tendon material

Module: solid

Category: material

Type string: "tendon material"

Parameters

Name	Description	Default	Units
density	density	1	[M/L^3]
k	bulk modulus	0	[P]
pressure_model	pressure_model	0	[]
g1	g1	0	[P]
g2	g2	0	[P]
l1	l1	0	[P]
l2	l2	0	[]
lam_max	lam_max	0	[]
fiber			[]

Description

The material type for the tendon material is tendon material. The tendon material is similar to the muscle material ¹ (also see muscle material). The only difference is the fiber function. For tendon material this is defined as:

\[ \lambda\frac{\partial F_{t}}{\partial\lambda}=\sigma\left(\lambda\right), \]

where

\[ \sigma\left(\lambda\right)=\begin{cases} 0 & \lambda\leqslant1\\ L_{1}\left(e^{L_{2}\left(\lambda-1\right)}-1\right) & 1<\lambda<\lambda^{\ast}\\ L_{3}\lambda+L_{4} & \lambda\geqslant\lambda^{\ast} \end{cases}\,. \]

The parameters \(L_{3}\) and \(L_{4}\) are determined by requiring \(C^{0}\) and \(C^{1}\) continuity at \(\lambda^{\ast}\).

The tendon fiber direction is specified similarly to the transversely isotropic Mooney-Rivlin model.

Example:

<material id="1" type="tendon material">
  <g1>5e4</g1>
  <g2>5e4</g2>
  <l1>2.7e6/l1>
  <l2>46.4</l2>
  <lambda>1.03</lambda>
  <k>1e7</k>
  <fiber type="vector">1,0,0</fiber>
</material>

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1. Blemker, SS, 3D Modeling of Complex Muscle Architecture and Geometry (2004). ↩