aniso_damage#

Description#

This model implements an anisotropic damage model for fibrous ceramic composites 1the model is coded in Aniso_damage.z in the source dir zZfrontBehavior. The damage is described by a number of scalar and tensorial variables as input by the user. The effect of closure strains and non-symmetric tension-compression behavior is handled as well.

The stress is calculated using the following definition of effective modulus:

(258)#\[\ten \sigma = \tenf C_0:\ten \varepsilon - \sum\tenf{C}^{eff}:(\ten \varepsilon - \ten \varepsilon_c)\]

where \(\tenf C_0\) is the undamaged elasticity tensor, \(\tenf C^{eff}\) is the damage modification of the elasticity, and \(\ten \varepsilon_c\) is a user loadable closure strain. Each scalar and tensorial variable will contribute a term to the summation of \(\tenf C^{eff}\).

Syntax#

***behavior aniso_damage [ modifier ] \(~\,\) **C0 <ELASTICITY> \(~\,\) [ **thermal_strain <THERMAL_STRAIN>] \(~\,\) [ **damage <ANISOTROPIC_DAMAGE> ] \(~\,\) [ **closure ] \(~\,~\,\) [ t1  …  t6 ] \(~\,\) [ **scalar_interaction (full | identity) ]

Stored Variables

prefix

size

description

default

eto

T-2

strain tensor

yes

sig

T-2

Cauchy stress

yes

d(i)

S

scalar damage variables

yes

D

T-2

tensor damage variable

yes

Example#

The following example shows the input format for a material with two scalar variables:

***behavior aniso_damage
  **closure 1.e-3 1.e-3 1.e-3  .5e-3 .5e-3 .5e-3   % 11 22 33 12 23 31
  **c0 orthotropic
    c11       2.5662e11
    c22       2.5662e11
    c33       2.6887e11
    c12       6.0439e10
    c13       8.2435e10
    c23       8.2435e10
    c44       8.5e9
    c55       8.5e9
    c66       8.5e9

  **damage scalar
    *eta 1.0
    *n         (1. 0. 0.)
    *K_coeffs  1. 0. 0. 0. 0. 0. 0.7 0.0 0.7
    *g g1
       Y0        1.69e4
       Yc        1.6e5
       delta_c   0.6
  **damage scalar
    *n         (0. 1. 0.)
    *K_coeffs  0. 1. 0. 0. 0. 0. 0.7 0.7 0.0
    *g g1
        delta_c 0.6
        Y0 1.69e4
        Yc 1.6e5
  **damage scalar
    *n         (0. 0. 1.)
    *K_coeffs  0. 0. 1. 0. 0. 0. 0.0 0.7 0.7
    *g g1
        delta_c   0.6
        Y0        1.69e4
        Yc        1.6e5

  **damage  elastic_tensorial
    *Q  diagonal   Q1  1.0
    *Qd diagonal   Qd1 1.0
    *K_coeffs     1. 1. 1. 0.7 0.7 0.7 0.5 0.5 0.5
    *g g1
        delta_c   0.6
        Y0        0.0
        Yc        1.6e5
***return