Models for the description of different biologial soft tissues. More...

Files
file	adiposeTissue_SommerHolzapfel.hh
	Model for adipose tissue of Sommer et al.: Multiaxial mechanical properties and constitutive modeling of human adipose tissue: A basis for preoperative simulations in plastic and reconstructive surgery. Acta Biomater., 9:9036-9048, 2013.

file	muscleTissue_Martins.hh
	Versions of the muscle model of Martins et al.: A numerical model of passive and active bahevaior of skeletal muscles. Comp. Meth. Appl. Mech. Eng. 151:419-433, 1998.

file	skinTissue_Hendriks.hh
	Versions of the skin model of Hendriks: Mechanical behavior of human epidermal and dermal layers in vivo. PhD thesis, Technische Universiteit Eindhoven, 2005.

Functions
template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	RFFGen::incompressibleAdiposeTissue_SommerHolzapfel (double cCells, double k1, double k2, double kappa, const Matrix &M, const Matrix &F)
	Model for adipose tissue of Sommer et al.: Multiaxial mechanical properties and constitutive modeling of human adipose tissue: A basis for preoperative simulations in plastic and reconstructive surgery. Acta Biomater., 9:9036-9048, 2013. More...

template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	RFFGen::incompressibleAdiposeTissue_SommerHolzapfel (const Matrix &M, const Matrix &F)
	Model for adipose tissue of Sommer et al.: Multiaxial mechanical properties and constitutive modeling of human adipose tissue: A basis for preoperative simulations in plastic and reconstructive surgery. Acta Biomater., 9:9036-9048, 2013. More...

template<class Inflation , class Compression , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	RFFGen::compressibleAdiposeTissue_SommerHolzapfel (double cCells, double k1, double k2, double kappa, double d0, double d1, const Matrix &M, const Matrix &F)
	Compressible version of the model for adipose tissue of Sommer et al.: Multiaxial mechanical properties and constitutive modeling of human adipose tissue: A basis for preoperative simulations in plastic and reconstructive surgery. Acta Biomater., 9:9036-9048, 2013. More...

template<class Inflation , class Compression , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	RFFGen::compressibleAdiposeTissue_SommerHolzapfel (double d0, double d1, const Matrix &M, const Matrix &F)
	Compressible version of the model for adipose tissue of Sommer et al.: Multiaxial mechanical properties and constitutive modeling of human adipose tissue: A basis for preoperative simulations in plastic and reconstructive surgery. Acta Biomater., 9:9036-9048, 2013. Material parameters are taken from the same publication, Table 2, i.e. $c_\mathrm{Cells}=0.15 (\,\mathrm{kPa})$ , $k_1=0.8 (\,\mathrm{kPa})$ , and $\kappa=0.09$ . More...

template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	RFFGen::incompressibleMuscleTissue_Martins (double c, double b, double A, double a, const Matrix &M, const Matrix &F)
	Incompressible version of the model for muscle tissue of Martins et al.: A numerical model of passive and active bahevaior of skeletal muscles. Comp. Meth. Appl. Mech. Eng. 151:419-433, 1998. More...

template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	RFFGen::incompressibleMuscleTissue_Martins (const Matrix &M, const Matrix &F)
	Incompressible version of the model for muscle tissue of Martins et al.: A numerical model of passive and active bahevaior of skeletal muscles. Comp. Meth. Appl. Mech. Eng. 151:419-433, 1998. More...

template<class Inflation , class Compression , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	RFFGen::compressibleMuscleTissue_Martins (double c, double b, double A, double a, double d0, double d1, const Matrix &M, const Matrix &F)
	Compressible version of the model for muscle tissue of Martins et al.: A numerical model of passive and active bahevaior of skeletal muscles. Comp. Meth. Appl. Mech. Eng. 151:419-433, 1998. More...

