Three-dimensional Euclidean displacement gradient dyadic tensor. Gradient of the displacement vector. May be symmetric or asymmetric. Contains nine components in Cartesian coordinates: xx, xy, xz, yx, yy, yz, zx, zy, and zz. For the scalar components or resultants of a displacement gradient tensor, see PhQ::ScalarDisplacementGradient. The time rate of change of a displacement gradient is a velocity gradient; see PhQ::VelocityGradient, PhQ::Time, and PhQ::Frequency. More...

#include "DisplacementGradient.hpp"

Public Member Functions
	DisplacementGradient ()=default
	Default constructor. Constructs a displacement gradient tensor with an uninitialized value. More...

constexpr	DisplacementGradient (const NumericType xx, const NumericType xy, const NumericType xz, const NumericType yx, const NumericType yy, const NumericType yz, const NumericType zx, const NumericType zy, const NumericType zz)
	Constructor. Constructs a displacement gradient tensor whose value has the given xx, xy, xz, yx, yy, yz, zx, zy, and zz Cartesian components. More...

constexpr	DisplacementGradient (const std::array< NumericType, 9 > &xx_xy_xz_yx_yy_yz_zx_zy_zz)
	Constructor. Constructs a displacement gradient tensor from a given array representing its value's xx, xy, xz, yx, yy, yz, zx, zy, and zz Cartesian components. More...

constexpr	DisplacementGradient (const Dyad< NumericType > &value)
	Constructor. Constructs a displacement gradient tensor with a given value. More...

constexpr	DisplacementGradient (const VelocityGradient< NumericType > &velocity_gradient, const Time< NumericType > &time)
	Constructor. Constructs a displacement gradient tensor from a given velocity gradient tensor and time using the definition of speed. More...

constexpr	DisplacementGradient (const VelocityGradient< NumericType > &velocity_gradient, const Frequency< NumericType > &frequency)
	Constructor. Constructs a displacement gradient tensor from a given velocity gradient tensor and frequency using the definition of speed. More...

	~DisplacementGradient () noexcept=default
	Destructor. Destroys this displacement gradient tensor. More...

constexpr	DisplacementGradient (const DisplacementGradient< NumericType > &other)=default
	Copy constructor. Constructs a displacement gradient tensor by copying another one. More...

template<typename OtherNumericType >
constexpr	DisplacementGradient (const DisplacementGradient< OtherNumericType > &other)
	Copy constructor. Constructs a displacement gradient tensor by copying another one. More...

constexpr	DisplacementGradient (DisplacementGradient< NumericType > &&other) noexcept=default
	Move constructor. Constructs a displacement gradient tensor by moving another one. More...

constexpr DisplacementGradient< NumericType > &	operator= (const DisplacementGradient< NumericType > &other)=default
	Copy assignment operator. Assigns this displacement gradient tensor by copying another one. More...

template<typename OtherNumericType >
constexpr DisplacementGradient< NumericType > &	operator= (const DisplacementGradient< OtherNumericType > &other)
	Copy assignment operator. Assigns this displacement gradient tensor by copying another one. More...

constexpr DisplacementGradient< NumericType > &	operator= (DisplacementGradient< NumericType > &&other) noexcept=default
	Move assignment operator. Assigns this displacement gradient tensor by moving another one. More...

constexpr ScalarDisplacementGradient< NumericType >	xx () const noexcept
	Returns the xx Cartesian component of this displacement gradient tensor. More...

constexpr ScalarDisplacementGradient< NumericType >	xy () const noexcept
	Returns the xy Cartesian component of this displacement gradient tensor. More...

constexpr ScalarDisplacementGradient< NumericType >	xz () const noexcept
	Returns the xz Cartesian component of this displacement gradient tensor. More...

constexpr ScalarDisplacementGradient< NumericType >	yx () const noexcept
	Returns the yx Cartesian component of this displacement gradient tensor. More...

constexpr ScalarDisplacementGradient< NumericType >	yy () const noexcept
	Returns the yy Cartesian component of this displacement gradient tensor. More...

