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Section 4.16: Continuous Damage Up Section 4.16: Continuous Damage Subsection 4.16.2: Damage Fiber Exponential

### 4.16.1 Damage Fiber Power

The material type for Damage Fiber Power is “damage fiber power”. The following material parameters must be defined:
 Parameter ( [M] Parameter ( [ ] 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>

Section 4.16: Continuous Damage Up Section 4.16: Continuous Damage Subsection 4.16.2: Damage Fiber Exponential