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ArrudaBoyceEightChainBase Class

Implements the Arruda-Boyce eight-chain model for incompressible hyperelastic rubber-like materials. Strain energy density (statistical form): W = mu * lambdaM^2 * ( (lambdaChain/lambdaM) * InverseLangevin(lambdaChain/lambdaM) + ln( (InverseLangevin(lambdaChain/lambdaM)) / sinh(InverseLangevin(lambdaChain/lambdaM)) ) ) with the chain stretch lambdaChain = sqrt(I1 / 3). Differentiating W with respect to the principal stretch for each deformation mode gives the nominal (engineering) stress: P = (mu / 3) * (lambdaM / lambdaChain) * InverseLangevin(lambdaChain / lambdaM) * dI1/dLambda where dI1/dLambda depends on the loading mode (incompressibility assumed, J = 1). Parameters: mu - initial shear modulus (small-strain), e.g. in MPa lambdaM - locking stretch (chain limiting stretch), typically 1.5 - 8, must be > 1 lambda - applied principal stretch (lambda = 1 + engineering strain)
Inheritance Hierarchy

Namespace: Altaxo.Calc.FitFunctions.RubberElasticity
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3618.0 (4.8.3618.0)
Syntax
C#
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public abstract class ArrudaBoyceEightChainBase : IEquatable<ArrudaBoyceEightChainBase>

The ArrudaBoyceEightChainBase type exposes the following members.

Constructors
 NameDescription
Protected methodArrudaBoyceEightChainBaseInitializes a new instance of the ArrudaBoyceEightChainBase class
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Methods
 NameDescription
Public methodStatic memberBiaxialStress Nominal (engineering) stress for equibiaxial loading. Deformation: lambda1 = lambda2 = lambda, lambda3 = 1/lambda^2 (incompressible). I1 = 2*lambda^2 + 1/lambda^4
Public methodStatic memberBiaxialStressGradient Gradient (d(sigma)/d(mu), d(sigma)/d(lambdaM)) of the equibiaxial nominal stress, for use as the Jacobian in a nonlinear least-squares fit.
Protected methodFinalizeAllows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object)
Public methodGetTypeGets the Type of the current instance.
(Inherited from Object)
Protected methodMemberwiseCloneCreates a shallow copy of the current Object.
(Inherited from Object)
Protected methodStatic memberNominalStress Core evaluation shared by all loading modes.
Public methodStatic memberPureShearStress Nominal (engineering) stress for pure shear (planar tension). Deformation: lambda1 = lambda, lambda2 = 1, lambda3 = 1/lambda (incompressible). I1 = lambda^2 + 1 + 1/lambda^2
Public methodStatic memberPureShearStressGradient Gradient (d(sigma)/d(mu), d(sigma)/d(lambdaM)) of the pure shear nominal stress, for use as the Jacobian in a nonlinear least-squares fit.
Public methodStatic memberUniaxialStress Nominal (engineering) stress for uniaxial loading. Deformation: lambda1 = lambda, lambda2 = lambda3 = 1/sqrt(lambda) (incompressible). I1 = lambda^2 + 2/lambda
Public methodStatic memberUniaxialStressGradient Gradient (d(sigma)/d(mu), d(sigma)/d(lambdaM)) of the uniaxial nominal stress, for use as the Jacobian in a nonlinear least-squares fit.
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See Also