System that comprises several layers (elastic or plastic). More...

#include <FrictionQPotFEM/UniformMultiLayerIndividualDrive2d.h>

Inheritance diagram for FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System:

Collaboration diagram for FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System:

[legend]

Public Member Functions
	System (const array_type::tensor< double, 2 > &coor, const array_type::tensor< size_t, 2 > &conn, const array_type::tensor< size_t, 2 > &dofs, const array_type::tensor< size_t, 1 > &iip, const std::vector< array_type::tensor< size_t, 1 > > &elem, const std::vector< array_type::tensor< size_t, 1 > > &node, const array_type::tensor< bool, 1 > &layer_is_plastic, const array_type::tensor< double, 2 > &elastic_K, const array_type::tensor< double, 2 > &elastic_G, const array_type::tensor< double, 2 > &plastic_K, const array_type::tensor< double, 2 > &plastic_G, const array_type::tensor< double, 3 > &plastic_epsy, double dt, double rho, double alpha, double eta, const array_type::tensor< bool, 2 > &drive_is_active, double k_drive)
	Define basic geometry. More...

size_t	N () const override
	Return the linear system size (in number of blocks). More...

std::string	type () const override
	Return the type of system. More...

size_t	nlayer () const
	Return number of layers. More...

array_type::tensor< size_t, 1 >	layerElements (size_t i) const
	Return the elements belonging to the i-th layer. More...

array_type::tensor< size_t, 1 >	layerNodes (size_t i) const
	Return the nodes belonging to the i-th layer. More...

const array_type::tensor< bool, 1 > &	layerIsPlastic () const
	Return if a layer is elastic (`false`) or plastic (`true`). More...

void	layerSetDriveStiffness (double k, bool symmetric=true)
	Set the stiffness of the springs connecting the average displacement of a layer ("ubar") to its set target value. More...

template<class S , class T >
double	initEventDriven (const S &ubar, const T &active)
	Initialise the event driven protocol by applying a perturbation to the loading springs and computing and storing the linear, purely elastic, response. More...

template<class S , class T , class U >
double	initEventDriven (const S &ubar, const T &active, const U &delta_u)
	Restore perturbation used from event driven protocol. More...

const array_type::tensor< double, 2 > &	eventDriven_deltaUbar () const
	Get target average position perturbation used for event driven code. More...

const array_type::tensor< bool, 2 > &	eventDriven_targetActive () const
	Get if the target average position is prescribed in the event driven code. More...

double	eventDrivenStep (double deps, bool kick, int direction=+1, bool yield_element=false, bool fallback=false) override
	Add event driven step for the boundary conditions that correspond to the displacement perturbation set in eventDriven_setDeltaU(). More...

template<class T >
void	layerSetTargetActive (const T &active)
	Turn on (or off) springs connecting the average displacement of a layer ("ubar") to its set target value. More...

array_type::tensor< double, 2 >	layerUbar ()
	List the average displacement of each layer. More...

const array_type::tensor< double, 2 > &	layerTargetUbar () const
	List the target average displacement per layer. More...

const array_type::tensor< bool, 2 > &	layerTargetActive () const
	List if the driving spring is activate. More...

template<class T >
void	layerSetTargetUbar (const T &ubar)
	Overwrite the target average displacement per layer. More...

template<class S , class T >
void	layerSetUbar (const S &ubar, const T &prescribe)
	Move the layer such that the average displacement is exactly equal to its input value. More...

template<class T >
array_type::tensor< double, 2 >	layerTargetUbar_affineSimpleShear (double delta_gamma, const T &height) const
	Get target average displacements that correspond to affine simple shear (with the bottom fixed). More...

const array_type::tensor< double, 2 > &	fdrive () const
	Nodal force induced by the driving springs. More...

array_type::tensor< double, 2 >	layerFdrive () const
	Force of each of the driving springs. More...

