Develop an efficient volumetric-constraint decomposition for arbitrary regular polygons

Develop and validate a decomposition of the additional volumetric constraint into axial, tangential, and rotational springs that is applicable to arbitrary regular polygonal IELSM elements and reduces element-assembly cost.

Background

The additional volumetric constraint in IELSM is assembled directly as an element stiffness contribution. In earlier work, the authors decomposed this constraint into axial, tangential, and rotational springs, which reduced computational cost. The present paper does not derive a corresponding formulation for arbitrary regular polygons because the derivation is cumbersome, leaving the general decomposition unresolved.

References

Such a decomposition is not adopted in the present study for two reasons. First, the assembly of the global stiffness matrix has only a minor influence on the total computational time of the present simulations. Second, deriving a decomposition strategy applicable to arbitrary regular polygonal elements is relatively cumbersome. Therefore, this decomposition is left for future work.

— Tessellated Isotropic Elastic Lattice Spring Model for Quasi-Brittle Fracture  (2609.28970 - Li et al., 24 Sep 2026) in Section 3.2, Hybrid Assembly Strategy for IELSM and Finite Elements