*MAT_156 (MUSCLE)

LS-DYNA Input Interface KeywordDefines a muscle model for safety applications. Used only with truss elements.

Format

Field	Contents	SI Unit Example
`mat_ID`	Material identifier. (Integer)
$ρ_{i}$	Initial density . (Real)	$[\frac{kg}{m^{3}}]$
`SR_MAX`	Maximum strain rate. (Real)	$[\frac{1}{s}]$
`STS_MAX`	Maximum stress.	$[Pa]$
`STR`	Strain at maximum stress. (Real)
`CER`	Strain scale factor in analytical exponential formula for `FUNCT_4` = 0. (Real)
`DAMP`	Damping coefficient. (Real)	$[Pa \cdot s]$
`FUNCT_1`	Activation stress factor versus time. < 0 Curve identifier of activation level versus time. > 0 Constant value used as activation level. (Real)
`FUNCT_2`	Active stress factor as function of strain. < 0 Curve identifier. > 0 Constant value of 1.0 is used. (Real)
`FUNCT_3`	Active stress factor as function of strain rate. < 0 Curve identifier. > 0 Constant value of 1.0 is used. (Integer)
`FUNCT_4`	Stress factor as function of strain for parallel elastic element. < 0 Curve identifier. = 0 Analytical equation is used. 4 > 0 Constant value of 1.0 is used. (Integer)

This keyword maps to /PROP/TYPE46 (SPR_MUSCLE).
This keyword is used only with truss elements. Truss area input is mandatory.
Total stress in the element is computed as:(1)
$σ = σ_{1} + σ_{2} + σ_{3}$

Where,

$σ_{1} = S T S_M A X \cdot F U N C T_1 (t) \cdot F U N C T_2 (Δ l) \cdot F U N C T_3 (\dot{\bar{ε}})$

Contractile stress

$σ_{2} = S T S_M A X \cdot F U N C T_4 (Δ l)$

Passive stress

$σ_{3} = D M P \cdot Δ l \cdot \dot{ε}$

Damping stress

With $Δ l = \frac{l_{c u r r e n t}}{l_{o r i g i n}}$ , $ε = Δ l - 1$ , $\dot{ε} = \frac{Δ ε}{Δ t}$ and $\dot{\bar{ε}} = \frac{Δ l \cdot \dot{ε}}{S R_M A X}$ .
If FUNCT_4 = 0, the passive stress factor is defined with:

If $Δ l < 1$

$F U N C T_4 (Δ l) = 0$

If $Δ l \geq 1$ and $C E R \neq 0$

$F U N C T_4 (Δ l) = \frac{1}{\exp (C E R) - 1} [\exp (\frac{C E R \cdot ε}{S T R}) - 1]$

If $Δ l \geq 1$ and $C E R = 0$

$F U N C T_4 (Δ l) = \frac{ε}{S T R}$
The option “_TITLE” can be added to the end of this keyword. When “_TITLE” is included, an extra 80 characters long line is added after the keyword input line which allows an entity title to be defined.