BilinearCC

Bilinear Hardening Modified Cam-Clay Model

Theory

This model defines a bilinear hardening rule for $a(\alpha)$, which is a non-negative function.

$$a(\alpha)=a_0+H\alpha\ge0,$$

in which $H$ is the hardening modulus, note $\alpha=\varepsilon_p=\varepsilon_1+\varepsilon_2+\varepsilon_3$ is the volumetric plastic strain.

The hardening modulus could be either positive or negative.

This hardening rule does not imply any physical soil behavior.

Syntax

material BilinearCC (1) (2) (3) (4) (5) (6) (7) (8) [9]
# (1) int, unique material tag
# (2) double, elastic modulus
# (3) double, poissons ratio
# (4) double, beta, controls compression side shape
# (5) double, m, slope of CSL
# (6) double, p_t, initial tension strength
# (7) double, a_0, initial a_0
# (8) double, H, slope of hardening function
# [9] double, density, default: 0.0

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

young_modulus = 1e5
yield_stress = 100.0
hardening_ratio = 0.05

with ErrorMap(
    f"material BilinearCC 1 {young_modulus} .4 .8 .8 {0.2 * yield_stress} {yield_stress} {hardening_ratio * young_modulus}",
    ref_strain=yield_stress / young_modulus,
    ref_stress=yield_stress,
    contour_samples=20,
) as error_map:
    error_map.contour("cam.clay.uniaxial", center=(-2, 0), size=1)
    error_map.contour("cam.clay.biaxial", center=(-2, -2), size=1)

absolute error uniaxial

absolute error biaxial