constexpr ScalarDisplacementGradient< NumericType >	yz () const noexcept
	Returns the yz Cartesian component of this displacement gradient tensor. More...

constexpr ScalarDisplacementGradient< NumericType >	zx () const noexcept
	Returns the zx Cartesian component of this displacement gradient tensor. More...

constexpr ScalarDisplacementGradient< NumericType >	zy () const noexcept
	Returns the zy Cartesian component of this displacement gradient tensor. More...

constexpr ScalarDisplacementGradient< NumericType >	zz () const noexcept
	Returns the zz Cartesian component of this displacement gradient tensor. More...

constexpr PhQ::Strain< NumericType >	Strain () const
	Creates a strain tensor from this displacement gradient tensor using the definition of the strain tensor. More...

constexpr DisplacementGradient< NumericType >	operator+ (const DisplacementGradient< NumericType > &displacement_gradient) const

constexpr DisplacementGradient< NumericType >	operator- (const DisplacementGradient< NumericType > &displacement_gradient) const

constexpr DisplacementGradient< NumericType >	operator* (const NumericType number) const

constexpr VelocityGradient< NumericType >	operator* (const Frequency< NumericType > &frequency) const

constexpr DisplacementGradient< NumericType >	operator/ (const NumericType number) const

constexpr VelocityGradient< NumericType >	operator/ (const Time< NumericType > &time) const

constexpr void	operator+= (const DisplacementGradient< NumericType > &displacement_gradient) noexcept

constexpr void	operator-= (const DisplacementGradient< NumericType > &displacement_gradient) noexcept

constexpr void	operator*= (const NumericType number) noexcept

constexpr void	operator/= (const NumericType number) noexcept

constexpr const PhQ::Dyad< double > &	Value () const noexcept
	Value of this physical quantity. More...

constexpr PhQ::Dyad< double > &	MutableValue () noexcept
	Returns the value of this physical quantity as a mutable value. More...

constexpr void	SetValue (const PhQ::Dyad< double > &value) noexcept
	Sets the value of this physical quantity to the given value. More...

std::string	Print () const
	Prints this physical quantity as a string. More...

std::string	JSON () const
	Serializes this physical quantity as a JSON message. More...

std::string	XML () const
	Serializes this physical quantity as an XML message. More...

std::string	YAML () const
	Serializes this physical quantity as a YAML message. More...

Static Public Member Functions
static constexpr DisplacementGradient< NumericType >	Zero ()
	Statically creates a displacement gradient tensor of zero. More...

static constexpr PhQ::Dimensions	Dimensions ()
	Physical dimension set of this physical quantity. Since this physical quantity is dimensionless, its physical dimension set is simply the null set. More...

Protected Attributes
PhQ::Dyad< double >	value
	Value of this physical quantity. More...

Detailed Description

template<typename NumericType = double>
class PhQ::DisplacementGradient< NumericType >

Three-dimensional Euclidean displacement gradient dyadic tensor. Gradient of the displacement vector. May be symmetric or asymmetric. Contains nine components in Cartesian coordinates: xx, xy, xz, yx, yy, yz, zx, zy, and zz. For the scalar components or resultants of a displacement gradient tensor, see PhQ::ScalarDisplacementGradient. The time rate of change of a displacement gradient is a velocity gradient; see PhQ::VelocityGradient, PhQ::Time, and PhQ::Frequency.

Definition at line 51 of file DisplacementGradient.hpp.

Constructor & Destructor Documentation

◆ DisplacementGradient() [1/9]

template<typename NumericType = double>

PhQ::DisplacementGradient< NumericType >::DisplacementGradient ( )

default

Default constructor. Constructs a displacement gradient tensor with an uninitialized value.

◆ DisplacementGradient() [2/9]

template<typename NumericType = double>

constexpr PhQ::DisplacementGradient< NumericType >::DisplacementGradient	(	const NumericType	xx,
		const NumericType	xy,
		const NumericType	xz,
		const NumericType	yx,
		const NumericType	yy,
		const NumericType	yz,
		const NumericType	zx,
		const NumericType	zy,
		const NumericType	zz
	)

inlineconstexpr

Constructor. Constructs a displacement gradient tensor whose value has the given xx, xy, xz, yx, yy, yz, zx, zy, and zz Cartesian components.