template<class Inflation , class Compression , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	RFFGen::compressibleMuscleTissue_Martins (double d0, double d1, const Matrix &M, const Matrix &F)
	Compressible version of the model for muscle tissue of Martins et al.: A numerical model of passive and active bahevaior of skeletal muscles. Comp. Meth. Appl. Mech. Eng. 151:419-433, 1998. More...

template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	RFFGen::incompressibleSkin_Hendriks (double c0, double c1, const Matrix &F)
	Model for skin tissue of Hendriks: Mechanical behavior of human epidermal and dermal layers in vivo. PhD thesis, Technische Universiteit Eindhoven, 2005. More...

template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	RFFGen::incompressibleSkin_Hendriks (const Matrix &F)
	Model for skin tissue of Hendriks: Mechanical behavior of human epidermal and dermal layers in vivo. PhD thesis, Technische Universiteit Eindhoven, 2005. More...

template<class InflationPenalty , class CompressionPenalty , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	RFFGen::compressibleSkin_Hendriks (double c0, double c1, double d0, double d1, const Matrix &F)
	Compressible version of the model for skin tissue of Hendriks: Mechanical behavior of human epidermal and dermal layers in vivo. PhD thesis, Technische Universiteit Eindhoven, 2005. More...

template<class InflationPenalty , class CompressionPenalty , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	RFFGen::compressibleSkin_Hendriks (double d0, double d1, const Matrix &F)
	Compressible version of the model for skin tissue of Hendriks: Mechanical behavior of human epidermal and dermal layers in vivo. PhD thesis, Technische Universiteit Eindhoven, 2005. More...

Detailed Description

Models for the description of different biologial soft tissues.

Function Documentation

template<class Inflation , class Compression , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>

auto RFFGen::compressibleAdiposeTissue_SommerHolzapfel	(	double	cCells,
		double	k1,
		double	k2,
		double	kappa,
		double	d0,
		double	d1,
		const Matrix &	M,
		const Matrix &	F
	)

Compressible version of the model for adipose tissue of Sommer et al.: Multiaxial mechanical properties and constitutive modeling of human adipose tissue: A basis for preoperative simulations in plastic and reconstructive surgery. Acta Biomater., 9:9036-9048, 2013.

Implementation of the stored energy function $W(F)= c_\mathrm{Cells}(\iota_1-3) + \frac{k_1}{k_2}\exp(k_2(\kappa\iota_1+(1-3\kappa)*\iota_4)^2-1) + d_0\Gamma_\mathrm{Inflation}(\det(F)) + d_1\Gamma_\mathrm{Compression}$ , where $\iota_1,\iota_4$ are the first and first mixed invariant of the strain tensor $F^T F$ .

Parameters

cCells	scaling of the neo-Hookean model for the description of the adipocytes as cell foam.
k1	stress-like parameter of the model for the interlobular septa
k2	dimensionless parameter of the model for the interlobular septa
kappa	fiber dispersion parameter $(0\le\kappa\le\frac{1}{3})$ .
M	structural tensor describing the fiber direction of the interlobular septa, i.e. $M=v\otimesv$ for a fiber direction
d0	scaling of the penalty function for inflation
d1	scaling of the penalty function for compression
F	initial deformation gradient

template<class Inflation , class Compression , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>

auto RFFGen::compressibleAdiposeTissue_SommerHolzapfel	(	double	d0,
		double	d1,
		const Matrix &	M,
		const Matrix &	F
	)

Compressible version of the model for adipose tissue of Sommer et al.: Multiaxial mechanical properties and constitutive modeling of human adipose tissue: A basis for preoperative simulations in plastic and reconstructive surgery. Acta Biomater., 9:9036-9048, 2013. Material parameters are taken from the same publication, Table 2, i.e. $c_\mathrm{Cells}=0.15 (\,\mathrm{kPa})$ , $k_1=0.8 (\,\mathrm{kPa})$ , $k_2=47.3$ and $\kappa=0.09$ .

