Numerical Study
Based on the experiment phenomenon and the three-dimensional combined elastic-plastic and damage model established by Wang et al.[5],in this study,the effective stress was divided into a tensile and a compressive components by spectral factorization[9]:
where
is the effective stress tensor;
is the effective tensile(or compressive)stress tensor.
The elastic-plastic model was developed using the Hill's yielding criterion in Voigt's notation as:
where
is the Hill's strength parameters matrix;and
is the isotropic hardening equivalent ef fective tensile(compress)stress.
The variation of the tensile stif fness caused by compressive damage was assumed based on a new hardening rule:
where
is equivalent plastic tensile strain;and s1,s2,s3,s4 are shape parameters.
Based on the algorithm in Eq.(1)to Eq.(3),a three-dimensional model of the timber specimens was developed,and the loading protocol was considered to run the numerical analysis.The model and the simulation results(in comparison with the test results)are shown in Figure 4 and Figure 5,respectively.
Figure 4 The finite element model of the specimen
Figure 5 Stress-strain curves from experiment and model prediction
It was found that not only the irreversible deformation and the softening behavior of wood under compression in the parallel-to-grain direction could be traced by the model,but also the variation of tensile stiffness caused by compressive damage could be predicted by the model with acceptable accuracy.