Public Member Functions inherited from FrictionQPotFEM::Generic2d::System
template<class C , class E , class L , class M , class Y >
	System (const C &coor, const E &conn, const E &dofs, const L &iip, const L &elastic_elem, const M &elastic_K, const M &elastic_G, const L &plastic_elem, const M &plastic_K, const M &plastic_G, const Y &plastic_epsy, double dt, double rho, double alpha, double eta)
	Define the geometry, including boundary conditions and element sets. More...

virtual size_t	N () const
	Return the linear system size (in number of blocks). More...

virtual std::string	type () const
	Return the type of system. More...

double	rho () const
	Mass density. More...

void	setRho (double rho)
	Overwrite the mass density to a homogeneous quantity. More...

template<class T >
void	setMassMatrix (const T &val_elem)
	Overwrite mass matrix, based on certain density that is uniform per element. More...

void	setEta (double eta)
	Overwrite the value of the damping at the interface. More...

double	eta () const
	Get the damping at the interface. More...

void	setAlpha (double alpha)
	Overwrite background damping density (proportional to the velocity), To use a non-homogeneous density use setDampingMatrix(). More...

double	alpha () const
	Background damping density. More...

template<class T >
void	setDampingMatrix (const T &val_elem)
	Overwrite damping matrix, based on certain density (taken uniform per element). More...

bool	isHomogeneousElastic () const
	Check if elasticity is homogeneous. More...

double	dt () const
	Get time step. More...

void	setDt (double dt)
	Overwrite time step. More...

template<class T >
void	setU (const T &u)
	Overwrite nodal displacements. More...

template<class T >
void	setV (const T &v)
	Overwrite nodal velocities. More...

template<class T >
void	setA (const T &a)
	Overwrite nodal accelerations. More...

virtual void	updated_u ()
	Evaluate relevant forces when m_u is updated. More...

void	updated_v ()
	Evaluate relevant forces when m_v is updated. More...

template<class T >
void	setFext (const T &fext)
	Overwrite external force. More...

const auto &	elastic_elem () const
	List of elastic elements. More...

const auto &	plastic_elem () const
	List of plastic elements. More...

const auto &	conn () const
	Connectivity. More...

const auto &	coor () const
	Nodal coordinates. More...

const auto &	dofs () const
	DOFs per node. More...

const auto &	u () const
	Nodal displacements. More...

const auto &	v () const
	Nodal velocities. More...

const auto &	a () const
	Nodal accelerations. More...

auto &	mass () const
	Mass matrix, see System::m_M. More...

auto &	damping () const
	Damping matrix, see setAlpha() and setDampingMatrix(). More...

const auto &	fext ()
	External force. More...

void	applyShearStress (double sigxy)
	Modify the external force such that a shear stress is applied to the top boundary. More...

const auto &	fint ()
	Internal force. More...

const auto &	fmaterial () const
	Force deriving from elasticity. More...

const auto &	fdamp () const
	Force deriving from damping. More...

double	residual () const
	Norm of the relative residual force (the external force at the top/bottom boundaries is used for normalisation). More...

void	quench ()
	Set nodal velocities and accelerations equal to zero. More...

double	t () const
	Current time. More...

void	setT (double arg)
	Overwrite time. More...

size_t	inc () const
	The increment, see setInc(). More...

virtual void	setInc (size_t arg)
	Set increment. More...

const auto &	dV () const
	Integration point volume (of each integration point) More...

const GooseFEM::VectorPartitioned &	vector () const
	GooseFEM vector definition. More...

const GooseFEM::Element::Quad4::Quadrature &	quad () const
	GooseFEM quadrature definition. More...

GMatElastoPlasticQPot::Cartesian2d::Elastic< 2 > &	elastic ()
	Elastic material mode, used for all elastic elements. More...

GMatElastoPlasticQPot::Cartesian2d::Cusp< 2 > &	plastic ()
	Elastic material mode, used for all elastic elements. More...

array_type::tensor< double, 2 >	K () const
	Bulk modulus per integration point. More...

array_type::tensor< double, 2 >	G () const
	Shear modulus per integration point. More...

const array_type::tensor< double, 4 > &	Sig ()
	Stress tensor of each integration point. More...

const array_type::tensor< double, 4 > &	Eps ()
	Strain tensor of each integration point. More...

array_type::tensor< double, 4 >	Epsdot () const
	Strain-rate tensor (the symmetric gradient of the nodal velocities) of each integration point. More...

array_type::tensor< double, 4 >	Epsddot () const
	Symmetric gradient of the nodal accelerations of each integration point. More...

