A class that simulates a membrane. More...

#include <membrane.hpp>

Inheritance diagram for netdem::Membrane:

Public Member Functions
	Membrane (double radius, double height)
	Constructs a new `Membrane` object with the given radius and height.

	Membrane (double radius, double height, double mesh_size)
	Constructs a new `Membrane` object with the given radius, height, and element size.

	Membrane (double radius, double height, double mesh_size, double center_x, double center_y, double center_z)
	Constructs a new `Membrane` object with the given radius, height, element size, and center.

void	Remesh (double ele_size)
	Remeshes the membrane.

void	Init ()
	Initializes the membrane.

void	SetBCNodalVelocity (int nid, double vx, double vy, double vz, bool use_prescribed_vx, bool use_prescribed_vy, bool use_prescribed_vz)
	Sets the nodal velocity and boundary condition for a given node.

void	Solve (double dt)
	Solves the membrane motion for a given timestep.

void	SaveAsVTK (std::string const &file_name)
	Saves the current state of the membrane as a VTK file.

	~Membrane ()
	Destroys the `Membrane` object.

Public Attributes
double	radius {0.25}
	The radius of the membrane.

double	height {1.0}
	The height of the membrane.

double	mesh_size {0.1}
	The size of the elements in the mesh used to represent the membrane.

Vec3d	center {0, 0, 0}
	The center of the membrane.

double	neo_k {6.94e5}
	Material properties of the membrane (neo-Hookean material model).

double	neo_mu {5.21e5}
	Material properties of the membrane (neo-Hookean material model).

double	density {500.0}
	Material properties of the membrane.

double	thickness {0.3e-3}
	Material properties of the membrane.

double	damp_coef {0.7}
	Damping coefficient for the membrane motion.

double	timestep {1.0e-4}
	Timestep for the simulation.

VecXT< Vec3d >	nodes
	Triangle mesh representing the membrane: nodes.

VecXT< Vec3i >	elements
	Triangle mesh representing the membrane: elements.

VecXT< Vec3d >	elemental_stress
	Elemental stress tensor for each element in the mesh.

VecXT< double >	nodal_vols
	Nodal volumes for each node in the mesh (used for updating motion using a lumped mass approach).

VecXT< Vec3d >	nodal_vels
	Nodal velocities for each node in the mesh (used for updating motion using a lumped mass approach).

VecXT< double >	bc_facet_pressure
	Facet pressures for the boundary conditions.

VecXT< Vec3d >	bc_facet_forces
	Facet forces for the boundary conditions.

VecXT< VecNT< double, 6 > >	bc_nodal_vels
	Nodal velocities for the boundary conditions. The last three elements indicate if prescribed velocities are used.

Protected Member Functions
void	Advance (double dt)
	Advances the membrane motion for a given timestep.

void	InitMesh ()
	Initializes the mesh used to represent the membrane.

void	InitInitialCondition ()
	Initializes the initial conditions for the simulation.

Mat2d	GetDeformationGradient (Vec3d const &v0, Vec3d const &v1, Vec3d const &v2)
	Calculates the deformation gradient tensor for an element.

Mat2d	GetCauchyStress (Mat2d const &def_grad)
	Calculates the Cauchy stress tensor for an element.

std::tuple< Mat3d, Mat3d >	GetGlobalForces (Mat2d const &cauchy_stress, double pressure, Vec3d const &v0, Vec3d const &v1, Vec3d const &v2)
	Calculates the global internal and external forces acting on an element.

Protected Attributes
double	ref_ele_width {0.1}
	Reference width and height of each element.

double	ref_ele_height {0.1}

double	ref_ele_area {0.05}
	Reference area of each element.

VecXT< Vec3d >	nodal_forces_int
	Nodal internal forces.

VecXT< Vec3d >	nodal_forces_ext
	Nodal external forces.

Detailed Description

A class that simulates a membrane.

The Membrane class is responsible for simulating a membrane. It provides functionality to initialize the membrane, set up boundary conditions, remesh the membrane, and solve the simulation using a lumped mass approach.

Constructor & Destructor Documentation

◆ Membrane() [1/3]

Membrane::Membrane	(	double	radius,
		double	height )

Constructs a new Membrane object with the given radius and height.

This constructor creates a new Membrane object with the given radius and height, and initializes the center to the origin.

Parameters

radius	The radius of the membrane.
height	The height of the membrane.

