A Finite Element Method (FEM) simulator used for simulating the deformation of objects. More...

#include <fem_simulator.hpp>

Public Member Functions
	FEMSimulator ()
	Constructs a new `FEMSimulator` object.

void	SetMesh (TetMesh const &tetmesh)
	Sets the tetrahedral mesh used in the simulation.

void	Init ()
	Initializes the FEM simulator object for this object.

void	SetBCNodalVelocity (int nid, double vx, double vy, double vz, bool use_prescribed_vx, bool use_prescribed_vy, bool use_prescribed_vz)
	Sets the prescribed velocity for a certain node on the boundary of the object.

void	AddBCFacetForce (int bc_fid, double fx, double fy, double fz)
	Adds a force to a facet on the surface of the object.

void	SetNodalVels (double v_x, double v_y, double v_z)
	Sets the nodal velocities for all nodes on the boundary of the object.

void	ClearBoundaryCondition ()
	Clears all boundary conditions from the object.

void	Solve (double dt)
	Solves for the motion and deformation of the object at each time step.

VecXT< Vec3d >	GetNodalPositions (VecXT< int > nids)
	Gets the positions of a set of nodes in the tetrahedral mesh.

VecXT< Vec3d >	GetNodalDisps (VecXT< int > nids)
	Gets the displacements of a set of nodes in the tetrahedral mesh.

VecXT< Vec3d >	GetNodalVels (VecXT< int > nids)
	Gets the velocities of a set of nodes in the tetrahedral mesh.

void	SaveAsVTK (std::string const &file_name)
	Saves the object as a VTK file.

Public Attributes
double	neo_k {6.94e5}
	The bulk modulus of the material being simulated.

double	neo_mu {5.21e5}
	The shear modulus of the material being simulated.

double	density {500.0}
	The density of the material being simulated.

double	damp_coef {0.7}
	The damping coefficient used in the simulation.

Vec3d	gravity_coef {0.0, 0.0, 0.0}
	The gravitational force acting on the object.

double	timestep {1.0e-4}
	The time step used in the simulation.

VecXT< Vec3d >	nodes
	The nodal positions of the tetrahedral mesh.

VecXT< Vec4i >	elements
	The elements of the tetrahedral mesh.

VecXT< Vec3d >	nodes_ref
	The reference nodal positions of the tetrahedral mesh.

VecXT< Vec3i >	bound_facets
	The facets of the object that define its bounding surface.

VecXT< int >	bound_nodes
	The IDs of the nodes on the bounding surface.

VecXT< double >	elemental_vol
	The volume of each element in the tetrahedral mesh.

VecXT< VecNT< double, 6 > >	elemental_stress
	The stress values of each element in the tetrahedral mesh.

VecXT< double >	nodal_vols
	The volume of each node in the tetrahedral mesh.

VecXT< Vec3d >	nodal_vels
	The velocity of each node in the tetrahedral mesh.

VecXT< Vec3d >	bc_facet_forces
	The forces applied to each facet on the boundary of the object.

VecXT< VecNT< double, 6 > >	bc_nodal_vels
	The prescribed velocities for each node on the boundary of the object.

Protected Member Functions
void	Advance (double dt)
	Advances the object by one time step.

void	InitInitialCondition ()
	Initializes the initial condition for the FEM simulator.

double	GetElementVolume (Vec3d const &v0, Vec3d const &v1, Vec3d const &v2, Vec3d const &v3)
	Calculates the volume of a tetrahedral element.

Mat3d	GetDeformationGradient (Vec3d const &v0_new, Vec3d const &v1_new, Vec3d const &v2_new, Vec3d const &v3_new, Vec3d const &v0_ref, Vec3d const &v1_ref, Vec3d const &v2_ref, Vec3d const &v3_ref)
	Calculates the deformation gradient of a tetrahedral element.

Mat3d	GetCauchyStress (Mat3d const &def_grad)
	Calculates the Cauchy stress tensor for a given deformation gradient.

MatNd< 4, 3 >	GetInternalForces (Mat3d const &cauchy_stress, Vec3d const &v0, Vec3d const &v1, Vec3d const &v2, Vec3d const &v3)
	Calculates the internal forces acting on each node of a tetrahedral element.

Protected Attributes
VecXT< Vec3d >	nodal_forces_int
	< The internal forces acting on each node.

VecXT< Vec3d >	nodal_forces_ext
	The average nodal velocities used in the simulation.

VecXT< Vec3d >	nodal_vels_ave

Detailed Description

A Finite Element Method (FEM) simulator used for simulating the deformation of objects.

