ug::SmallStrainMechanics::HookeLaw< TDomain > Class Template Reference

#include <hooke.h>

Inheritance diagram for ug::SmallStrainMechanics::HookeLaw< TDomain >:

Public Member Functions
virtual SmartPtr< MathTensor4< TDomain::dim, TDomain::dim, TDomain::dim, TDomain::dim > >	elasticityTensor ()
	computes the elasticity tensor; commonly denoted by C More...
virtual SmartPtr< MathTensor4< TDomain::dim, TDomain::dim, TDomain::dim, TDomain::dim > >	elasticityTensor (const size_t ip, const MathMatrix< dim, dim > &GradU)
	HookeLaw ()
	constructor More...
virtual void	init ()
void	strainTensor (MathMatrix< dim, dim > &strainTens, const MathMatrix< dim, dim > &GradU)
virtual void	stressTensor (MathMatrix< dim, dim > &stressTens, const size_t ip, const MathMatrix< dim, dim > &GradU)
	computes the cauchy stress tensor sigma at an integration point 'ip' More...
	~HookeLaw ()
	Destructor. More...
void	set_hooke_elasticity_tensor (const number lambda, const number mu)
void	set_hooke_elasticity_tensor_E_nu (const number E, const number nu)
void	set_hooke_elasticity_tensor_plain_stress_E_nu (const number E, const number nu)
void	set_hooke_elasticity_tensor_plain_strain_E_nu (const number E, const number nu)
void	set_elasticity_tensor_orthotropic (const number C11, const number C12, const number C13, const number C22, const number C23, const number C33, const number C44, const number C55, const number C66)
void	set_elasticity_tensor_orthotropic_E_G_nu (const number E1, const number E2, const number E3, const number G12, const number G13, const number G23, const number v12, const number v13, const number v23)
void	set_elasticity_tensor_orthotropic_plain_stress_E_G_nu (const number E1, const number E2, const number G12, const number v12)
void	set_elasticity_tensor_orthotropic_plain_strain_E_G_nu (const number E1, const number E2, const number E3, const number G12, const number G13, const number G23, const number v12, const number v13, const number v23)
Public Member Functions inherited from ug::SmallStrainMechanics::IMaterialLaw< TDomain >
virtual void	attach_internal_vars (typename TDomain::grid_type &grid)
virtual void	clear_attachments (typename TDomain::grid_type &grid)
template<typename TFEGeom >
void	DisplacementGradient (MathMatrix< dim, dim > &GradU, const size_t ip, const TFEGeom &geo, const LocalVector &u)
virtual SmartPtr< MathTensor4< dim, dim, dim, dim > >	elasticityTensor (const size_t ip, const MathVector< dim > &x, const MathMatrix< dim, dim > &GradU)
bool	elastTensIsConstant ()
virtual number	hardening_parameter (const size_t ip)
	IMaterialLaw ()
	constructor More...
virtual SmartPtr< MathMatrix< dim, dim > >	inelastic_strain_tensor (const size_t ip)
virtual void	init_internal_vars (TBaseElem *elem, const size_t numIP)
virtual void	internal_vars (TBaseElem *elem)
bool	is_initialized ()
virtual bool	needs_to_add_jac_m ()
virtual number	plastic_multiplier (const size_t ip, const MathMatrix< dim, dim > &GradU)
virtual void	stressTensor (MathMatrix< dim, dim > &stressTens, const size_t ip, const MathVector< dim > &x, const MathMatrix< dim, dim > &GradU)
virtual void	update_internal_vars (const size_t ip, const MathMatrix< dim, dim > &GradU)
virtual void	write_data_to_console (const number t)
virtual	~IMaterialLaw ()
	destructor More...

Public Attributes
std::string	m_materialConfiguration
Public Attributes inherited from ug::SmallStrainMechanics::IMaterialLaw< TDomain >
std::string	m_materialConfiguration

Static Public Attributes
static const int	dim = base_type::dim
	World dimension. More...
Static Public Attributes inherited from ug::SmallStrainMechanics::IMaterialLaw< TDomain >
static const int	dim = TDomain::dim
	World dimension. More...

Protected Attributes
SmartPtr< MathTensor4< dim, dim, dim, dim > >	m_spElastTensorFunct
	elasticity tensor More...
Protected Attributes inherited from ug::SmallStrainMechanics::IMaterialLaw< TDomain >
bool	m_bConstElastTens
	flag indicating, if elasticity tensor is constant More...
bool	m_bInit
	flag indicating, if material law has been initialized More...

Private Types
typedef IMaterialLaw< TDomain >	base_type
	Base class type. More...

Additional Inherited Members
Public Types inherited from ug::SmallStrainMechanics::IMaterialLaw< TDomain >
typedef domain_traits< TDomain::dim >::grid_base_object	TBaseElem
	base element type of associated domain More...

Detailed Description

template<typename TDomain>
class ug::SmallStrainMechanics::HookeLaw< TDomain >

The classical material law to describe linear elastic behavior for isotropic, homogeneous materials. This law is based on the assumption of small strains, since only the linearized strain tensor (commonly denoted with \epsilon) is used. With $u$ being the displacement vector, the strain tensor \epsilon is defined by

\epsilon = \frac{1}{2}(\nabla u + (\nabla u)^T),

i.e. higher orders of the gradient of u are neglected here (-> 'linearized strain tensor').

Additionally Hooke`s law assumes a linear connection of stresses and strains. Therefore, the stresses \sigma are described by a law of the form,

\sigma = C : \epsilon

with C being a constant tensor of rank 4, called 'ElasticityTensor'. \sigma denotes the cauchy-stress tensor, which is, just like the strain tensor \epsilon, a symmetric tensor of rank 2. ':' denotes the tensor contraction, in components,

\sigma_{ij} = C_{ijkl} \epsilon{kl}.

Template Parameters

int

dim

References:

• D. Braess. Finite Elemente. Theorie, schnelle L�ser und Anwendungen in der
• Elastizit�tstheorie, Springer

Member Data Documentation

m_materialConfiguration

template<typename TDomain >

std::string ug::SmallStrainMechanics::IMaterialLaw< TDomain >::m_materialConfiguration

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

• /home/runner/work/docs/docs/ug4/plugins/SmallStrainMechanics/material_laws/hooke.h
• /home/runner/work/docs/docs/ug4/plugins/SmallStrainMechanics/material_laws/hooke_impl.h