Definition at line 59 of file DisplacementGradient.hpp.

◆ DisplacementGradient() [3/9]

template<typename NumericType = double>

constexpr PhQ::DisplacementGradient< NumericType >::DisplacementGradient ( const std::array< NumericType, 9 > & xx_xy_xz_yx_yy_yz_zx_zy_zz )

inlineexplicitconstexpr

Constructor. Constructs a displacement gradient tensor from a given array representing its value's xx, xy, xz, yx, yy, yz, zx, zy, and zz Cartesian components.

Definition at line 66 of file DisplacementGradient.hpp.

◆ DisplacementGradient() [4/9]

template<typename NumericType = double>

constexpr PhQ::DisplacementGradient< NumericType >::DisplacementGradient ( const Dyad< NumericType > & value )

inlineexplicitconstexpr

Constructor. Constructs a displacement gradient tensor with a given value.

Definition at line 71 of file DisplacementGradient.hpp.

◆ DisplacementGradient() [5/9]

template<typename NumericType >

constexpr PhQ::DisplacementGradient< NumericType >::DisplacementGradient	(	const VelocityGradient< NumericType > &	velocity_gradient,
		const Time< NumericType > &	time
	)

inlineconstexpr

Constructor. Constructs a displacement gradient tensor from a given velocity gradient tensor and time using the definition of speed.

Definition at line 311 of file VelocityGradient.hpp.

◆ DisplacementGradient() [6/9]

template<typename NumericType >

constexpr PhQ::DisplacementGradient< NumericType >::DisplacementGradient	(	const VelocityGradient< NumericType > &	velocity_gradient,
		const Frequency< NumericType > &	frequency
	)

inlineconstexpr

Constructor. Constructs a displacement gradient tensor from a given velocity gradient tensor and frequency using the definition of speed.

Definition at line 316 of file VelocityGradient.hpp.

◆ ~DisplacementGradient()

template<typename NumericType = double>

PhQ::DisplacementGradient< NumericType >::~DisplacementGradient ( )

defaultnoexcept

Destructor. Destroys this displacement gradient tensor.

◆ DisplacementGradient() [7/9]

template<typename NumericType = double>

constexpr PhQ::DisplacementGradient< NumericType >::DisplacementGradient ( const DisplacementGradient< NumericType > & other )

constexprdefault

Copy constructor. Constructs a displacement gradient tensor by copying another one.

◆ DisplacementGradient() [8/9]

template<typename NumericType = double>

template<typename OtherNumericType >

constexpr PhQ::DisplacementGradient< NumericType >::DisplacementGradient ( const DisplacementGradient< OtherNumericType > & other )

inlineexplicitconstexpr

Copy constructor. Constructs a displacement gradient tensor by copying another one.

Definition at line 92 of file DisplacementGradient.hpp.

◆ DisplacementGradient() [9/9]

template<typename NumericType = double>

constexpr PhQ::DisplacementGradient< NumericType >::DisplacementGradient ( DisplacementGradient< NumericType > && other )

constexprdefaultnoexcept

Move constructor. Constructs a displacement gradient tensor by moving another one.

Member Function Documentation

◆ Dimensions()

static constexpr PhQ::Dimensions PhQ::DimensionlessDyad< double >::Dimensions ( )

inlinestaticconstexprinherited

Physical dimension set of this physical quantity. Since this physical quantity is dimensionless, its physical dimension set is simply the null set.

Definition at line 56 of file DimensionlessDyad.hpp.

◆ JSON()

std::string PhQ::DimensionlessDyad< double >::JSON ( ) const

inlineinherited

Serializes this physical quantity as a JSON message.

Definition at line 81 of file DimensionlessDyad.hpp.

◆ MutableValue()

constexpr PhQ::Dyad<double >& PhQ::DimensionlessDyad< double >::MutableValue ( )

inlineconstexprnoexceptinherited

Returns the value of this physical quantity as a mutable value.