This class contains all the necessary data and functions to simulate the motion and deformation of an object using FEM. It includes a tetrahedral mesh, elemental stress values, nodal velocities, and boundary conditions. Functions are provided to initialize the simulation, set boundary conditions, and solve for the motion and deformation of the object at each time step.

Constructor & Destructor Documentation

◆ FEMSimulator()

FEMSimulator::FEMSimulator ( )

Constructs a new FEMSimulator object.

Member Function Documentation

◆ AddBCFacetForce()

void FEMSimulator::AddBCFacetForce	(	int	bc_fid,
		double	fx,
		double	fy,
		double	fz )

Adds a force to a facet on the surface of the object.

This function adds a force to a specified facet on the surface of the object. The force is applied only at the nodes of the facet.

Parameters

bc_fid	The ID of the facet to add the force to.
fx	The X component of the force to apply.
fy	The Y component of the force to apply.
fz	The Z component of the force to apply.

◆ Advance()

void FEMSimulator::Advance ( double dt )

protected

Advances the object by one time step.

This function advances the object by one time step. It calculates the internal and external forces acting on each node, applies any prescribed boundary conditions, and then updates the positions and velocities of each node based on these forces using an explicit Euler method.

Parameters

dt	The time step to use for the simulation.

◆ ClearBoundaryCondition()

void FEMSimulator::ClearBoundaryCondition ( )

Clears all boundary conditions from the object.

This function clears all boundary conditions from the object by setting all values in bc_nodal_vels and bc_facet_forces to zero.

◆ GetCauchyStress()

Mat3d FEMSimulator::GetCauchyStress ( Mat3d const & def_grad )

protected

Calculates the Cauchy stress tensor for a given deformation gradient.

This function calculates the Cauchy stress tensor for a given deformation gradient using the neo-Hookean model of hyperelasticity.

Parameters

def_grad The deformation gradient of an element in the mesh.

Returns: The Cauchy stress tensor as a Mat3d object.

◆ GetDeformationGradient()

Mat3d FEMSimulator::GetDeformationGradient	(	Vec3d const &	v0_new,
		Vec3d const &	v1_new,
		Vec3d const &	v2_new,
		Vec3d const &	v3_new,
		Vec3d const &	v0_ref,
		Vec3d const &	v1_ref,
		Vec3d const &	v2_ref,
		Vec3d const &	v3_ref )

protected

Calculates the deformation gradient of a tetrahedral element.

This function calculates the deformation gradient of a tetrahedral element specified by its four new vertices and their corresponding reference vertices.

Parameters

v0_new	The new position of the first vertex of the tetrahedron.
v1_new	The new position of the second vertex of the tetrahedron.
v2_new	The new position of the third vertex of the tetrahedron.
v3_new	The new position of the fourth vertex of the tetrahedron.
v0_ref	The reference position of the first vertex of the tetrahedron.
v1_ref	The reference position of the second vertex of the tetrahedron.
v2_ref	The reference position of the third vertex of the tetrahedron.
v3_ref	The reference position of the fourth vertex of the tetrahedron.

Returns: The deformation gradient of the tetrahedron as a Mat3d object.

◆ GetElementVolume()

double FEMSimulator::GetElementVolume	(	Vec3d const &	v0,
		Vec3d const &	v1,
		Vec3d const &	v2,
		Vec3d const &	v3 )

protected

Calculates the volume of a tetrahedral element.

This function calculates the volume of a tetrahedral element specified by its four vertices.

Parameters

v0	The first vertex of the tetrahedron.
v1	The second vertex of the tetrahedron.
v2	The third vertex of the tetrahedron.
v3	The fourth vertex of the tetrahedron.

Returns: The volume of the tetrahedron.

◆ GetInternalForces()

MatNd< 4, 3 > FEMSimulator::GetInternalForces	(	Mat3d const &	cauchy_stress,
		Vec3d const &	v0,
		Vec3d const &	v1,
		Vec3d const &	v2,
		Vec3d const &	v3 )

protected

Calculates the internal forces acting on each node of a tetrahedral element.

This function calculates the internal forces acting on each node of a tetrahedral element using the Cauchy stress tensor and the deformation gradient of the element.

Parameters

cauchy_stress	The Cauchy stress tensor of the element.
v0,v1,v2,v3	The vertices of the tetrahedron.

Returns: The internal forces acting on each node as a MatNd<4, 3> object.

