Quantitatively compare damage-variable definitions

Quantitatively compare node-based, element-based, and spring-based definitions of the damage variable in IELSM coupled with isotropic damage models, including their computational cost, localization behavior, mesh sensitivity, and compatibility with finite-element coupling.

Background

The paper adopts a node-based damage variable and notes that alternative formulations could define damage on regular polygonal elements or individual springs. These alternatives involve different trade-offs: node-based damage offers strong localization and continuity but higher computational cost, element-based damage is cheaper but more mesh-sensitive and discontinuous, and spring-based damage has a direct physical interpretation but creates compatibility difficulties when coupled with finite elements. Their relative performance is not quantitatively established.