Definition at line 66 of file DimensionlessDyad.hpp.

◆ operator*() [1/2]

template<typename NumericType >

constexpr VelocityGradient< NumericType > PhQ::DisplacementGradient< NumericType >::operator* ( const Frequency< NumericType > & frequency ) const

inlineconstexpr

Definition at line 322 of file VelocityGradient.hpp.

◆ operator*() [2/2]

template<typename NumericType = double>

constexpr DisplacementGradient<NumericType> PhQ::DisplacementGradient< NumericType >::operator* ( const NumericType number ) const

inlineconstexpr

Definition at line 183 of file DisplacementGradient.hpp.

References PhQ::DimensionlessDyad< double >::value.

◆ operator*=()

template<typename NumericType = double>

constexpr void PhQ::DisplacementGradient< NumericType >::operator*= ( const NumericType number )

inlineconstexprnoexcept

Definition at line 205 of file DisplacementGradient.hpp.

References PhQ::DimensionlessDyad< double >::value.

◆ operator+()

template<typename NumericType = double>

constexpr DisplacementGradient<NumericType> PhQ::DisplacementGradient< NumericType >::operator+ ( const DisplacementGradient< NumericType > & displacement_gradient ) const

inlineconstexpr

Definition at line 173 of file DisplacementGradient.hpp.

References PhQ::DimensionlessDyad< NumericType >::value, and PhQ::DimensionlessDyad< double >::value.

◆ operator+=()

template<typename NumericType = double>

constexpr void PhQ::DisplacementGradient< NumericType >::operator+= ( const DisplacementGradient< NumericType > & displacement_gradient )

inlineconstexprnoexcept

Definition at line 195 of file DisplacementGradient.hpp.

References PhQ::DimensionlessDyad< double >::value.

◆ operator-()

template<typename NumericType = double>

constexpr DisplacementGradient<NumericType> PhQ::DisplacementGradient< NumericType >::operator- ( const DisplacementGradient< NumericType > & displacement_gradient ) const

inlineconstexpr

Definition at line 178 of file DisplacementGradient.hpp.

References PhQ::DimensionlessDyad< NumericType >::value, and PhQ::DimensionlessDyad< double >::value.

◆ operator-=()

template<typename NumericType = double>

constexpr void PhQ::DisplacementGradient< NumericType >::operator-= ( const DisplacementGradient< NumericType > & displacement_gradient )

inlineconstexprnoexcept

Definition at line 200 of file DisplacementGradient.hpp.

References PhQ::DimensionlessDyad< double >::value.

◆ operator/() [1/2]

template<typename NumericType = double>

constexpr DisplacementGradient<NumericType> PhQ::DisplacementGradient< NumericType >::operator/ ( const NumericType number ) const

inlineconstexpr

Definition at line 189 of file DisplacementGradient.hpp.

References PhQ::DimensionlessDyad< double >::value.

◆ operator/() [2/2]

template<typename NumericType >

constexpr VelocityGradient< NumericType > PhQ::DisplacementGradient< NumericType >::operator/ ( const Time< NumericType > & time ) const

inlineconstexpr

Definition at line 328 of file VelocityGradient.hpp.

◆ operator/=()

template<typename NumericType = double>

constexpr void PhQ::DisplacementGradient< NumericType >::operator/= ( const NumericType number )

inlineconstexprnoexcept

Definition at line 209 of file DisplacementGradient.hpp.

References PhQ::DimensionlessDyad< double >::value.

◆ operator=() [1/3]

template<typename NumericType = double>

constexpr DisplacementGradient<NumericType>& PhQ::DisplacementGradient< NumericType >::operator= ( const DisplacementGradient< NumericType > & other )

constexprdefault

Copy assignment operator. Assigns this displacement gradient tensor by copying another one.

◆ operator=() [2/3]

template<typename NumericType = double>

template<typename OtherNumericType >

constexpr DisplacementGradient<NumericType>& PhQ::DisplacementGradient< NumericType >::operator= ( const DisplacementGradient< OtherNumericType > & other )

inlineconstexpr

Copy assignment operator. Assigns this displacement gradient tensor by copying another one.

