Prev Section 4.16: Continuous Damage Up Section 4.16: Continuous Damage Subsection 4.16.2: Damage Fiber Exponential Next
4.16.1 Damage Fiber Power
The material type for Damage Fiber Power is “damage fiber power”. The following material parameters must be defined:
| <a1> | Parameter ( | [M] |
| <a2> | Parameter ( | [ ] |
| <kappa> | Parameter ( | [ ] |
The strain energy is assumed to be of the following form,
,
where the modified internal energy function with the scalar damage variable (defined in section 4.16↑). is the arbitrary convex and monotonically increasing function, whose first derivative is zero in the origin. Possible functions of are given by
, , , ,
( ),
where denotes the direction of the fibers.
The subtraction of ensures the stress-free reference configuration for the undamaged case is satisfied, is the value of the function in the natural state and is given by
= for
By setting,
and the strain-energy form above can be made suitable for modeling damage,
.
The fifth invariant is not polyconvex, therefore alternative polyconvex invariant functions are defined as
,
,
.
The Cauchy stress takes on the following form,
.
Example:
<solid type="damage fiber power">
<a1>1400</a1>
<a2>2.2</a2>
<kappa>1e-08</kappa>
<t0>0.98</t0>
<Dmax>0.96</Dmax>
<beta_s>0.06</beta_s>
<gamma_max>17.98</gamma_max>
<fiber type="angles">
<theta>-39.87</theta>
<phi>90</phi>
</fiber>
</solid>