CubbyFlow::SnowConstitutiveModel< N > Class Template Reference

Snow-specific elastoplastic constitutive model. More...

#include <Core/Particle/MPM/SnowConstitutiveModel.hpp>

Public Types
using	MatrixType = Matrix< double, N, N >
using	State = SnowDeformationState< N >

Public Member Functions
	SnowConstitutiveModel (double youngsModulus=1.4e5, double poissonRatio=0.2, double criticalCompression=2.5e-2, double criticalStretch=7.5e-3, double hardeningCoefficient=10.0)
	Constructs a snow constitutive model.
State	Update (const MatrixType &deformationGradientIncrement, const State &state) const
	Projects a deformation increment into elastic and plastic parts.
MatrixType	ComputeKirchhoffStress (const State &state) const
	Computes the fixed-corotated Kirchhoff stress for the state.
MatrixType	ComputeFirstPiolaStressDifferential (const State &state, const MatrixType &differential) const
	Computes the first Piola stress differential.
double	ComputeWaveSpeed (const State &state, double referenceDensity) const
	Estimates the fastest elastic wave speed for the state.

Detailed Description

template<size_t N>
class CubbyFlow::SnowConstitutiveModel< N >

Snow-specific elastoplastic constitutive model.

Implements the fixed-corotated hyperelastic snow model from "A Material Point Method for Snow Simulation" by A. Stomakhin et al. (2013) for MPM simulations.

Member Typedef Documentation

MatrixType

template<size_t N>

using CubbyFlow::SnowConstitutiveModel< N >::MatrixType = Matrix<double, N, N>

State

template<size_t N>

using CubbyFlow::SnowConstitutiveModel< N >::State = SnowDeformationState<N>

Constructor & Destructor Documentation

SnowConstitutiveModel()

template<size_t N>

CubbyFlow::SnowConstitutiveModel< N >::SnowConstitutiveModel ( double  youngsModulus = 1.4e5, double  poissonRatio = 0.2, double  criticalCompression = 2.5e-2, double  criticalStretch = 7.5e-3, double  hardeningCoefficient = 10.0  )

explicit

Constructs a snow constitutive model.

Parameters

[in]	youngsModulus	Initial Young's modulus; must be positive and finite.
[in]	poissonRatio	Poisson's ratio in (-1, 0.5).
[in]	criticalCompression	Principal-stretch compression offset in [0, 1).
[in]	criticalStretch	Non-negative principal-stretch extension offset.
[in]	hardeningCoefficient	Non-negative hardening coefficient.

Member Function Documentation

ComputeFirstPiolaStressDifferential()

template<size_t N>

SnowConstitutiveModel< N >::MatrixType CubbyFlow::SnowConstitutiveModel< N >::ComputeFirstPiolaStressDifferential	(	const State &	state,
		const MatrixType &	differential
	)		const

Computes the first Piola stress differential.

Evaluates (d^2 Psi / d F_E d F_E) : differential while holding the plastic deformation fixed.

Parameters

[in]	state	Current elastic and plastic deformation state.
[in]	differential	Elastic deformation differential.

Returns

First Piola stress differential.

Exceptions

std::invalid_argument

If the state, differential, or computed stress differential is invalid or non-finite.

ComputeKirchhoffStress()

template<size_t N>

SnowConstitutiveModel< N >::MatrixType CubbyFlow::SnowConstitutiveModel< N >::ComputeKirchhoffStress

(

const State &

state

)

const

Computes the fixed-corotated Kirchhoff stress for the state.

Applies the det(F_P)-dependent hardening/softening factor to the elastic response.

Parameters

[in]

state

Current deformation state.

Returns

Fixed-corotated Kirchhoff stress.

ComputeWaveSpeed()

template<size_t N>

double CubbyFlow::SnowConstitutiveModel< N >::ComputeWaveSpeed	(	const State &	state,
		double	referenceDensity
	)		const

Estimates the fastest elastic wave speed for the state.

Evaluates the principal-basis acoustic-tensor candidates for the fixed-corotated snow energy.

Parameters

[in]	state	Current deformation state.
[in]	referenceDensity	Positive material density at rest.

Returns

Estimated elastic wave speed.

Update()

template<size_t N>

SnowConstitutiveModel< N >::State CubbyFlow::SnowConstitutiveModel< N >::Update	(	const MatrixType &	deformationGradientIncrement,
		const State &	state
	)		const

Projects a deformation increment into elastic and plastic parts.

Forms F_E_trial = D F_E, clamps its principal stretches, and transfers the remainder to F_P while preserving the trial total deformation.

Parameters

[in]	deformationGradientIncrement	Multiplicative increment D applied on the left.
[in]	state	Current deformation state.

Returns

Updated deformation state.

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

• Core/Particle/MPM/SnowConstitutiveModel.hpp
• Core/Particle/MPM/SnowConstitutiveModel-Impl.hpp