Implementation of the stored energy function $W(F)= c_\mathrm{Cells}(\iota_1-3) + \frac{k_1}{k_2}\exp(k_2(\kappa\iota_1+(1-3\kappa)*\iota_4)^2-1) + d_0\Gamma_\mathrm{Inflation}(\det(F)) + d_1\Gamma_\mathrm{Compression}$ , where $\iota_1,\iota_4$ are the first and first mixed invariant of the strain tensor $F^T F$ .

Parameters

d0	scaling of the penalty function for inflation
d1	scaling of the penalty function for compression
M	structural tensor describing the fiber direction of the interlobular septa, i.e. $M=v\otimesv$ for a fiber direction
F	initial deformation gradient

template<class Inflation , class Compression , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>

auto RFFGen::compressibleMuscleTissue_Martins	(	double	c,
		double	b,
		double	A,
		double	a,
		double	d0,
		double	d1,
		const Matrix &	M,
		const Matrix &	F
	)

Compressible version of the model for muscle tissue of Martins et al.: A numerical model of passive and active bahevaior of skeletal muscles. Comp. Meth. Appl. Mech. Eng. 151:419-433, 1998.

Implementation of the stored energy function $W(F)=c(\exp(b(\bar\iota_1-3))-1) + A(\exp(a(\bar\iota_6-1)^2)-1) + d_0\Gamma_\mathrm{Inflation}(\det(F)) + d_1\Gamma_\mathrm{Compression}$ , where $\bar\iota_1,\bar\iota_6=\bar\iota_4$ are the first modified principal and the third modified mixed invariant of the strain tensor $F^T F$ .

Parameters

c	first material parameter for the isotropic part
b	second material parameter for the isotropic part
A	first material parameter for the anisotropic part
a	second material parameter for the anisotropic part
d0	material parameter for the penalty for inflation
d1	material parameter for the penalty for compression
M	structural (rank-one) tensor describing the initial orientation of muscle fibers for , where is the unit matrix.
F	deformation gradient

template<class Inflation , class Compression , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>

auto RFFGen::compressibleMuscleTissue_Martins	(	double	d0,
		double	d1,
		const Matrix &	M,
		const Matrix &	F
	)

Compressible version of the model for muscle tissue of Martins et al.: A numerical model of passive and active bahevaior of skeletal muscles. Comp. Meth. Appl. Mech. Eng. 151:419-433, 1998.

Implementation of the stored energy function $W(F)=c(\exp(b(\bar\iota_1-3))-1) + A(\exp(a(\bar\iota_6-1)^2)-1) + d_0\Gamma_\mathrm{Inflation}(\det(F)) + d_1\Gamma_\mathrm{Compression}(\det(F))$ , where $\bar\iota_1,\bar\iota_6=\bar\iota_4$ are the first modified principal and the third modified mixed invariant of the strain tensor $F^T F$ .

Material parameters taken from the above mentioned publication, i.e. $a=0.387 (\,\mathrm{kPa})$ , $ b = 23.46 $ , $A = 0.584 (\,\mathrm{kPa})$ and $ a = 12.43$ .

Parameters

d0	material parameter for the penalty for inflation
d1	material parameter for the penalty for compression
M	structural (rank-one) tensor describing the initial orientation of muscle fibers for , where is the unit matrix.
F	deformation gradient

template<class InflationPenalty , class CompressionPenalty , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>

auto RFFGen::compressibleSkin_Hendriks	(	double	c0,
		double	c1,
		double	d0,
		double	d1,
		const Matrix &	F
	)

Compressible version of the model for skin tissue of Hendriks: Mechanical behavior of human epidermal and dermal layers in vivo. PhD thesis, Technische Universiteit Eindhoven, 2005.

