The Failure Prediction of Reinforced Composite Quasi-Brittle Structures by an Improved Version of the Extended Lumped Damage Approach

This study presents an improved version of the Extended Lumped Damage Mechanics (XLDM) formulation within a position-based approach of the Finite Element Method (FEM). In the XLDM, the strain field has been assessed from the elongations of numerical extensometers, which connect the finite element nodes. In addition, localisation bands positioned along the elements' boundaries depict the mechanical effects of material degradation. The position-based approach of FEM enables the accurate modelling of geometrically non-linear effects and its computational implementation is straightforward. In this approach, the equilibrium configuration has been evaluated in relation to the nodal positions instead of its displacements. Thus, one improvement proposed herein involves the coupling of the XLDM failure predictions within an exact geometrically non-linear framework. Besides, in this study, the XLDM has been further improved by incorporating the damage growth caused by compressive stresses. The non-linear formulation proposed herein enables the presence of reinforcements, which have been added by an embedded scheme and lead to another improvement in the XLDM context. Three applications demonstrate the accuracy of the proposed non-linear scheme, in which the numerical responses obtained by the proposed improved formulation have been compared to experimental results available in the literature.