# *MAT_156 (MUSCLE)

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

## Format

(1) (2) (3) (4) (5) (6) (7) (8)
*MAT_156 or *MAT_MUSCLE
mat_ID ${\rho }_{i}$ SR_MAX STS_MAX STR CER DAMP
FUNCT_1 FUNCT_2 FUNCT_3 FUNCT_4

## Definition

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer)

${\rho }_{i}$ Initial density .

(Real)

$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$
SR_MAX Maximum strain rate.

(Real)

$\left[\frac{\text{1}}{\text{s}}\right]$
STS_MAX Maximum stress.

$\left[\text{Pa}\right]$
STR Strain at maximum stress.

(Real)

CER Strain scale factor in analytical exponential formula for FUNCT_4 = 0.

(Real)

DAMP Damping coefficient.

(Real)

$\left[\text{Pa}\cdot \text{s}\right]$
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)

1. This keyword maps to /PROP/TYPE46 (SPR_MUSCLE).
2. This keyword is used only with truss elements. Truss area input is mandatory.
3. Total stress in the element is computed as:
$\sigma ={\sigma }_{1}+{\sigma }_{2}+{\sigma }_{3}$
Where,
${\sigma }_{1}=STS_MAX\cdot FUNCT_1\left(t\right)\cdot FUNCT_2\left(\text{Δ}l\right)\cdot FUNCT_3\left(\stackrel{˙}{\overline{\epsilon }}\right)$
Contractile stress
${\sigma }_{2}=STS_MAX\cdot FUNCT_4\left(\text{Δ}l\right)$
Passive stress
${\sigma }_{3}=DMP\cdot \text{Δ}l\cdot \stackrel{˙}{\epsilon }$
Damping stress

With $\text{Δ}l=\frac{{l}_{current}}{{l}_{origin}}$ , $\epsilon =\text{Δ}l-1$ , $\stackrel{˙}{\epsilon }=\frac{\text{Δ}\epsilon }{\text{Δ}t}$ and $\stackrel{˙}{\overline{\epsilon }}=\frac{\text{Δ}l\cdot \stackrel{˙}{\epsilon }}{SR_MAX}$ .

4. If FUNCT_4 = 0, the passive stress factor is defined with:
If $\text{Δ}l<1$
$FUNCT_4\left(\text{Δ}l\right)=0$
If $\text{Δ}l\ge 1$ and $CER\ne 0$
$FUNCT_4\left(\text{Δ}l\right)=\frac{1}{\mathrm{exp}\left(CER\right)-1}\left[\mathrm{exp}\left(\frac{CER\cdot \epsilon }{STR}\right)-1\right]$
If $\text{Δ}l\ge 1$ and $CER=0$
$FUNCT_4\left(\text{Δ}l\right)=\frac{\epsilon }{STR}$
5. 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.