GooseFEM::MatrixPartitioned	stiffness () const
	Stiffness tensor of each integration point. More...

const array_type::tensor< double, 4 > &	plastic_Epsdot ()
	Strain-rate tensor of integration points of plastic elements only, see System::plastic. More...

void	refresh ()
	Recompute all forces. More...

template<class T >
double	eventDriven_setDeltaU (const T &delta_u, bool autoscale=true)
	Set purely elastic and linear response to specific boundary conditions. More...

const auto &	eventDriven_deltaU () const
	Get displacement perturbation used for event driven code, see eventDriven_setDeltaU(). More...

virtual double	eventDrivenStep (double deps, bool kick, int direction=1, bool yield_element=false, bool iterative=false)
	Add event driven step for the boundary conditions that correspond to the displacement perturbation set in eventDriven_setDeltaU(). More...

void	timeStep ()
	Make a time-step: apply velocity-Verlet integration. More...

long	timeSteps (size_t n, size_t nmargin=0)
	Make a number of time steps, see timeStep(). More...

size_t	timeStepsUntilEvent (size_t nmargin=0, double tol=1e-5, size_t niter_tol=20, size_t max_iter=1e7)
	Perform a series of time-steps until the next plastic event, or equilibrium. More...

std::tuple< array_type::tensor< double, 1 >, array_type::tensor< double, 2 >, array_type::tensor< double, 2 > >	minimise_highfrequency (const array_type::tensor< size_t, 1 > &nodes, const array_type::tensor< size_t, 1 > &top, size_t t_step=1, size_t nmargin=0, double tol=1e-5, size_t niter_tol=20, size_t max_iter=1e7)
	Minimise energy while doing a high-frequency measurement of: More...

template<class T >
long	flowSteps (size_t n, const T &v, size_t nmargin=0)
	Make a number of steps with the following protocol. More...

long	minimise (size_t nmargin=0, double tol=1e-5, size_t niter_tol=20, size_t max_iter=1e7, bool time_activity=false, bool max_iter_is_error=true)
	Minimise energy: run System::timeStep until a mechanical equilibrium has been reached. More...

size_t	quasistaticActivityFirst () const
	Increment with the first plastic event. More...

size_t	quasistaticActivityLast () const
	Increment with the last plastic event. More...

template<class T >
size_t	minimise_truncate (const T &idx_n, size_t A_truncate=0, size_t S_truncate=0, double tol=1e-5, size_t niter_tol=20, size_t max_iter=1e7)
	Like Generic2d::minimise(), but stops when a certain number of blocks has yielded at least once. More...

size_t	minimise_truncate (size_t A_truncate=0, size_t S_truncate=0, double tol=1e-5, size_t niter_tol=20, size_t max_iter=1e7)
	Like Generic2d::minimise(), but stops when a certain number of blocks has yielded at least once. More...

array_type::tensor< double, 2 >	affineSimpleShear (double delta_gamma) const
	Get the displacement field that corresponds to an affine simple shear of a certain strain. More...

array_type::tensor< double, 2 >	affineSimpleShearCentered (double delta_gamma) const
	Get the displacement field that corresponds to an affine simple shear of a certain strain. More...

Protected Member Functions
void	computeLayerUbarActive ()
	Compute the average displacement of all layers with an active driving spring. More...

void	computeForceFromTargetUbar ()
	Compute force deriving from the activate springs between the average displacement of the layer and its target value. More...

void	updated_u () override
	Evaluate relevant forces when m_u is updated. More...

void	computeInternalExternalResidualForce () override
	Compute: More...