◆ Membrane() [2/3]

Membrane::Membrane	(	double	radius,
		double	height,
		double	mesh_size )

Constructs a new Membrane object with the given radius, height, and element size.

This constructor creates a new Membrane object with the given radius, height, and element size, and initializes the center to the origin.

Parameters

radius	The radius of the membrane.
height	The height of the membrane.
mesh_size	The size of the elements in the mesh used to represent the membrane.

◆ Membrane() [3/3]

Membrane::Membrane	(	double	radius,
		double	height,
		double	mesh_size,
		double	center_x,
		double	center_y,
		double	center_z )

Constructs a new Membrane object with the given radius, height, element size, and center.

This constructor creates a new Membrane object with the given radius, height, element size, and center.

Parameters

radius	The radius of the membrane.
height	The height of the membrane.
mesh_size	The size of the elements in the mesh used to represent the membrane.
center_x	The x-coordinate of the center of the membrane.
center_y	The y-coordinate of the center of the membrane.
center_z	The z-coordinate of the center of the membrane.

◆ ~Membrane()

Membrane::~Membrane ( )

Destroys the Membrane object.

This destructor destroys the Membrane object and frees all the resources it allocated.

Member Function Documentation

◆ Advance()

void Membrane::Advance ( double dt )

protected

Advances the membrane motion for a given timestep.

This function advances the membrane motion for the given timestep dt.

Parameters

dt	The timestep for the simulation.

◆ GetCauchyStress()

Mat2d Membrane::GetCauchyStress ( Mat2d const & def_grad )

protected

Calculates the Cauchy stress tensor for an element.

This function calculates the Cauchy stress tensor for an element with deformation gradient tensor def_grad.

Parameters

def_grad The deformation gradient tensor for the element.

Returns: The Cauchy stress tensor for the element.

◆ GetDeformationGradient()

Mat2d Membrane::GetDeformationGradient	(	Vec3d const &	v0,
		Vec3d const &	v1,
		Vec3d const &	v2 )

protected

Calculates the deformation gradient tensor for an element.

This function calculates the deformation gradient tensor for an element with vertices v0, v1, and v2.

Parameters

v0	The first vertex of the element.
v1	The second vertex of the element.
v2	The third vertex of the element.

Returns: The deformation gradient tensor for the element.

◆ GetGlobalForces()

tuple< Mat3d, Mat3d > Membrane::GetGlobalForces	(	Mat2d const &	cauchy_stress,
		double	pressure,
		Vec3d const &	v0,
		Vec3d const &	v1,
		Vec3d const &	v2 )

protected

Calculates the global internal and external forces acting on an element.

This function calculates the global internal and external forces acting on an element with Cauchy stress tensor cauchy_stress, pressure pressure, and vertices v0, v1, and v2.

Parameters

cauchy_stress	The Cauchy stress tensor for the element.
pressure	The pressure acting on the element.
v0	The first vertex of the element.
v1	The second vertex of the element.
v2	The third vertex of the element.

Returns: A tuple containing the global internal and external forces acting on the element.

◆ Init()

void Membrane::Init ( )

Initializes the membrane.

This function initializes the membrane by calling InitMesh() and InitInitialCondition().

◆ InitInitialCondition()

void Membrane::InitInitialCondition ( )

protected

Initializes the initial conditions for the simulation.

◆ InitMesh()

void Membrane::InitMesh ( )

protected

Initializes the mesh used to represent the membrane.

◆ Remesh()

void Membrane::Remesh ( double ele_size )

Remeshes the membrane.

This function remeshes the membrane with the given element size.

Parameters

ele_size The new size for the elements in the mesh used to represent the membrane.

◆ SaveAsVTK()

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

Saves the current state of the membrane as a VTK file.

This function saves the current state of the membrane with the given filename as a VTK file.

Parameters

file_name The name of the file to save the membrane state to.

◆ SetBCNodalVelocity()

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

Sets the nodal velocity and boundary condition for a given node.

This function sets the nodal velocity and boundary condition for the given node. The nodal velocity is specified using vx, vy, and vz. The last three arguments (use_prescribed_vx, use_prescribed_vy, and use_prescribed_vz) indicate whether prescribed velocities are used in each respective dimension.

