Plasticity-Damage Material Constitutive Model for Timber Subjected To Cyclic Loading

Abstract eng:
A plasticity-damage constitutive model for timber, which builds upon previous models developed for other quasi-brittle materials like concrete, is proposed in this article. Timber failure modes can be broadly defined as ductile failure due to compression stresses and brittle failure due to the combination of shear and tension stresses. This paper presents the formulation and implementation of a detailed and practical material constitutive model for timber subjected to cyclic loading, which can deal with both types of failure modes. Due to the anisotropic characteristics of timber, Hill’s expression was used as equivalent stress damage criterion for both compressive and shear-tensile failure. The damage evolution process starts once the failure criterion is reached, and is handled by two different monotonically increasing functions of the equivalent stresses for tension (exponential softening) and compression (perfect plasticity). The damage variables associated with these functions gradually reduce the timber stiffness material parameters (elastic moduli and shear moduli). The main advantage of incorporating a continuous damage model for timber is to capture the post-elastic stiffness degradation and thus enable an accurate prediction of experimental results. On the other hand, plasticity allows the incorporation of timber plastic flow in compression and its associated permanent deformations. This study discusses the theoretical framework and consistency of both models and presents the equations required for their coupling and implementation. Preliminary numerical results are presented for uniaxial cyclic loading in both directions, parallel and perpendicular to the grain. It is shown that tensile softening brittle failure, stiffness cyclic degradation and recovery after load-reversal, in addition to compressive permanent plastic deformation, are key characteristics of the non-linear behaviour of timber. These characteristics can be captured by the proposed constitutive model, which represents the first step towards a faithful estimation of the earthquake-induced collapse capacity of timber structures.

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