Protected Member Functions inherited from FrictionQPotFEM::Generic2d::System
void	computeEpsSig ()
	Compute m_Sig and m_Eps using m_u. More...

void	computeForceMaterial ()
	Update m_fmaterial based on the current displacement field m_u. More...

virtual void	computeInternalExternalResidualForce ()
	Compute: More...

Protected Attributes
size_t	m_N
	Linear system size. More...

size_t	m_n_layer
	Number of layers. More...

std::vector< array_type::tensor< size_t, 1 > >	m_layer_node
	Nodes per layer. More...

std::vector< array_type::tensor< size_t, 1 > >	m_layer_elem
	Elements per layer. More...

array_type::tensor< bool, 1 >	m_layer_is_plastic
	Per layer `true` if the layer is plastic. More...

array_type::tensor< size_t, 1 >	m_slice_index
	Per layer the index in m_slice_plas or m_slice_elas. More...

array_type::tensor< size_t, 1 >	m_slice_plas
	How to slice elastic_elem(): start & end index. More...

array_type::tensor< size_t, 1 >	m_slice_elas
	How to slice plastic_elem(): start & end index. More...

bool	m_drive_spring_symmetric
	If false the drive spring buckles in compression. More...

double	m_drive_k
	Stiffness of the drive control frame. More...

array_type::tensor< bool, 2 >	m_layerdrive_active
	See `prescribe` in layerSetTargetUbar() More...

array_type::tensor< double, 2 >	m_layerdrive_targetubar
	Per layer, the prescribed average position. More...

array_type::tensor< double, 2 >	m_layer_ubar
	See computeLayerUbarActive(). More...

array_type::tensor< double, 2 >	m_fdrive
	Force related to driving frame. More...

array_type::tensor< double, 2 >	m_layer_dV1
	volume per layer (as vector, same for all dimensions) More...

array_type::tensor< double, 2 >	m_dV
	copy of m_quad.dV() More...

array_type::tensor< double, 3 >	m_uq
	qvector More...

array_type::tensor< double, 1 >	m_ud
	dofval More...

array_type::tensor< bool, 2 >	m_pert_layerdrive_active
	Event driven: applied lever setting. More...

array_type::tensor< double, 2 >	m_pert_layerdrive_targetubar
	Event driven: applied lever setting. More...

Protected Attributes inherited from FrictionQPotFEM::Generic2d::System
array_type::tensor< double, 2 >	m_coor
	Nodal coordinates, see coor(). More...

size_t	m_N
	Number of plastic elements, alias of m_nelem_plas. More...

size_t	m_nelem
	Number of elements. More...

size_t	m_nelem_elas
	Number of elastic elements. More...

size_t	m_nelem_plas
	Number of plastic elements. More...

size_t	m_nne
	Number of nodes per element. More...

size_t	m_nnode
	Number of nodes. More...

size_t	m_ndim
	Number of spatial dimensions. More...

size_t	m_nip
	Number of integration points. More...

array_type::tensor< size_t, 1 >	m_elem_elas
	Elastic elements. More...

array_type::tensor< size_t, 1 >	m_elem_plas
	Plastic elements. More...

GooseFEM::Element::Quad4::Quadrature	m_quad
	Quadrature for all elements. More...

GooseFEM::Element::Quad4::Quadrature	m_quad_elas
	m_quad for elastic elements only. More...

GooseFEM::Element::Quad4::Quadrature	m_quad_plas
	m_quad for plastic elements only. More...

GooseFEM::VectorPartitioned	m_vector
	Convert vectors between 'nodevec', 'elemvec', .... More...

GooseFEM::VectorPartitioned	m_vector_elas
	m_vector for elastic elements only. More...

GooseFEM::VectorPartitioned	m_vector_plas
	m_vector for plastic elements only. More...

GooseFEM::MatrixDiagonalPartitioned	m_M
	Mass matrix (diagonal). More...

GooseFEM::MatrixDiagonal	m_D
	Damping matrix (diagonal). More...

GMatElastoPlasticQPot::Cartesian2d::Elastic< 2 >	m_elas
	Material for elastic el. More...