Definition at line 106 of file DisplacementGradient.hpp.

References PhQ::DimensionlessDyad< NumericType >::Value(), and PhQ::DimensionlessDyad< double >::value.

◆ operator=() [3/3]

template<typename NumericType = double>

constexpr DisplacementGradient<NumericType>& PhQ::DisplacementGradient< NumericType >::operator= ( DisplacementGradient< NumericType > && other )

constexprdefaultnoexcept

Move assignment operator. Assigns this displacement gradient tensor by moving another one.

◆ Print()

std::string PhQ::DimensionlessDyad< double >::Print ( ) const

inlineinherited

Prints this physical quantity as a string.

Definition at line 76 of file DimensionlessDyad.hpp.

◆ SetValue()

constexpr void PhQ::DimensionlessDyad< double >::SetValue ( const PhQ::Dyad< double > & value )

inlineconstexprnoexceptinherited

Sets the value of this physical quantity to the given value.

Definition at line 71 of file DimensionlessDyad.hpp.

◆ Strain()

template<typename NumericType = double>

constexpr PhQ::Strain<NumericType> PhQ::DisplacementGradient< NumericType >::Strain ( ) const

inlineconstexpr

Creates a strain tensor from this displacement gradient tensor using the definition of the strain tensor.

Definition at line 169 of file DisplacementGradient.hpp.

◆ Value()

constexpr const PhQ::Dyad<double >& PhQ::DimensionlessDyad< double >::Value ( ) const

inlineconstexprnoexceptinherited

Value of this physical quantity.

Definition at line 61 of file DimensionlessDyad.hpp.

◆ XML()

std::string PhQ::DimensionlessDyad< double >::XML ( ) const

inlineinherited

Serializes this physical quantity as an XML message.

Definition at line 86 of file DimensionlessDyad.hpp.

◆ xx()

template<typename NumericType = double>

constexpr ScalarDisplacementGradient<NumericType> PhQ::DisplacementGradient< NumericType >::xx ( ) const

inlineconstexprnoexcept

Returns the xx Cartesian component of this displacement gradient tensor.

Definition at line 123 of file DisplacementGradient.hpp.

References PhQ::DimensionlessDyad< double >::value, and PhQ::Dyad< NumericType >::xx().

◆ xy()

template<typename NumericType = double>

constexpr ScalarDisplacementGradient<NumericType> PhQ::DisplacementGradient< NumericType >::xy ( ) const

inlineconstexprnoexcept

Returns the xy Cartesian component of this displacement gradient tensor.

Definition at line 128 of file DisplacementGradient.hpp.

References PhQ::DimensionlessDyad< double >::value, and PhQ::Dyad< NumericType >::xy().

◆ xz()

template<typename NumericType = double>

constexpr ScalarDisplacementGradient<NumericType> PhQ::DisplacementGradient< NumericType >::xz ( ) const

inlineconstexprnoexcept

Returns the xz Cartesian component of this displacement gradient tensor.

Definition at line 133 of file DisplacementGradient.hpp.

References PhQ::DimensionlessDyad< double >::value, and PhQ::Dyad< NumericType >::xz().

◆ YAML()

std::string PhQ::DimensionlessDyad< double >::YAML ( ) const

inlineinherited

Serializes this physical quantity as a YAML message.

Definition at line 91 of file DimensionlessDyad.hpp.

◆ yx()

template<typename NumericType = double>

constexpr ScalarDisplacementGradient<NumericType> PhQ::DisplacementGradient< NumericType >::yx ( ) const

inlineconstexprnoexcept

Returns the yx Cartesian component of this displacement gradient tensor.

Definition at line 138 of file DisplacementGradient.hpp.

References PhQ::DimensionlessDyad< double >::value, and PhQ::Dyad< NumericType >::yx().

◆ yy()

template<typename NumericType = double>

constexpr ScalarDisplacementGradient<NumericType> PhQ::DisplacementGradient< NumericType >::yy ( ) const

inlineconstexprnoexcept

Returns the yy Cartesian component of this displacement gradient tensor.