Parameters

nid	The index of the node to set the boundary condition for.
vx	The x-component of the nodal velocity.
vy	The y-component of the nodal velocity.
vz	The z-component of the nodal velocity.
use_prescribed_vx	Whether prescribed velocities are used in the x-dimension.
use_prescribed_vy	Whether prescribed velocities are used in the y-dimension.
use_prescribed_vz	Whether prescribed velocities are used in the z-dimension.

◆ Solve()

void Membrane::Solve ( double dt )

Solves the membrane motion for a given timestep.

This function solves for the membrane motion for the given timestep dt.

Parameters

dt	The timestep for the simulation.

Member Data Documentation

◆ bc_facet_forces

VecXT<Vec3d> netdem::Membrane::bc_facet_forces

Facet forces for the boundary conditions.

◆ bc_facet_pressure

VecXT<double> netdem::Membrane::bc_facet_pressure

Facet pressures for the boundary conditions.

◆ bc_nodal_vels

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

Nodal velocities for the boundary conditions. The last three elements indicate if prescribed velocities are used.

◆ center

Vec3d netdem::Membrane::center {0, 0, 0}

The center of the membrane.

◆ damp_coef

double netdem::Membrane::damp_coef {0.7}

Damping coefficient for the membrane motion.

◆ density

double netdem::Membrane::density {500.0}

Material properties of the membrane.

◆ elemental_stress

VecXT<Vec3d> netdem::Membrane::elemental_stress

Elemental stress tensor for each element in the mesh.

◆ elements

VecXT<Vec3i> netdem::Membrane::elements

Triangle mesh representing the membrane: elements.

◆ height

double netdem::Membrane::height {1.0}

The height of the membrane.

◆ mesh_size

double netdem::Membrane::mesh_size {0.1}

The size of the elements in the mesh used to represent the membrane.

◆ neo_k

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

Material properties of the membrane (neo-Hookean material model).

The material properties are based on Qu et al., "A continuum model for simulation of 3D cell migration with realistic biophysical constraints", Computer Graphics Forum, vol. 38, no. 6, pp. 283-294, 2019.

◆ neo_mu

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

Material properties of the membrane (neo-Hookean material model).

◆ nodal_forces_ext

VecXT<Vec3d> netdem::Membrane::nodal_forces_ext

protected

Nodal external forces.

◆ nodal_forces_int

VecXT<Vec3d> netdem::Membrane::nodal_forces_int

protected

Nodal internal forces.

◆ nodal_vels

VecXT<Vec3d> netdem::Membrane::nodal_vels

Nodal velocities for each node in the mesh (used for updating motion using a lumped mass approach).

◆ nodal_vols

VecXT<double> netdem::Membrane::nodal_vols

Nodal volumes for each node in the mesh (used for updating motion using a lumped mass approach).

◆ nodes

VecXT<Vec3d> netdem::Membrane::nodes

Triangle mesh representing the membrane: nodes.

◆ radius

double netdem::Membrane::radius {0.25}

The radius of the membrane.

◆ ref_ele_area

double netdem::Membrane::ref_ele_area {0.05}

protected

Reference area of each element.

◆ ref_ele_height

double netdem::Membrane::ref_ele_height {0.1}

protected

◆ ref_ele_width

double netdem::Membrane::ref_ele_width {0.1}

protected

Reference width and height of each element.

◆ thickness

double netdem::Membrane::thickness {0.3e-3}

Material properties of the membrane.

◆ timestep

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

Timestep for the simulation.

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

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

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Membrane() [1/3]

◆ Membrane() [2/3]

◆ Membrane() [3/3]

◆ ~Membrane()

Member Function Documentation

◆ Advance()

◆ GetCauchyStress()

◆ GetDeformationGradient()

◆ GetGlobalForces()

◆ Init()

◆ InitInitialCondition()

◆ InitMesh()

◆ Remesh()

◆ SaveAsVTK()

◆ SetBCNodalVelocity()

◆ Solve()

Member Data Documentation

◆ bc_facet_forces

◆ bc_facet_pressure

◆ bc_nodal_vels

◆ center

◆ damp_coef

◆ density

◆ elemental_stress

◆ elements

◆ height

◆ mesh_size

◆ neo_k

◆ neo_mu

◆ nodal_forces_ext

◆ nodal_forces_int

◆ nodal_vels

◆ nodal_vols

◆ nodes

◆ radius

◆ ref_ele_area

◆ ref_ele_height

◆ ref_ele_width

◆ thickness

◆ timestep