Mechanics of Time-Dependent Materials

, Volume 11, Issue 2, pp 127–142 | Cite as

Constitutive equations for orthotropic nonlinear viscoelastic behaviour using a generalized Maxwell model Application to wood material



This paper presents a nonlinear viscoelastic orthotropic constitutive equation applied to wood material. The proposed model takes into account mechanical and mechanosorptive creep via a 3D stress ratio and moisture change rate for a cylindrical orthotropic material. Orthotropic frame is based on the grain direction (L), radial (R) and hoop (T) directions, which are natural wood directions. Particular attention is taken to ensure the model to fulfill the necessary dissipation conditions. It is based on a rheological generalized Maxwell model with two elements in parallel in addition with a single linear spring taking into account the long term response. The proposed model is implemented in the finite element code ABAQUS/Standard® via a user subroutine UMAT and simple example is shown to demonstrate the capability of the proposed model. Future works would deal with damage and fracture prediction for wooden structures submitted to climate variations and mechanical loading.


Nonlinear viscoelastic constitutive law Mechanosorption Cylindrical orthotropy ABAQUS code 


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© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Laboratory of Solid and Contact Mechanics (LaMCoS) UMR 5259INSA de LyonVilleurbanne CedexFrance

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