An extensometer-free version of the Extended Lumped Damage Mechanics for the failure analysis of anisotropic materials in geometrically nonlinear regime

This study presents an enhanced formulation of the Extended Lumped Damage Mechanics (XLDM) framework, which improves computational performance and extends its applicability to anisotropic materials. Traditionally, XLDM estimates strain fields through the elongation of numerical extensometers positioned between finite element nodes. Despite effective, this strategy introduces implementation complexity and computational burdens. In the present study, a novel extensometer-free approach is proposed, in which the damaged strain field has been directly derived from the current nodal configuration. This eliminates the need for trigonometric reconstruction of extensometer paths and significantly reduces computational cost, while preserving the mesh objectivity and predictive capability of XLDM. Furthermore, the formulation is extended to handle anisotropic media, incorporating directional stiffness degradation and failure evolution laws compatible with anisotropic behaviour—marking the first application of XLDM in this context. The framework is grounded in a position-based finite element method, where equilibrium is formulated directly in terms of nodal positions, naturally accounting for geometric nonlinearities. The proposed approach is implemented in an in-house Fortran code, and its performance is evaluated through three numerical applications, including compact tension, three-point bending, and orthotropic tensile failure with complex stress states. The results demonstrate the accuracy, robustness, and mesh independence of the proposed formulation, highlighting its potential for failure analysis in structures composed of anisotropic materials.