Linear elastic isotropic material model. More...

#include <IsotropicMaterial.hpp>

Collaboration diagram for Phyth::IsotropicMaterial:

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Public Member Functions
	IsotropicMaterial ()=default
	Default constructor.

	IsotropicMaterial (const Quantity< Pascal > youngs_modulus, const Scalar poisson_ratio)
	Construct from Young's modulus and Poisson's ratio.

	IsotropicMaterial (const Quantity< Pascal > shear_modulus, const Quantity< Pascal > bulk_modulus)
	Construct from shear modulus and bulk modulus.

Quantity< Pascal >	GetYoungsModulus () const
	Get Young's modulus.

Scalar	GetPoissonRatio () const
	Get Poisson's ratio.

Quantity< Pascal >	GetShearModulus () const
	Get shear modulus.

Quantity< Pascal >	GetBulkModulus () const
	Get bulk modulus.

Quantity< Pascal >	GetLameLambda () const
	Get Lame's first parameter.

Matrix3x3< Quantity< Pascal > >	ComputeStress (const Matrix3x3< Scalar > &strain) const
	Compute stress tensor from strain tensor.

Matrix3x3< Scalar >	ComputeStrain (const Matrix3x3< Quantity< Pascal > > &stress) const
	Compute strain tensor from stress tensor.

Private Member Functions
void	UpdateDerivedParameters ()
	Update derived parameters from (E, nu)

void	UpdateDerivedParametersFromGK ()
	Update derived parameters from (G, K)

Private Attributes
Quantity< Pascal >	youngs_modulus_

Scalar	poisson_ratio_

Quantity< Pascal >	shear_modulus_

Quantity< Pascal >	bulk_modulus_

Quantity< Pascal >	lame_lambda_

Detailed Description

Linear elastic isotropic material model.

IsotropicMaterial implements the constitutive relationship for linear elastic materials with direction-independent mechanical properties. The material is fully defined by any two independent elastic constants, with automatic derivation of all other parameters.

The stress-strain relationship follows Hooke's law: sigma_ij = lambda * delta_ij * epsilon_kk + 2 * mu * epsilon_ij

where lambda is Lame's first parameter and mu is the shear modulus.

Supported material parameter pairs for construction:

(Young's modulus E, Poisson's ratio nu)
(Shear modulus G, Bulk modulus K)

All quantities maintain physical dimensions through the Quantity system, ensuring dimensional consistency at compile time.

Example: // Steel-like material IsotropicMaterial steel(210.0e9_Pa, 0.3);

// Compute stress from strain Matrix3x3<Scalar> strain = ...; auto stress = steel.ComputeStress(strain);

Definition at line 39 of file IsotropicMaterial.hpp.

Constructor & Destructor Documentation

◆ IsotropicMaterial() [1/3]

Phyth::IsotropicMaterial::IsotropicMaterial ( )

default

Default constructor.

Creates an uninitialized material. All elastic moduli are zero. Use this only when the material will be assigned later.

◆ IsotropicMaterial() [2/3]

Phyth::IsotropicMaterial::IsotropicMaterial	(	const Quantity< Pascal >	youngs_modulus,
		const Scalar	poisson_ratio
	)

inline

Construct from Young's modulus and Poisson's ratio.

This is the most common construction method for engineering materials. All other elastic constants (shear modulus G, bulk modulus K, and Lame's first parameter lambda) are derived automatically.

Valid range: -1 < nu < 0.5 for thermodynamic stability

nu > 0.5: material becomes incompressible or auxetic
nu < -1: violates stability criteria

Parameters

youngs_modulus	Young's modulus E (Pa)
poisson_ratio	Poisson's ratio nu (dimensionless)

Definition at line 63 of file IsotropicMaterial.hpp.

◆ IsotropicMaterial() [3/3]

Phyth::IsotropicMaterial::IsotropicMaterial	(	const Quantity< Pascal >	shear_modulus,
		const Quantity< Pascal >	bulk_modulus
	)

inline

Construct from shear modulus and bulk modulus.

This construction method is useful when the material properties are derived from wave propagation measurements or high-pressure experiments.

All other constants (Young's modulus E, Poisson's ratio nu, and Lame's first parameter lambda) are derived automatically.

Parameters

shear_modulus	Shear modulus G (Pa), must be positive
bulk_modulus	Bulk modulus K (Pa), must be positive

Definition at line 81 of file IsotropicMaterial.hpp.

Member Function Documentation

◆ ComputeStrain()

Matrix3x3< Scalar > Phyth::IsotropicMaterial::ComputeStrain ( const Matrix3x3< Quantity< Pascal > > & stress ) const

inline

Compute strain tensor from stress tensor.

Implements the inverse form of Hooke's law: epsilon_ij = (1 + nu) / E * sigma_ij - nu / E * trace(sigma) * delta_ij

This is the compliance form of the constitutive relationship, useful for displacement-based formulations.

