PolynomialSpringsForceField

This component belongs to the category of ForceField. This component allows to simulate springs with Polynomial stress strain behavior. If we note:

$Spring force$ the spring force
$Cross section$ the cross section (always 1.0)
$Stress-strain non-linear function$ the stress-strain non-linear function
$Original length of the spring$ the original length and $Current length of the spring$ the current length of the spring
$Point displacement$ the point displacement

the generic non-linear force can thus be written: $Generic non-linear spring force$ where $Stress-strain non-linear function$ is polynom as follows: $Stress-strain non-linear function$ and $Derivative of the stress-strain non-linear function$

The dedication of jacobian matrix for PolynomialSpringForceField is given below:

$Jacobian of the spring$

Note that a RestShapePolynomialSpringsForceField does exist. It will compute the same non-linear force with regards to the rest shape of one single object. To avoid Nan problems when a spring has a zero length, an exponential addition to the denominator has been added. As a result, the stress simulation is shifted compared with polynomial values, but it keeps its nonlinearity:

$Modified Jacobian of the RestShapePolynomialSpringsForceField$

More details were given in the pull-request #1342.

Data

The polynomial parameters are set as two arrays:

polynomialDegree: describing the set of polynomial degrees for every spring
polynomialStiffness: describing the set of polynomial coefficients sequentially combined in one vector.

The coefficients are put from smaller degree to bigger one, and the free coefficient is always zero (since for no strain we have no stress). For examples the coefficients for polynomials [3,2,4] will be put as [a1,a2,a3,b1,b2,c1,c2,c3,c4].

firstObjectPoints corresponding to the indices of the points related to the first object
secondObjectPoints corresponding to the indices of the points related to the second object
compressible: indicating if object compresses without reaction force

Usage

The PolynomialSpringsForceField requires two different objects to link, which means two MechanicalObjects on which the non-linear spring will act. On the other hand, RestShapePolynomialSpringsForceField will act on one single body, i.e. one MechanicalObject.

Example

This component is used as follows in XML format:

<DiagonalMass massDensity="1000" />

or using Python:

node.createObject('DiagonalMass', massDensity='1000')

An example scene involving a PolynomialSpringsForceField is available in examples/Component/SolidMechanics/Spring/PolynomialSpringsForceField.scn

Target: Sofa.Component.SolidMechanics.Spring

namespace: sofa::component::solidmechanics::spring

parents:

PairInteractionForceField

Data:

Name	Description	Default value
name	object name	unnamed
printLog	if true, emits extra messages at runtime.	0
tags	list of the subsets the objet belongs to
bbox	this object bounding box
componentState	The state of the component among (Dirty, Valid, Undefined, Loading, Invalid).	Undefined
listening	if true, handle the events, otherwise ignore the events	0
isCompliance	Consider the component as a compliance, else as a stiffness	0
rayleighStiffness	Rayleigh damping - stiffness matrix coefficient	0
firstObjectPoints	points related to the first object
secondObjectPoints	points related to the second object
polynomialStiffness	coefficients for all spring polynomials
polynomialDegree	vector of values that show polynomials degrees
computeZeroLength	flag to compute initial length for springs	1
zeroLength	initial length for springs
recompute_indices	Recompute indices (should be false for BBOX)	0
compressible	Indicates if object compresses without reactio force	0
springColor	spring color	0 1 0 1
Visualization
drawMode	The way springs will be drawn: - 0: Line - 1:Cylinder - 2: Arrow	0
showArrowSize	size of the axis	0.01
showIndicesScale	Scale for indices display. (default=0.02)	0.02

Links:

Name	Description
context	Graph Node containing this object (or BaseContext::getDefault() if no graph is used)
slaves	Sub-objects used internally by this object
master	nullptr for regular objects, or master object for which this object is one sub-objects
mechanicalStates	List of mechanical states to which this component is associated
object1	First object associated to this component
object2	Second object associated to this component

