Skip to content

active_contraction

Module: solid

Category: materialprop

Type string: "active_contraction"

Parameters

Name Description Default Units
ascl ascl 0 []
Tmax Tmax 1 []
ca0 ca0 1 []
camax camax 0 []
beta beta -6.27744e+66 []
l0 l0 -6.27744e+66 []
refl refl -6.27744e+66 []

Description

The default active contraction model is active_contraction. It is based on the formulation of Guccione et al. 1 and reviewed in the FEBio Theory Manual. The active stress is evaluated as \(T^{a}\mathbf{a}\otimes\mathbf{a}\), where \(\mathbf{a}\) is the unit vector along the fiber in the current configuration, and

\[ T^{a}=T_{\max}\frac{Ca_{0}^{2}}{Ca_{0}^{2}+ECa_{50}^{2}}C\left(t\right) \]

where

\[ ECa_{50}=\frac{\left(\text{Ca}_{0}\right)_{\max}}{\sqrt{\exp\left[\beta\left(\lambda\left(t\right)l_{r}-l_{0}\right)\right]-1}} \]

In this expression, \(\lambda\left(t\right)\) is the fiber stretch ratio at the current time. The activation curve \(C\left(t\right)\) is represented by the ascl property that takes an optional attribute, lc, which defines the load controller.

Example:

This example defines a transversely isotropic material with a Mooney-Rivlin basis. It defines a homogeneous fiber direction and uses the active fiber contraction feature.

<material id="3" type="trans iso Mooney-Rivlin">
  <c1>13.85</c1>
  <c2>0.0</c2>
  <c3>2.07</c3>
  <c4>61.44</c4>
  <c5>640.7</c5>
  <k>100.0</k>
  <lam_max>1.03</lam_max>
  <fiber type="vector">1,0,0</fiber>
  <active_contraction type="active_contraction">
    <ascl lc="1">1</ascl>
    <ca0>4.35</ca0>
    <beta>4.75</beta>
    <l0>1.58</l0>
    <refl>2.04</refl>
  </active_contraction>
</material>

  1. Guccione, J.M. and McCulloch, A.D., "Mechanics of active contraction in cardiac muscle: part I - constitutive relations for fiber stress that describe deactivation", J. Biomechanical Engineering vol. 115, no. 1 (1993), pp. 72-83. ↩