Implementation of the stored energy function $W(F)=c_0(\iota_1-3) + c_1(\iota_1-3)(\iota_2-3) + d_0\Gamma_\mathrm{Inflation}(\det(F)) + d_1\Gamma_\mathrm{Compression}$ , where $\iota_1,\iota_2$ are the first and second principal invariants of the strain tensor $F^T F$ .

Parameters

c0	scaling of the shifted first principal invariant
c1	scaling of the product of shifted first and second principal invariant
d0	scaling of the penalty function for inflation
d1	scaling of the penalty function for compression
F	initial deformation gradient

template<class InflationPenalty , class CompressionPenalty , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>

auto RFFGen::compressibleSkin_Hendriks	(	double	d0,
		double	d1,
		const Matrix &	F
	)

Compressible version of the model for skin tissue of Hendriks: Mechanical behavior of human epidermal and dermal layers in vivo. PhD thesis, Technische Universiteit Eindhoven, 2005.

Implementation of the stored energy function $W(F)=c_0(\iota_1-3) + c_1(\iota_1-3)(\iota_2-3) + d_0\Gamma_\mathrm{Inflation}(\det(F)) + d_1\Gamma_\mathrm{Compression}$ , where $\iota_1,\iota_2$ are the first and second principal invariants of the strain tensor $F^T F$ .

Material parameters are taken from Xu and Lu: Introduction to Skin Biothermomechanics and Thermal Pain, chapter Skin Biomechanics Modeling, pages 154-206, Springer and Science Press Beijing, 2011, i.e $c_0=9.4 (\,\mathrm{kPa})$ and $c_1 = 82 (\,\mathrm{kPa})$ .

Parameters

d0	scaling of the penalty function for inflation
d1	scaling of the penalty function for compression
F	initial deformation gradient

template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>

auto RFFGen::incompressibleAdiposeTissue_SommerHolzapfel	(	double	cCells,
		double	k1,
		double	k2,
		double	kappa,
		const Matrix &	M,
		const Matrix &	F
	)

Model for adipose tissue of Sommer et al.: Multiaxial mechanical properties and constitutive modeling of human adipose tissue: A basis for preoperative simulations in plastic and reconstructive surgery. Acta Biomater., 9:9036-9048, 2013.

Implementation of the stored energy function $W(F)= c_\mathrm{Cells}(\iota_1-3) + \frac{k_1}{k_2}\exp(k_2(\kappa\iota_1+(1-3\kappa)*\iota_4)^2-1)$ , where $\iota_1,\iota_4$ are the first and first mixed invariant of the strain tensor $F^T F$ .

Parameters

cCells	scaling of the neo-Hookean model for the description of the adipocytes as cell foam.
k1	stress-like parameter of the model for the interlobular septa
k2	dimensionless parameter of the model for the interlobular septa
kappa	fiber dispersion parameter $(0\le\kappa\le\frac{1}{3})$ .
M	structural tensor describing the fiber direction of the interlobular septa, i.e. $M=v\otimesv$ for a fiber direction
F	initial deformation gradient

template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>

auto RFFGen::incompressibleAdiposeTissue_SommerHolzapfel	(	const Matrix &	M,
		const Matrix &	F
	)

Model for adipose tissue of Sommer et al.: Multiaxial mechanical properties and constitutive modeling of human adipose tissue: A basis for preoperative simulations in plastic and reconstructive surgery. Acta Biomater., 9:9036-9048, 2013.

Implementation of the stored energy function $W(F)= c_\mathrm{Cells}(\iota_1-3) + \frac{k_1}{k_2}\exp(k_2(\kappa\iota_1+(1-3\kappa)*\iota_4)^2-1)$ , where $\iota_1,\iota_4$ are the first and first mixed invariant of the strain tensor $F^T F$ .

Material parameters are taken from the above mentioned publication, Table 2, i.e. $c_\mathrm{Cells}=0.15 (\,\mathrm{kPa})$ , $k_1=0.8 (\,\mathrm{kPa})$ , $k_2=47.3$ and $\kappa=0.09$ .

