TimberPD

Timber Plastic-Damage Model

References

1. Constitutive Modelling Cookbook

2. 10.1016/j.compstruc.2017.09.010

Syntax

material TimberPD (1) (2...7) (8...10) (11...19) (20) (21) (22) (23) (24) (25) (26) [27]
# (1) int, unique material tag
# (2...7) double, six moduli: E_{xx}, E_{yy}, E_{zz}, E_{xy}, E_{yz}, E_{zx}
# (8...10) double, three poissions ratios: v_{xy}, v_{yz}, v_{zx}
# (11...19) double, nine yield stress
# (20) double, h
# (21) double, r_t^0
# (22) double, b_t
# (23) double, m_t
# (24) double, r_c^0
# (25) double, b_c
# (26) double, m_c
# [27] double, density, default: 0.0

Remarks

1. The yield stress shall be arranged in the following order: $\sigma_{11}^t$, $\sigma_{11}^c$, $\sigma_{22}^t$, $\sigma_{22}^c$, $\sigma_{33}^t$, $\sigma_{33}^c$, $\sigma_{12}^0$, $\sigma_{23}^0$, $\sigma_{13}^0$.

2. The original paper documents a comprehensive procedure to determine hardening parameter $h$.

Damage

The damage evolutions are identical to the original formulation but with different notations.

The final stress $\sigma$ is calculated as

$$\sigma=\left(1-\omega_t\right)\bar{\sigma}_t+\left(1-\omega_c\right)\bar{\sigma}_c$$

Tension Damage Evolution

$$\omega_t=1-\dfrac{r_t^0}{r_t}\left(1-b_t+b_t\exp\left(m_t\left(r_t^0-r_t\right)\right)\right)$$

Compression Damage Evolution

$$\omega_c=b_c\left(1-\dfrac{r_c^0}{r_c}\right)^{m_c}$$

View and edit parameters to see how they affect the damage evolution.