Parameters

stress Stress tensor in pascals (symmetric)

Returns: Strain tensor (dimensionless, symmetric)

Example: Matrix3x3<Quantity<Pascal>> stress; stress(0, 0) = 100.0e6_Pa; // uniaxial tension auto strain = material.ComputeStrain(stress);

Definition at line 166 of file IsotropicMaterial.hpp.

◆ ComputeStress()

Matrix3x3< Quantity< Pascal > > Phyth::IsotropicMaterial::ComputeStress ( const Matrix3x3< Scalar > & strain ) const

inline

Compute stress tensor from strain tensor.

Implements the generalized Hooke's law for isotropic materials: sigma_ij = lambda * trace(epsilon) * delta_ij + 2 * mu * epsilon_ij

The strain tensor is expected to represent infinitesimal strain (small deformation theory). For finite strain, use appropriate hyperelastic models instead.

Parameters

strain Strain tensor (dimensionless, symmetric)

Returns: Stress tensor in pascals (symmetric)

Example: Matrix3x3<Scalar> strain; strain(0, 0) = 0.001; // 0.1% axial strain auto stress = material.ComputeStress(strain);

Definition at line 134 of file IsotropicMaterial.hpp.

◆ GetBulkModulus()

Quantity< Pascal > Phyth::IsotropicMaterial::GetBulkModulus ( ) const

inline

Get bulk modulus.

Returns: Bulk modulus K in pascals

Definition at line 108 of file IsotropicMaterial.hpp.

◆ GetLameLambda()

Quantity< Pascal > Phyth::IsotropicMaterial::GetLameLambda ( ) const

inline

Get Lame's first parameter.

Returns: Lame's first parameter lambda in pascals

Definition at line 114 of file IsotropicMaterial.hpp.

◆ GetPoissonRatio()

Scalar Phyth::IsotropicMaterial::GetPoissonRatio ( ) const

inline

Get Poisson's ratio.

Returns: Poisson's ratio nu (dimensionless)

Definition at line 96 of file IsotropicMaterial.hpp.

◆ GetShearModulus()

Quantity< Pascal > Phyth::IsotropicMaterial::GetShearModulus ( ) const

inline

Get shear modulus.

Returns: Shear modulus G in pascals

Definition at line 102 of file IsotropicMaterial.hpp.

◆ GetYoungsModulus()

Quantity< Pascal > Phyth::IsotropicMaterial::GetYoungsModulus ( ) const

inline

Get Young's modulus.

Returns: Young's modulus E in pascals

Definition at line 90 of file IsotropicMaterial.hpp.

◆ UpdateDerivedParameters()

void Phyth::IsotropicMaterial::UpdateDerivedParameters ( )

inlineprivate

Update derived parameters from (E, nu)

Relations: G = E / (2 * (1 + nu)) K = E / (3 * (1 - 2 * nu)) lambda = E * nu / ((1 + nu) * (1 - 2 * nu))

Note: These formulas are singular for nu = 0.5 (incompressible limit) and nu = -1 (stability limit).

Definition at line 202 of file IsotropicMaterial.hpp.

◆ UpdateDerivedParametersFromGK()

void Phyth::IsotropicMaterial::UpdateDerivedParametersFromGK ( )

inlineprivate

Update derived parameters from (G, K)

Relations: E = 9 * G * K / (3 * K + G) nu = (3 * K - 2 * G) / (2 * (3 * K + G)) lambda = K - 2/3 * G

This formulation is more stable near the incompressible limit.

Definition at line 218 of file IsotropicMaterial.hpp.

Member Data Documentation

◆ bulk_modulus_

Quantity<Pascal> Phyth::IsotropicMaterial::bulk_modulus_

private

Definition at line 188 of file IsotropicMaterial.hpp.

◆ lame_lambda_

Quantity<Pascal> Phyth::IsotropicMaterial::lame_lambda_

private

Definition at line 189 of file IsotropicMaterial.hpp.

◆ poisson_ratio_

Scalar Phyth::IsotropicMaterial::poisson_ratio_

private

Definition at line 185 of file IsotropicMaterial.hpp.

◆ shear_modulus_

Quantity<Pascal> Phyth::IsotropicMaterial::shear_modulus_

private

Definition at line 187 of file IsotropicMaterial.hpp.

◆ youngs_modulus_

Quantity<Pascal> Phyth::IsotropicMaterial::youngs_modulus_

private

Definition at line 184 of file IsotropicMaterial.hpp.

The documentation for this class was generated from the following file:

include/Phyth/Elements/Mechanics/IsotropicMaterial.hpp

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ IsotropicMaterial() [1/3]

◆ IsotropicMaterial() [2/3]

◆ IsotropicMaterial() [3/3]

Member Function Documentation

◆ ComputeStrain()

◆ ComputeStress()

◆ GetBulkModulus()

◆ GetLameLambda()

◆ GetPoissonRatio()

◆ GetShearModulus()

◆ GetYoungsModulus()

◆ UpdateDerivedParameters()

◆ UpdateDerivedParametersFromGK()

Member Data Documentation

◆ bulk_modulus_

◆ lame_lambda_

◆ poisson_ratio_

◆ shear_modulus_

◆ youngs_modulus_