Parameters

M	structural tensor describing the fiber direction of the interlobular septa, i.e. $M=v\otimesv$ for a fiber direction
F	initial deformation gradient

template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>

auto RFFGen::incompressibleMuscleTissue_Martins	(	double	c,
		double	b,
		double	A,
		double	a,
		const Matrix &	M,
		const Matrix &	F
	)

Incompressible version of the model for muscle tissue of Martins et al.: A numerical model of passive and active bahevaior of skeletal muscles. Comp. Meth. Appl. Mech. Eng. 151:419-433, 1998.

Implementation of the stored energy function $W(F)=c(\exp(b(\bar\iota_1-3))-1) + A(\exp(a(\bar\iota_6-1)^2)-1)$ , where $\bar\iota_1,\bar\iota_6=\bar\iota_4$ are the first modified principal and the third modified mixed invariant of the strain tensor $F^T F$ .

Parameters

c	first material parameter for the isotropic part
b	second material parameter for the isotropic part
A	first material parameter for the anisotropic part
a	second material parameter for the anisotropic part
M	structural (rank-one) tensor describing the initial orientation of muscle fibers for , where is the unit matrix.
F	deformation gradient

template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>

auto RFFGen::incompressibleMuscleTissue_Martins	(	const Matrix &	M,
		const Matrix &	F
	)

Incompressible version of the model for muscle tissue of Martins et al.: A numerical model of passive and active bahevaior of skeletal muscles. Comp. Meth. Appl. Mech. Eng. 151:419-433, 1998.

Implementation of the stored energy function $W(F)=c(\exp(b(\bar\iota_1-3))-1) + A(\exp(a(\bar\iota_6-1)^2)-1)$ , where $\bar\iota_1,\bar\iota_6=\bar\iota_4$ are the first modified principal and the third modified mixed invariant of the strain tensor $F^T F$ .

Material parameters taken from the same above mentioned publication, i.e. $a=0.387 (\,\mathrm{kPa})$ , $ b = 23.46 $ , $A = 0.584 (\,\mathrm{kPa})$ and $ a = 12.43$ .

Parameters

M	structural (rank-one) tensor describing the initial orientation of muscle fibers for , where is the unit matrix.
F	deformation gradient

template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>

auto RFFGen::incompressibleSkin_Hendriks	(	double	c0,
		double	c1,
		const Matrix &	F
	)

Model for skin tissue of Hendriks: Mechanical behavior of human epidermal and dermal layers in vivo. PhD thesis, Technische Universiteit Eindhoven, 2005.

Implementation of the stored energy function $W(F)=c_0(\iota_1-3) + c_1(\iota_1-3)(\iota_2-3)$ , where $\iota_1,\iota_2$ are the first and second principal invariants of the strain tensor $F^T F$ .

Parameters

c0	scaling of the shifted first principal invariant
c1	scaling of the product of shifted first and second principal invariant
F	initial deformation gradient

template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>

auto RFFGen::incompressibleSkin_Hendriks ( const Matrix & F )

Model for skin tissue of Hendriks: Mechanical behavior of human epidermal and dermal layers in vivo. PhD thesis, Technische Universiteit Eindhoven, 2005.

Implementation of the stored energy function $W(F)=c_0(\iota_1-3) + c_1(\iota_1-3)(\iota_2-3)$ , where $\iota_1,\iota_2$ are the first and second principal invariants of the strain tensor $F^T F$ .

Material parameters are taken from Xu and Lu: Introduction to Skin Biothermomechanics and Thermal Pain, chapter Skin Biomechanics Modeling, pages 154-206, Springer and Science Press Beijing, 2011, i.e $c_0=9.4 (\,\mathrm{kPa})$ and $c_1 = 82 (\,\mathrm{kPa})$ .

Parameters

F	initial deformation gradient

Files

Functions

Detailed Description

Function Documentation