GMatElastoPlasticQPot::Cartesian2d::Cusp< 2 >	m_plas
	Material for plastic el. More...

array_type::tensor< double, 2 >	m_u
	Nodal displacements. More...

array_type::tensor< double, 2 >	m_v
	Nodal velocities. More...

array_type::tensor< double, 2 >	m_a
	Nodal accelerations. More...

array_type::tensor< double, 2 >	m_v_n
	Nodal velocities last time-step. More...

array_type::tensor< double, 2 >	m_a_n
	Nodal accelerations last time-step. More...

array_type::tensor< double, 3 >	m_ue
	Element vector (used for displacements). More...

array_type::tensor< double, 3 >	m_fe
	Element vector (used for forces). More...

array_type::tensor< double, 3 >	m_ue_elas
	m_ue for elastic element only More...

array_type::tensor< double, 3 >	m_fe_elas
	m_fe for elastic element only More...

array_type::tensor< double, 3 >	m_ue_plas
	m_ue for plastic element only More...

array_type::tensor< double, 3 >	m_fe_plas
	m_fe for plastic element only More...

array_type::tensor< double, 2 >	m_fmaterial
	Nodal force, deriving from elasticity. More...

array_type::tensor< double, 2 >	m_felas
	Nodal force from elasticity of elastic elements. More...

array_type::tensor< double, 2 >	m_fplas
	Nodal force from elasticity of plastic elements. More...

array_type::tensor< double, 2 >	m_fdamp
	Nodal force from damping. More...

array_type::tensor< double, 2 >	m_fvisco
	Nodal force from damping at the interface. More...

array_type::tensor< double, 2 >	m_ftmp
	Temporary for internal use. More...

array_type::tensor< double, 2 >	m_fint
	Nodal force: total internal force. More...

array_type::tensor< double, 2 >	m_fext
	Nodal force: total external force (reaction force) More...

array_type::tensor< double, 2 >	m_fres
	Nodal force: residual force. More...

array_type::tensor< double, 4 >	m_Eps
	Quad-point tensor: strain. More...

array_type::tensor< double, 4 >	m_Sig
	Quad-point tensor: stress. More...

array_type::tensor< double, 4 >	m_Epsdot_plas
	Quad-point tensor: strain-rate for plastic el. More...

GooseFEM::Matrix	m_K_elas
	Stiffness matrix for elastic elements only. More...

size_t	m_qs_inc_first = 0
	First increment with plastic activity during minimisation. More...

size_t	m_qs_inc_last = 0
	Last increment with plastic activity during minimisation. More...

size_t	m_inc
	Current increment (current time = m_dt * m_inc). More...

double	m_dt
	Time-step. More...

double	m_eta
	Damping at the interface. More...

double	m_rho
	Mass density (non-zero only if homogeneous). More...

double	m_alpha
	Background damping density (non-zero only if homogeneous). More...

bool	m_set_D
	Use m_D only if it is non-zero. More...

bool	m_set_visco
	Use m_eta only if it is non-zero. More...

bool	m_full_outdated
	Keep track of the need to recompute fields on full geometry. More...

array_type::tensor< double, 2 >	m_pert_u
	See eventDriven_setDeltaU() More...

array_type::tensor< double, 4 >	m_pert_Epsd_plastic
	Strain deviator for m_pert_u. More...

Detailed Description

System that comprises several layers (elastic or plastic).

The average displacement of each layer can be coupled to a prescribed target value using a linear spring (one spring per spatial dimension):

To set its stiffness use layerSetDriveStiffness().
Each spring can be switched on individually using layerSetTargetActive(). By default all springs are inactive (their stiffness is effectively zero).

Terminology:

ubar: the average displacement per layer [nlayer, 2], see layerUbar() and layerSetUbar().
target_ubar: the target average displacement per layer [nlayer, 2], see layerTargetUbar() and layerSetTargetUbar().
target_active: the average displacement per layer/DOF is only enforced if the spring is active, see layerTargetActive() and layerSetTargetActive().