Definition at line 143 of file DisplacementGradient.hpp.

References PhQ::DimensionlessDyad< double >::value, and PhQ::Dyad< NumericType >::yy().

◆ yz()

template<typename NumericType = double>

constexpr ScalarDisplacementGradient<NumericType> PhQ::DisplacementGradient< NumericType >::yz ( ) const

inlineconstexprnoexcept

Returns the yz Cartesian component of this displacement gradient tensor.

Definition at line 148 of file DisplacementGradient.hpp.

References PhQ::DimensionlessDyad< double >::value, and PhQ::Dyad< NumericType >::yz().

◆ Zero()

template<typename NumericType = double>

static constexpr DisplacementGradient<NumericType> PhQ::DisplacementGradient< NumericType >::Zero ( )

inlinestaticconstexpr

Statically creates a displacement gradient tensor of zero.

Definition at line 118 of file DisplacementGradient.hpp.

References PhQ::Dyad< NumericType >::Zero().

◆ zx()

template<typename NumericType = double>

constexpr ScalarDisplacementGradient<NumericType> PhQ::DisplacementGradient< NumericType >::zx ( ) const

inlineconstexprnoexcept

Returns the zx Cartesian component of this displacement gradient tensor.

Definition at line 153 of file DisplacementGradient.hpp.

References PhQ::DimensionlessDyad< double >::value, and PhQ::Dyad< NumericType >::zx().

◆ zy()

template<typename NumericType = double>

constexpr ScalarDisplacementGradient<NumericType> PhQ::DisplacementGradient< NumericType >::zy ( ) const

inlineconstexprnoexcept

Returns the zy Cartesian component of this displacement gradient tensor.

Definition at line 158 of file DisplacementGradient.hpp.

References PhQ::DimensionlessDyad< double >::value, and PhQ::Dyad< NumericType >::zy().

◆ zz()

template<typename NumericType = double>

constexpr ScalarDisplacementGradient<NumericType> PhQ::DisplacementGradient< NumericType >::zz ( ) const

inlineconstexprnoexcept

Returns the zz Cartesian component of this displacement gradient tensor.

Definition at line 163 of file DisplacementGradient.hpp.

References PhQ::DimensionlessDyad< double >::value, and PhQ::Dyad< NumericType >::zz().

Member Data Documentation

◆ value

PhQ::Dyad<double > PhQ::DimensionlessDyad< double >::value

protectedinherited

Value of this physical quantity.

Definition at line 157 of file DimensionlessDyad.hpp.

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

PhQ/DisplacementGradient.hpp
PhQ/VelocityGradient.hpp

Public Member Functions

Static Public Member Functions

Protected Attributes

Detailed Description

template<typename NumericType = double> class PhQ::DisplacementGradient< NumericType >

Constructor & Destructor Documentation

◆ DisplacementGradient() [1/9]

◆ DisplacementGradient() [2/9]

◆ DisplacementGradient() [3/9]

◆ DisplacementGradient() [4/9]

◆ DisplacementGradient() [5/9]

◆ DisplacementGradient() [6/9]

◆ ~DisplacementGradient()

◆ DisplacementGradient() [7/9]

◆ DisplacementGradient() [8/9]

◆ DisplacementGradient() [9/9]

Member Function Documentation

◆ Dimensions()

◆ JSON()

◆ MutableValue()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=()

◆ operator+()

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator/() [1/2]

◆ operator/() [2/2]

◆ operator/=()

◆ operator=() [1/3]

◆ operator=() [2/3]

◆ operator=() [3/3]

◆ Print()

◆ SetValue()

◆ Strain()

◆ Value()

◆ XML()

◆ xx()

◆ xy()

◆ xz()

◆ YAML()

◆ yx()

◆ yy()

◆ yz()

◆ Zero()

◆ zx()

◆ zy()

◆ zz()

Member Data Documentation

◆ value

template<typename NumericType = double>
class PhQ::DisplacementGradient< NumericType >