◆ GetNodalDisps()

VecXT< Vec3d > FEMSimulator::GetNodalDisps ( VecXT< int > nids )

Gets the displacements of a set of nodes in the tetrahedral mesh.

This function returns the displacements of a set of nodes in the tetrahedral mesh specified by their IDs. The displacements are calculated as the difference between the current and reference positions of each node, and are returned as a VecXT<Vec3d> object containing a vector of Vec3d objects representing the displacement of each node.

Parameters

nids	A vector of node IDs to get the displacements of.

Returns: A VecXT<Vec3d> object containing the displacements of the specified nodes.

◆ GetNodalPositions()

VecXT< Vec3d > FEMSimulator::GetNodalPositions ( VecXT< int > nids )

Gets the positions of a set of nodes in the tetrahedral mesh.

This function returns the positions of a set of nodes in the tetrahedral mesh specified by their IDs. The positions are returned as a VecXT<Vec3d> object containing a vector of Vec3d objects representing the position of each node.

Parameters

nids	A vector of node IDs to get the positions of.

Returns: A VecXT<Vec3d> object containing the positions of the specified nodes.

◆ GetNodalVels()

VecXT< Vec3d > FEMSimulator::GetNodalVels ( VecXT< int > nids )

Gets the velocities of a set of nodes in the tetrahedral mesh.

This function returns the velocities of a set of nodes in the tetrahedral mesh specified by their IDs. The velocities are returned as a VecXT<Vec3d> object containing a vector of Vec3d objects representing the velocity of each node.

Parameters

nids	A vector of node IDs to get the velocities of.

Returns: A VecXT<Vec3d> object containing the velocities of the specified nodes.

◆ Init()

void FEMSimulator::Init ( )

Initializes the FEM simulator object for this object.

This function initializes the FEM simulator object for this object by setting up the nodal forces and velocities, elemental volumes and stresses, and boundary conditions for the simulation.

◆ InitInitialCondition()

void FEMSimulator::InitInitialCondition ( )

protected

Initializes the initial condition for the FEM simulator.

This function initializes the initial condition for the FEM simulator by setting up the nodal volumes and velocities that will be used in the simulation.

◆ SaveAsVTK()

void FEMSimulator::SaveAsVTK ( std::string const & file_name )

Saves the object as a VTK file.

This function saves the object, including its tetrahedral mesh and nodal properties, to a VTK file.

Parameters

file_name The name of the file to save the data in.

◆ SetBCNodalVelocity()

void FEMSimulator::SetBCNodalVelocity	(	int	nid,
		double	vx,
		double	vy,
		double	vz,
		bool	use_prescribed_vx,
		bool	use_prescribed_vy,
		bool	use_prescribed_vz )

Sets the prescribed velocity for a certain node on the boundary of the object.

This function sets the prescribed velocity for a certain node on the boundary of the object, specifying the velocity components in each dimension and whether or not to use velocity as a prescribed value in that dimension.

Parameters

nid	The ID of the node to set the velocity for.
vx	The X component of the prescribed velocity.
vy	The Y component of the prescribed velocity.
vz	The Z component of the prescribed velocity.
use_prescribed_vx	Whether or not to use the X-component of the velocity as a prescribed value.
use_prescribed_vy	Whether or not to use the Y-component of the velocity as a prescribed value.
use_prescribed_vz	Whether or not to use the Z-component of the velocity as a prescribed value.

◆ SetMesh()

void FEMSimulator::SetMesh ( TetMesh const & tetmesh )

Sets the tetrahedral mesh used in the simulation.

This function sets the tetrahedral mesh used in the simulation by copying its nodes and elements into the nodes and elements member variables of this object.

Parameters

tetmesh A reference to the TetMesh object representing the tetrahedral mesh.

◆ SetNodalVels()

void FEMSimulator::SetNodalVels	(	double	v_x,
		double	v_y,
		double	v_z )

Sets the nodal velocities for all nodes on the boundary of the object.

This function sets the nodal velocities for all nodes on the boundary of the object, specifying the velocity components in each dimension.

Parameters

v_x	The X component of the nodal velocity.
v_y	The Y component of the nodal velocity.
v_z	The Z component of the nodal velocity.

◆ Solve()

void FEMSimulator::Solve ( double dt )

Solves for the motion and deformation of the object at each time step.

This function solves for the motion and deformation of the object at each time step using FEM. It first calculates the internal and external forces acting on each node, applies any prescribed boundary conditions, and then updates the positions and velocities of each node based on these forces using an explicit Euler method.

