COMSOL 6.3 - Solid Mechanics Material Properties: Nonlinear Structural Materials Module

Solid Mechanics Material Properties: Nonlinear Structural Materials Module

These material property groups for material models in solid mechanics are used by the Nonlinear Structural Materials Module.

Table 9-25: Hyperelastic, Elastoplastic, phase Transformation, and Damage Material Properties.
Property Group and Property	Name/Variable	SI Unit
Elastoplastic material
Hardening function	sigmagh	Pa
Hill’s coefficients	{Hillcoefficients1, …, Hillcoefficients6}	(m2·s4)/kg2
Initial tensile and shear yield stresses	{ys1, ys2, ys3, ys4, ys5, ys6}	N/m2
Initial yield stress	sigmags	Pa
Isotropic tangent modulus	Et	Pa
Kinematic tangent modulus	Ek	Pa
Armstrong–Frederick
Kinematic hardening modulus	Ck	Pa
Kinematic hardening parameter	gammak	1
Cap and Cutoff
Initial pressure limit	pc0	Pa
Initial ellipse centroid	pcc0	Pa
Hardening function	pch	Pa
Hardening modulus	Kc	Pa
Maximum volumetric plastic strain	epvolmax	1
Mean stress limit	svolt	Pa
Chaboche
Kinematic hardening modulus	Ck0_cha	Pa
Foam Plasticity
Initial hydrostatic yield stress, compression	pc0	Pa
Hardening function	pch	Pa
Hydrostatic yield stress, tension	pt	Pa
Initial uniaxial compressive yield stress	sigmauc0	Pa
Hardening function, uniaxial data	sigmauch	Pa
Plastic Poisson's ratio	bup	1
Johnson–Cook
Strength coefficient	k_jcook	Pa
Hardening coefficient	n_jcook	1
Reference strain rate	epet0_jcook	1/s
Temperature exponent	m_jcook
Ludwik
Strength coefficient	k_lud	Pa
Hardening exponent	n_lud	1
Nonlinear elastic Fiber
Uniaxial stress function	saxa	N/m2
Pressure-dependent plasticity
Yield function parameter	a1yield	1
Yield function parameter	a2yield	1/Pa
Yield function parameter	a3yield	Pa
Yield function parameter	a4yield	1/Pa
Potential parameter	a1potential	1
Potential parameter	a2potential	1/Pa
Potential parameter	a3potential	Pa
Potential parameter	a4potential	1/Pa
Yield function parameter	b1yield	Pa
Yield function parameter	b2yield	1
Yield function parameter	b3yield	Pa
Potential parameter	b1potential	Pa
Potential parameter	b2potential	1
Potential parameter	b3potential	Pa
Octahedral shape parameter	c1Lagioia	1
Octahedral shape parameter	c2Lagioia	1
Octahedral shape parameter	c3Lagioia	1
Swift
Reference strain	e0_swi	1
Hardening exponent	n_swi	1
Voce
Saturation flow stress	sigma_voc	Pa
Saturation exponent	beta_voc	1
Hockett–Sherby
Steady-state flow stress	sigma_hoc	Pa
Saturation coefficient	m_hoc	1
Saturation exponent	n_hoc	1
Creep
Norton
Creep rate coefficient	A_nor	1/s
Reference stress	sigRef_nor	Pa
Stress exponent	n_nor	1
Garofalo (hyperbolic sine)
Creep rate coefficient	A_gar	1/s
Reference stress	sigRef_gar	Pa
Stress exponent	n_gar	1
Hill’s coefficients
Hill’s coefficients	{Hillcoefficients1, …, Hillcoefficients6}	(m2·s4)/kg2
Nabarro–Herring
Volume diffusivity	D_nav	m2/s
Burgers vector	b_nav	m
Grain diameter	dg_nav	m
Coble
Ionic diffusivity	D_cob	m2/s
Burgers vector	b_cob	m
Grain diameter	dg_cob	m
Weertman
Diffusivity	D_wee	m2/s
Burgers vector	b_wee	m
Stress exponent	n_wee	1
Reference stress	sigRef_wee	Pa
Viscoplastic Material
Anand
Viscoplastic rate coefficient	A_ana	1/s
Activation energy	Q_ana	J/mol
Multiplier of stress	xi_ana	1
Stress sensitivity	m_ana	1
Deformation resistance saturation coefficient	s0_ana	Pa
Deformation resistance initial value	sa_init	Pa
Hardening constant	h0_ana	Pa
Hardening sensitivity	a_ana	1
Deformation resistance sensitivity	n_ana	1
Bergstrom–Boyce viscoplasticity
Viscoplastic rate coefficient	A_BB	1/s
Flow resistance	sigRes_BB	N/m2
Stress exponent	n_BB	1
Strain exponent	c_BB	1
Cutoff stress	sigmaco_BB	N/m2
Bergstrom–Bischoff viscoplasticity