Definition at line 57 of file UniformMultiLayerIndividualDrive2d.h.

Constructor & Destructor Documentation

◆ ~System()

virtual FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::~System ( )

inlinevirtual

Reimplemented from FrictionQPotFEM::Generic2d::System.

Definition at line 62 of file UniformMultiLayerIndividualDrive2d.h.

◆ System()

FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::System	(	const array_type::tensor< double, 2 > &	coor,
		const array_type::tensor< size_t, 2 > &	conn,
		const array_type::tensor< size_t, 2 > &	dofs,
		const array_type::tensor< size_t, 1 > &	iip,
		const std::vector< array_type::tensor< size_t, 1 > > &	elem,
		const std::vector< array_type::tensor< size_t, 1 > > &	node,
		const array_type::tensor< bool, 1 > &	layer_is_plastic,
		const array_type::tensor< double, 2 > &	elastic_K,
		const array_type::tensor< double, 2 > &	elastic_G,
		const array_type::tensor< double, 2 > &	plastic_K,
		const array_type::tensor< double, 2 > &	plastic_G,
		const array_type::tensor< double, 3 > &	plastic_epsy,
		double	dt,
		double	rho,
		double	alpha,
		double	eta,
		const array_type::tensor< bool, 2 > &	drive_is_active,
		double	k_drive
	)

inline

Define basic geometry.

Parameters

coor	Nodal coordinates.
conn	Connectivity.
dofs	DOFs per node.
iip	DOFs whose displacement is fixed.
elem	Elements per layer.
node	Nodes per layer.
layer_is_plastic	Per layer set if elastic (= 0) or plastic (= 1).
elastic_K	Bulk modulus per quad. point of each elastic element, see setElastic().
elastic_G	Shear modulus per quad. point of each elastic element, see setElastic().
plastic_K	Bulk modulus per quad. point of each plastic element, see Plastic().
plastic_G	Shear modulus per quad. point of each plastic element, see Plastic().
plastic_epsy	Yield strain per quad. point of each plastic element, see Plastic().
dt	Time step, set setDt().
rho	Mass density, see setMassMatrix().
alpha	Background damping density, see setDampingMatrix().
eta	Damping at the interface (homogeneous), see setEta().
drive_is_active	Per layer (de)activate drive for each DOF, see layerSetTargetActive().
k_drive	Stiffness of driving spring, see layerSetDriveStiffness().

Definition at line 86 of file UniformMultiLayerIndividualDrive2d.h.

Member Function Documentation

◆ computeForceFromTargetUbar()

void FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::computeForceFromTargetUbar ( )

inlineprotected

Compute force deriving from the activate springs between the average displacement of the layer and its target value.

The force is applied as a force density.

Internal rule: computeLayerUbarActive() is called before this function, if the displacement changed since the last time the average was computed.

Definition at line 721 of file UniformMultiLayerIndividualDrive2d.h.

◆ computeInternalExternalResidualForce()

void FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::computeInternalExternalResidualForce ( )

inlineoverrideprotectedvirtual

Compute:

m_fint = m_fdrive + m_fmaterial + m_fdamp
m_fext[iip] = m_fint[iip]
m_fres = m_fext - m_fint

Internal rule: all relevant forces are expected to be updated before this function is called.

Reimplemented from FrictionQPotFEM::Generic2d::System.

Definition at line 765 of file UniformMultiLayerIndividualDrive2d.h.

◆ computeLayerUbarActive()

void FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::computeLayerUbarActive ( )

inlineprotected

Compute the average displacement of all layers with an active driving spring.

Definition at line 690 of file UniformMultiLayerIndividualDrive2d.h.

◆ eventDriven_deltaUbar()

const array_type::tensor< double, 2 > & FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::eventDriven_deltaUbar ( ) const

inline

Get target average position perturbation used for event driven code.

Returns: [nlayer, 2]

Definition at line 475 of file UniformMultiLayerIndividualDrive2d.h.

