Isotropic Elastic Lattice Spring Model for Quasi-Brittle Fracture

Abstract

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.