Viscoplastic rate coefficient	A_BeBi	1/s
Flow resistance	sigRes1_BeBi	N/m2
Flow resistance	sigRes2_BeBi	N/m2
Stress exponent	n1_BeBi	1
Stress exponent	n2_BeBi	1
Pressure hardening coefficient	a1_BeBi	1
Pressure hardening coefficient	a2_BeBi	1
Bingham viscoplasticity
Viscosity	eta_bing	Pa·s
Chaboche viscoplasticity
Viscoplastic rate coefficient	A_cha	1/s
Reference stress	sigRef_cha	Pa
Stress exponent	n_cha	1
Parallel network viscoplasticity
Viscoplastic rate coefficient	A_PN	1/s
Flow resistance	sigRes_PN	N/m2
Stress exponent	n_PN	1
Stress exponent	c_PN	1
Cutoff stress	sigmaco_PN	N/m2
Pressure hardening coefficient	a_PN
Peric viscoplasticity
Viscoplastic rate coefficient	A_peric	1/s
Stress exponent	n_peric	1
PeRzyna
Viscoplastic rate coefficient	A_per	1/s
Reference stress	sigRef_per	Pa
Poroplastic material
Initial yield stress	sigmags	Pa
Shima–Oyane alpha parameter	alphaShima	1
Shima–Oyane gamma parameter	gammaShima	1
Shima–Oyane m parameter	mShima	1
Initial void volume fraction	f0	1
Critical void volume fraction	fc	1
Failure void volume fraction	ff	1
Tvergaard correction coefficient q1	q1GTN	1
Tvergaard correction coefficient q2	q2GTN	1
Tvergaard correction coefficient q3	q3GTN	1
Maximum void volume fraction	fmax	1
Nonlinear elastic material
Reference stress	sigRef	Pa
Reference strain	eRef	1
Stress exponent	n_stress	1
Reference shear strain	gammaRef	1
Strain exponent	n_strain	1
Bulk modulus in tension	Kt	Pa
Bulk modulus in compression	Kc	Pa
Ultimate deviatoric stress	q_ult	Pa
Ultimate strain	e_ult	1
Elastoplastic soil material
Cam-Clay
Swelling index	kappaSwelling	1
Compression index	lambdaComp	1
Void ratio at reference pressure	evoidref	1
Slope of critical state line	M	1
Structured Cam-Clay
Swelling index for structured clay	kappaSwellingS	1
Compression index for destructured clay	lambdaCompS	1
Void ratio at reference pressure for destructured clay	evoidrefS	1
Destructuring index for volumetric deformation	dvS	1
Destructuring index for shear deformation	dsS	1
Slope of critical state line	M	1
Additional void ratio at initial yielding	Deltaei	1
Initial structure strength	pbi	Pa
Plastic potential shape parameter	zetaS	1
Critical effective deviatoric plastic strain	epdevc	1
Barcelona Basic
Swelling index	kappaSwelling	1
Swelling index for changes in suction	kappaSwellings	1
Compression index at saturation	lambdaComp0	1
Weight parameter	wB	1
Soil stiffness parameter	mB	Pa
Plastic potential smoothing parameter	bB	1
Tension to suction ratio	kB	1
Void ratio at reference pressure and saturation	evoidref0	1
Initial yield value for suction	sy0	Pa
Hardening soil
Reference stiffness for primary loading	E50Ref	Pa
Reference stiffness for unloading and reloading	EurRef	Pa
Stress exponent	mH	1
Bulk modulus in compression	Kc	Pa
Void ratio at reference pressure	evoidref	1
Hyperelastic and viscoelastic Materials
Arruda–Boyce
Macroscopic shear modulus	mu0	N/m2
Number of segments	Nseg	1
Blatz–Ko
Model parameters	phiBK	1
Model parameters	betaBK	1
Shear modulus	muBK	Pa
Delfino
Model parameters	aDelf	Pa
Model parameters	bDelf	1
Extended tube
Model parameters	GcET	Pa
Model parameters	GeET	Pa
Model parameters	alphaET	1
Model parameters	betaET	1
Fung
Coefficient matrix	AFung_iso (6-by-6 matrix)	1
Fung parameter c	cFung	Pa
Gao
Model parameters	aG	Pa
Model parameters	nG	1
Gent
Macroscopic shear modulus	muG	Pa
Model parameters	jmG	1
Holzapfel–Gasser–Ogden
Fiber stiffness	k1HGO	Pa
Model parameters	k2HGO	1
Model parameters	k3HGO	1
Mooney–Rivlin
Model parameters	C01, C02, C03, C10, C11, C12, C20, C21, C30	Pa
Murnaghan	The Murnaghan node adds five model parameters. The model is based on strain invariants and is typically used in acoustoelasticity.