◆ eventDriven_targetActive()

const array_type::tensor< bool, 2 > & FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::eventDriven_targetActive ( ) const

inline

Get if the target average position is prescribed in the event driven code.

Returns: [nlayer, 2]

Definition at line 484 of file UniformMultiLayerIndividualDrive2d.h.

◆ eventDrivenStep()

double FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::eventDrivenStep	(	double	deps,
		bool	kick,
		int	direction = `+1`,
		bool	yield_element = `false`,
		bool	iterative = `false`
	)

inlineoverridevirtual

Add event driven step for the boundary conditions that correspond to the displacement perturbation set in eventDriven_setDeltaU().

Todo:: The current implementation is suited for unloading, but only until the first yield strain. An improved implementation is needed to deal with the symmetry of the equivalent strain. A FRICTIONQPOTFEM_WIP assertion is made.

Parameters

deps	Size of the local stain kick to apply.
kick	If `false`, increment displacements to `deps / 2` of yielding again. If `true`, increment displacements by a affine simple shear increment `deps`.
direction	If `+1`: apply shear to the right. If `-1` applying shear to the left.
yield_element	If `true` and `kick == true` then the element closest to yielding is selected (as normal), but of that element the displacement update is the maximum of the element, such that all integration points of the element are forced to yield.
iterative	If `true` the step is iteratively searched. This is more costly by recommended, if the perturbation is non-analytical (and contains numerical errors).

Returns: Factor with which the displacement perturbation, see eventDriven_deltaU(), is scaled.

Reimplemented from FrictionQPotFEM::Generic2d::System.

Reimplemented in FrictionQPotFEM::UniformMultiLayerLeverDrive2d::System.

Definition at line 489 of file UniformMultiLayerIndividualDrive2d.h.

◆ fdrive()

const array_type::tensor< double, 2 > & FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::fdrive ( ) const

inline

Nodal force induced by the driving springs.

The only non-zero contribution comes from:

springs that are active, see layerSetTargetActive(), and
layers whose average displacement is different from its target value.

Returns: nodevec [nnode, ndim].

Definition at line 658 of file UniformMultiLayerIndividualDrive2d.h.

◆ initEventDriven() [1/2]

template<class S , class T >

double FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::initEventDriven	(	const S &	ubar,
		const T &	active
	)

inline

Initialise the event driven protocol by applying a perturbation to the loading springs and computing and storing the linear, purely elastic, response.

The system can thereafter be moved forward to the next event. Note that this function itself does not change the system in any way, it just stores the relevant perturbations.

Template Parameters

S	`array_type::tensor<double, 2>`

Parameters

ubar	The perturbation in the target average position of each layer [nlayer, 2].

Template Parameters

T	`array_type::tensor<bool, 2>`

Parameters

active For each layer and each degree-of-freedom specify if the spring is active (true) or not (false) [nlayer, 2].

Returns: Value with which the input perturbation is scaled, see also eventDriven_deltaUbar().

Definition at line 388 of file UniformMultiLayerIndividualDrive2d.h.

◆ initEventDriven() [2/2]

template<class S , class T , class U >

double FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::initEventDriven	(	const S &	ubar,
		const T &	active,
		const U &	delta_u
	)

inline

Restore perturbation used from event driven protocol.

Parameters

ubar	See eventDriven_deltaUbar().
active	See eventDriven_targetActive().
delta_u	See eventDriven_deltaU().

Returns: Value with which the input perturbation is scaled, see also eventDriven_deltaU().

Definition at line 460 of file UniformMultiLayerIndividualDrive2d.h.

◆ layerElements()

array_type::tensor< size_t, 1 > FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::layerElements ( size_t i ) const

inline

Return the elements belonging to the i-th layer.

Parameters

i	Index of the layer.

Returns: List of element numbers.

Definition at line 325 of file UniformMultiLayerIndividualDrive2d.h.

◆ layerFdrive()

array_type::tensor< double, 2 > FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::layerFdrive ( ) const

inline

Force of each of the driving springs.

The only non-zero contribution comes from:

springs that are active, see layerSetTargetActive(), and
layers whose average displacement is different from its target value.

