A computational framework for spruce failure: anisotropic plasticity with discrete cracking
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This work presents a finite-strain computational framework for modelling progressive failure in Norway spruce (Picea abies) under multiaxial loading conditions relevant to timber structures. The approach targets the characteristic interaction between ductile compressive property and quasi-brittle tensile/shear cracking that governs the macroscopic response and failure patterns of spruce. The constitutive response is described by an orthotropic, multi-surface, rate-independent plasticity model formulated in terms of logarithmic (Hencky) strain, enabling a small-strain-like additive structure while admitting large deformations, following Fleischhauer and Kaliske [1]. Brittle degradation is featured by an explicit node-splitting strategy that introduces displacement discontinuities, when the stress exceeds a stress-based criterion, suitable for wood. Crack-plane orientation is determined by the local stress state in the material coordinate system (L,R,T), and crack advancement is enforced quasi-statically by an inner crack-iteration loop that alternates between equilibrium iterations and limited split updates. Moreover, to suppress nonphysical patterns of dense, nearly-parallel cracks, a neighborhood-based propagation rule with parallel-crack prevention is employed following the cracking-node methodology of Song and Belytschko [2]. The constitutive parameters are identified by reproducing uniaxial reference tests [3]. The parameters controlling crack initiation/propagation and neighborhood-based updates are chosen case-wise and scaled to the mesh resolution and characteristic geometric length scales. The framework is assessed on three benchmark configurations: (i) uniaxial tension/compression and shear tests for material parameter identification, (ii) a Brazilian disc test to evaluate crack-path prediction under mixed stress states, and (iii) three-point bending test to validate the global force--displacement response and macroscopic crack evolution, where the interaction between wood specimen and loading pins is simulated using a displacement-driven contact approach [4]. The results indicate that the coupled plasticity--quasi-brittle failure formulation reproduces the experimental response trends and dominant crack patterns across the considered benchmarks, supporting predictive simulation of failure in contact-driven timber loading scenarios.