Murnaghan third-order elastic moduli	l	Pa
Murnaghan third-order elastic moduli	m	Pa
Murnaghan third-order elastic moduli	n	Pa
Lamé parameter λ	lambLame	Pa
Lamé parameter μ	muLame	Pa
van der Waals
Shear modulus	muW	Pa
Maximum chain stretch	lambdaW	1
Chain network interaction	alphaW	1
Weight	betaW	1
Varga
Model parameters	c1VA	Pa
Model parameters	c2VA	Pa
Yeoh
Model parameters	c1YE	Pa
Model parameters	c2YE	Pa
Model parameters	c3YE	Pa
Lagoudas Model
Reference temperature	T0	K
Martensite start temperature	TMs	K
Martensite finish temperature	TMf	K
Austenite start temperature	TAs	K
Austenite finish temperature	TAf	K
Slope of martensite limit curve	CM	Pa/K
Slope of austenite limit curve	CA	Pa/K
Maximum transformation strain	etrmaxLagoudas	1
Calibration stress level	sigmaStar	N/m2
Lagoudas Model, Stress
Martensite start stress	sMs	N/m2
Martensite finish stress	sMf	N/m2
Austenite start stress	sAs	N/m2
Austenite finish stress	sAf	N/m2
Measurement temperature	Tstress	K
Lagoudas Model, exponential law
Initial maximum transformation strain	etrmin	1
Ultimate transformation strain	etrsat	1
Critical stress	scrit	N/m2
Saturation exponent	kcrit	1/Pa
Austenite phase
Young’s modulus	E_A	Pa
Heat capacity at constant pressure	Cp_A	J/(kg·K)
Thermal conductivity	k_A_iso	W/(m·K)
Martensite phase
Young’s modulus	E_M	Pa
Heat capacity at constant pressure	Cp_M	J/(kg·K)
Thermal conductivity	k_M_iso	W/(m·K)
Thermal expansion, austenite phase
Coefficient of thermal expansion	alpha_A_iso (3-by-3 matrix)	1/K
Tangent coefficient of thermal expansion	alphatan_A_iso (3-by-3 matrix)	1/K
Thermal strain	dL_A_iso (3-by-3 matrix)	1
Thermal expansion, martensite phase
Coefficient of thermal expansion	alpha_M_iso (3-by-3 matrix)	1/K
Tangent coefficient of thermal expansion	alphatan_M_iso (3-by-3 matrix)	1/K
Thermal strain	dL_M_iso (3-by-3 matrix)	1
Souza–Auricchio Model
Reference temperature	TStar	K
Slope of limit curve	beta	Pa/K
Maximum transformation strain	etrmaxAuricchio	1
Elastic domain radius	sAf	N/m2
Hardening modulus	Hk	N/m2
Martensite start temperature	TMs_SA	K
Martensite finish temperature	TMf_SA	K
Austenite finish temperature	TAf_SA	K
Martensite start stress	sMs_SA	N/m2
Martensite finish stress	sMf_SA	N/m2
Austenite finish stress	sAf_SA	N/m2
Measurement temperature	Tstress_SA	K
Damage Material
Mazars damage for concrete
Tensile strength	sigmat	N/m2
Fracture energy per area	Gft	J/m2
Fracture energy per volume	gft	J/m3
Phase-field damage
Critical fracture stress	sigmacr	N/m2
Critical energy release rate	Gc	J/m2
Scalar damage
Peak strength	sigmap	N/m2
Fracture energy per area	Gf	J/m2
Fracture energy per volume	gf	J/m3