Returns: [nlayer, ndim].

Definition at line 671 of file UniformMultiLayerIndividualDrive2d.h.

◆ layerIsPlastic()

const array_type::tensor< bool, 1 > & FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::layerIsPlastic ( ) const

inline

Return if a layer is elastic (false) or plastic (true).

Returns: [nlayer].

Definition at line 346 of file UniformMultiLayerIndividualDrive2d.h.

◆ layerNodes()

array_type::tensor< size_t, 1 > FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::layerNodes ( size_t i ) const

inline

Return the nodes belonging to the i-th layer.

Parameters

i	Index of the layer.

Returns: List of node numbers.

Definition at line 336 of file UniformMultiLayerIndividualDrive2d.h.

◆ layerSetDriveStiffness()

void FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::layerSetDriveStiffness	(	double	k,
		bool	symmetric = `true`
	)

inline

Set the stiffness of the springs connecting the average displacement of a layer ("ubar") to its set target value.

Note that the stiffness of all springs is taken the same.

Parameters

k	The stiffness.
symmetric	If `true` the spring is a normal spring. If `false` the spring has no stiffness under compression.

Definition at line 361 of file UniformMultiLayerIndividualDrive2d.h.

◆ layerSetTargetActive()

template<class T >

void FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::layerSetTargetActive ( const T & active )

inline

Turn on (or off) springs connecting the average displacement of a layer ("ubar") to its set target value.

Template Parameters

T	e.g. `array_type::tensor<bool, 2>`

Parameters

active For each layer and each degree-of-freedom specify if the spring is active (true) or not (false) [nlayer, 2].

Definition at line 512 of file UniformMultiLayerIndividualDrive2d.h.

◆ layerSetTargetUbar()

template<class T >

void FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::layerSetTargetUbar ( const T & ubar )

inline

Overwrite the target average displacement per layer.

Only layers that have an active driving spring will feel a force (if its average displacement is different from the target displacement), see layerSetTargetActive().

Template Parameters

T	e.g. `array_type::tensor<double, 2>`

Parameters

ubar	The target average position of each layer [nlayer, 2].

Definition at line 582 of file UniformMultiLayerIndividualDrive2d.h.

◆ layerSetUbar()

template<class S , class T >

void FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::layerSetUbar	(	const S &	ubar,
		const T &	prescribe
	)

inline

Move the layer such that the average displacement is exactly equal to its input value.

Template Parameters

S	e.g. `array_type::tensor<double, 2>`
T	e.g. `array_type::tensor<bool, 2>`

Parameters

ubar	The target average position of each layer [nlayer, 2].
prescribe	Per layers/degree-of-freedom specify if its average is modified [nlayer, 2]. Note that this not modify which of the driving springs is active or not, that can only be changed using layerSetTargetActive().

Definition at line 604 of file UniformMultiLayerIndividualDrive2d.h.

◆ layerTargetActive()

const array_type::tensor< bool, 2 > & FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::layerTargetActive ( ) const

inline

List if the driving spring is activate.

Returns: [nlayer, 2]

Definition at line 567 of file UniformMultiLayerIndividualDrive2d.h.

◆ layerTargetUbar()

const array_type::tensor< double, 2 > & FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::layerTargetUbar ( ) const

inline

List the target average displacement per layer.

Returns: [nlayer, 2]

Definition at line 558 of file UniformMultiLayerIndividualDrive2d.h.

◆ layerTargetUbar_affineSimpleShear()

template<class T >

array_type::tensor< double, 2 > FrictionQPotFEM::UniformMultiLayerIndividualDrive2d::System::layerTargetUbar_affineSimpleShear	(	double	delta_gamma,
		const T &	height
	)		const

inline

Get target average displacements that correspond to affine simple shear (with the bottom fixed).

In particular \( \bar{u}_x^i = 2 \Delta \gamma h_i \) with \( \bar{u}_x^i \) the \( x \)-component of the target average displacement of layer \( i \).

Template Parameters