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3.15.1.3 Hill
The Hill discrete material defines the following parameters.
- Vmax: maximum shortening velocity
- ac: activation level
- Fmax: maximum force
- Ksh: shape parameter
- Lmax: relative length at which Fmax occurs.
- L0: initial reference length
- Sv: max velocity scale
- Ftl: normalized tension-length curve
- Ftv: normalized tension-velocity curve
The force in the Hill discrete element is the sum of the passive element and the active element.
The passive force is given by,
where l is the relative stretch defined by, and is the discrete element length and is either the L0 parameter, or the initial discrete element length (if L0 is set to zero).
The active force is given by,
Here, , a measure of the relative discrete element's growth speed, is defined by,
where is the actual discrete element's growth speed.
The properties Sv, Ftl, and Ftv, are optional and will evaluate to 1 if omitted. They can be defined as load curves. See the exampe below.
Example:
<discrete_material id="1" name="test" type="Hill">
<Vmax>1</Vmax>
<ac>0.1</ac>
<Fmax>50</Fmax>
<Ksh>5</Ksh>
<Lmax>1.5</Lmax>
<L0>10</L0>
<Ftl type="point">
<interpolate>smooth</interpolate>
<points>
<pt>0.0, 0</pt>
<pt>0.1, 0.000258139</pt>
<pt>0.2, 0.00161616</pt>
<pt>0.3, 0.00740118</pt>
<pt>0.4, 0.0272783</pt>
<pt>0.5, 0.0820396</pt>
<pt>0.6, 0.201851</pt>
<pt>0.7, 0.406524</pt>
<pt>0.8, 0.670275</pt>
<pt>0.9, 0.904792</pt>
<pt>1.0, 0.999955</pt>
<pt>1.1, 0.904792</pt>
<pt>1.2, 0.670275</pt>
<pt>1.3, 0.406524</pt>
<pt>1.4, 0.201851</pt>
<pt>1.5, 0.0820396</pt>
<pt>1.6, 0.0272783</pt>
<pt>1.7, 0.00740118</pt>
<pt>1.8, 0.00161616</pt>
<pt>1.9, 0.000258139</pt>
<pt>2.0, 0</pt>
</points>
</Ftl>
</discrete_material>