Parameters

dt	The time step to use for the simulation.

Member Data Documentation

◆ bc_facet_forces

VecXT<Vec3d> netdem::FEMSimulator::bc_facet_forces

The forces applied to each facet on the boundary of the object.

◆ bc_nodal_vels

VecXT<VecNT<double, 6> > netdem::FEMSimulator::bc_nodal_vels

The prescribed velocities for each node on the boundary of the object.

◆ bound_facets

VecXT<Vec3i> netdem::FEMSimulator::bound_facets

The facets of the object that define its bounding surface.

◆ bound_nodes

VecXT<int> netdem::FEMSimulator::bound_nodes

The IDs of the nodes on the bounding surface.

◆ damp_coef

double netdem::FEMSimulator::damp_coef {0.7}

The damping coefficient used in the simulation.

Examples: 81_golf_ball_impact.cpp.

◆ density

double netdem::FEMSimulator::density {500.0}

The density of the material being simulated.

◆ elemental_stress

VecXT<VecNT<double, 6> > netdem::FEMSimulator::elemental_stress

The stress values of each element in the tetrahedral mesh.

◆ elemental_vol

VecXT<double> netdem::FEMSimulator::elemental_vol

The volume of each element in the tetrahedral mesh.

◆ elements

VecXT<Vec4i> netdem::FEMSimulator::elements

The elements of the tetrahedral mesh.

◆ gravity_coef

Vec3d netdem::FEMSimulator::gravity_coef {0.0, 0.0, 0.0}

The gravitational force acting on the object.

Examples: 00_hertz_contact.cpp.

◆ neo_k

double netdem::FEMSimulator::neo_k {6.94e5}

The bulk modulus of the material being simulated.

Examples: 81_golf_ball_impact.cpp.

◆ neo_mu

double netdem::FEMSimulator::neo_mu {5.21e5}

The shear modulus of the material being simulated.

Examples: 81_golf_ball_impact.cpp.

◆ nodal_forces_ext

VecXT<Vec3d> netdem::FEMSimulator::nodal_forces_ext

protected

The average nodal velocities used in the simulation.

◆ nodal_forces_int

VecXT<Vec3d> netdem::FEMSimulator::nodal_forces_int

protected

< The internal forces acting on each node.

The external forces acting on each node.

◆ nodal_vels

VecXT<Vec3d> netdem::FEMSimulator::nodal_vels

The velocity of each node in the tetrahedral mesh.

◆ nodal_vels_ave

VecXT<Vec3d> netdem::FEMSimulator::nodal_vels_ave

protected

◆ nodal_vols

VecXT<double> netdem::FEMSimulator::nodal_vols

The volume of each node in the tetrahedral mesh.

◆ nodes

VecXT<Vec3d> netdem::FEMSimulator::nodes

The nodal positions of the tetrahedral mesh.

◆ nodes_ref

VecXT<Vec3d> netdem::FEMSimulator::nodes_ref

The reference nodal positions of the tetrahedral mesh.

◆ timestep

double netdem::FEMSimulator::timestep {1.0e-4}

The time step used in the simulation.

Examples: 00_hertz_contact.cpp, and 81_golf_ball_impact.cpp.

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

/Users/lzhshou/Documents/Research/myProjects/apaam/repo/netdem/src/fem/fem_simulator.hpp
/Users/lzhshou/Documents/Research/myProjects/apaam/repo/netdem/src/fem/fem_simulator.cpp

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ FEMSimulator()

Member Function Documentation

◆ AddBCFacetForce()

◆ Advance()

◆ ClearBoundaryCondition()

◆ GetCauchyStress()

◆ GetDeformationGradient()

◆ GetElementVolume()

◆ GetInternalForces()

◆ GetNodalDisps()

◆ GetNodalPositions()

◆ GetNodalVels()

◆ Init()

◆ InitInitialCondition()

◆ SaveAsVTK()

◆ SetBCNodalVelocity()

◆ SetMesh()

◆ SetNodalVels()

◆ Solve()

Member Data Documentation

◆ bc_facet_forces

◆ bc_nodal_vels

◆ bound_facets

◆ bound_nodes

◆ damp_coef

◆ density

◆ elemental_stress

◆ elemental_vol

◆ elements

◆ gravity_coef

◆ neo_k

◆ neo_mu

◆ nodal_forces_ext

◆ nodal_forces_int

◆ nodal_vels

◆ nodal_vels_ave

◆ nodal_vols

◆ nodes

◆ nodes_ref

◆ timestep