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}, G_{xy}, G_{yz}, G_{zx}
# (8...10) double, three poissions ratios: v_{xy}, v_{yz}, v_{xz}
# (11...19) double, nine yield stress
# (20) double, h
# (21) double, r_t^0
# (22) double, b_t, [0,1]
# (23) double, m_t
# (24) double, r_c^0
# (25) double, b_c, [0,1]
# (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

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

The parameter $b_t$ will be clamped to $0\leq{}b_t\leq1$.

Compression Damage Evolution

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

The parameter $b_c$ will be clamped to $0\leq{}b_c\leq1$.

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

Recording

This model supports the following additional history variables to be recorded.

variable label	physical meaning
DT	tensile damage
DC	compressive damage

Iso-error Map

The following example iso-error maps are obtained via the following script.

from plugins import ErrorMap
# note: the dependency `ErrorMap` can be found in the following link
# https://github.com/TLCFEM/suanPan-manual/blob/dev/plugins/scripts/ErrorMap.py

with ErrorMap(
    """material TimberPD 1 \
9936 345 345 690 125.9 690 \
.41 .37 .41 \
20 40 2 4 2 4 4 4 4 \
12.9 \
1 .98 .3 \
1 .95 2""",
    ref_strain=1e-2,
    ref_stress=5,
    contour_samples=30,
) as error_map:
    error_map.contour("timberpd.uniaxial", center=(-2, 0), size=2, type={"rel", "abs"})
    error_map.contour("timberpd.biaxial", center=(-2, -2), size=2, type={"rel", "abs"})

absolute error uniaxial

absolute error biaxial

relative error uniaxial

relative error biaxial