A three-dimensional plasticity-damage constitutive model for timber under cyclic loads

Abstract

The performance of timber structures is governed by the nonlinear response at their connections, where high deformation levels and stress concentrations are developed, particularly when subjected to load reversals. To date, no constitutive model for wood under cyclic load exists which is able to incorporate its most important failure modes while considering plastic deformations and cyclic sti↵ness and strength degradation simultaneously. This paper presents the formulation and implementation of a plasticitydamage model with these characteristics within a continuum mechanics approach. The theoretical framework of both plasticity and damage models is described, and a detailed derivation of the constitutive equations required for their computational implementation and coupling as well as the return mapping and iterative algorithms for their integration are presented. The damage evolution process is handled by two independent scalar variables for tension and compression. A general orthotropic plasticity yield surface with isotropic hardening is employed to incorporate timber plastic flow in compression. A closed-form expression for the plasticity-damage consistent tangent operator is derived. It is demonstrated that the proposed constitutive model captures all the key characteristics required for an accurate modelling of timber under large deformation levels until failure.

Degradation of Mechanical Properties of Pine Wood Under Symmetric Axial Cyclic Loading Parallel to Grain

“…Degradation of mechanical properties of wood samples subjected to symmetrical cyclic stresses accompanied by microstructure degradation of wood. If the structural damage in tension does not affect the stiffness degradation or the strength of the wood when a reversed load is applied in compression (stiffness recovery) as was shown in Figure 4 , in contrary, the constitutive damage does reduce the tensile capacity of the material when a reverse loading from compression to tension is applied as Sirumbal-Zapata et al [ 27 ] demonstrate in their study. In Figure 10 b–d, all effects of mechanical phenomena as tensile softening brittle failure, stiffness cyclic degradation, and recovery after load-reversal, as well as compressive permanent plastic deformation due to ductile failure can be observed at microscopic levels.…”

“…At compression parallel to the fibers, the structural changes begin with the increase of the stress level, and the instability of the fibers is observed by the appearance of some macroscopic kinks [ 6 , 21 , 25 ]. The yielding of a material represents the transition from the initial state of a volume element from an elastic material to a different and irreversible state [ 12 , 26 , 27 ]. In the case of the specimen made of material with predominantly ductile behavior that is subjected to traction, the rupture occurs in successive stages ( Figure 10 ): The peripheral areas yield under the action of tangential stresses, and the central area yields under the action of normal stresses.…”

Experimental assessment and damage modelling of hybrid timber beam-to-steel column connections under cyclic loads

“…Nevertheless, the load and sti↵ness of the laminated veneer lumber (LVL) specimens was slightly overestimated. More recently, Sirumbal-Zapata et al [27] developed a 3D model coupling orthotropic plasticity in compression with isotropic damage in both tension and compression stress states. The model was able to reproduce the response of timber-to-steel connections subjected to load reversals.…”

“…This section introduces the numerical strategies followed to model the test specimens described above. The DIANA FE software [41] incorporating a purposely defined damage-plasticity model [27,42] is employed. First, the wood plasticity-damage constitutive model is employed.…”

“…However, there is a lack of three-dimensional wood constitutive models aimed at reporducing the nonlinear cyclic response of timber dowelled connections. The constitutive model employed in this paper was developed by Sirumbal et al [27] and consists on a plasticity-damage model able to simulate the complex behaviour of wood under three-dimensional stress conditions, within a continuum mechanics approach and with a good level of precision for a natural material such as wood. This model is based on the most relevant characteristics of timber inelastic behaviour when subjected to reversed cyclic loading, allowing to monitor the evolution of damage, to identify potential rupture zones through a smeared continuous approach, and to reproduce the di↵erent inelastic responses of wood in tension and compression.…”