Examples

Component/SolidMechanics/Spring/PolynomialSpringsForceField.scn

XMLPython

<?xml version="1.0" ?>
<Node name="lroot" gravity="0 0 0" dt="0.02">
    <RequiredPlugin name="Sofa.Component.Constraint.Projective"/> <!-- Needed to use components [FixedProjectiveConstraint] -->
    <RequiredPlugin name="Sofa.Component.IO.Mesh"/> <!-- Needed to use components [MeshGmshLoader MeshOBJLoader] -->
    <RequiredPlugin name="Sofa.Component.LinearSolver.Iterative"/> <!-- Needed to use components [CGLinearSolver] -->
    <RequiredPlugin name="Sofa.Component.Mapping.Linear"/> <!-- Needed to use components [BarycentricMapping] -->
    <RequiredPlugin name="Sofa.Component.Mass"/> <!-- Needed to use components [DiagonalMass UniformMass] -->
    <RequiredPlugin name="Sofa.Component.ODESolver.Backward"/> <!-- Needed to use components [EulerImplicitSolver] -->
    <RequiredPlugin name="Sofa.Component.SolidMechanics.FEM.Elastic"/> <!-- Needed to use components [TetrahedralCorotationalFEMForceField] -->
    <RequiredPlugin name="Sofa.Component.SolidMechanics.Spring"/> <!-- Needed to use components [PolynomialSpringsForceField] -->
    <RequiredPlugin name="Sofa.Component.StateContainer"/> <!-- Needed to use components [MechanicalObject] -->
    <RequiredPlugin name="Sofa.Component.Topology.Container.Dynamic"/> <!-- Needed to use components [TetrahedronSetGeometryAlgorithms TetrahedronSetTopologyContainer] -->
    <RequiredPlugin name="Sofa.Component.Visual"/> <!-- Needed to use components [VisualStyle] -->
    <RequiredPlugin name="Sofa.GL.Component.Rendering3D"/> <!-- Needed to use components [OglModel] -->

    <VisualStyle displayFlags="showInteractionForceFields"/>
    <DefaultAnimationLoop/>
    <MeshOBJLoader name="LiverSurface" filename="mesh/liver-smooth.obj" />

    <Node name="Liver" >
        <EulerImplicitSolver name="cg_odesolver"   rayleighStiffness="0.1" rayleighMass="0.1" />
        <CGLinearSolver name="linear solver" iterations="25" tolerance="1e-09" threshold="1e-09" />
        <MeshGmshLoader name="meshLoader" filename="mesh/liver.msh" />
        <TetrahedronSetTopologyContainer name="topo" src="@meshLoader" />
        <MechanicalObject name="dofs" src="@meshLoader" />
        <TetrahedronSetGeometryAlgorithms template="Vec3" name="GeomAlgo" />
        <DiagonalMass  name="computed using mass density" massDensity="1" />
        <TetrahedralCorotationalFEMForceField template="Vec3" name="FEM" method="large" poissonRatio="0.3" youngModulus="3000" computeGlobalMatrix="0" />
        <FixedProjectiveConstraint  name="FixedProjectiveConstraint" indices="3 39 64" />
        <Node name="Visu" tags="Visual" gravity="0 -9.81 0">
            <OglModel  name="VisualModel" src="@../../LiverSurface" />
            <BarycentricMapping name="visual mapping" input="@../dofs" output="@VisualModel" />
        </Node>

        <Node name="Weight" >
            <MechanicalObject template="Vec3" name="myParticle" rest_position="0 0 0" position="0 0 0" />
            <UniformMass totalMass="30" />
            <PolynomialSpringsForceField polynomialDegree="3" polynomialStiffness="20 10 50" object1='@.' firstObjectPoints='0' object2='@../dofs' secondObjectPoints='15' drawMode='0' showIndicesScale="1"/>
        </Node>
    </Node>

</Node>

def createScene(rootNode):

    lroot = rootNode.addChild('lroot', gravity="0 0 0", dt="0.02")
    lroot.addObject('RequiredPlugin', name="Sofa.Component.Constraint.Projective")
    lroot.addObject('RequiredPlugin', name="Sofa.Component.IO.Mesh")
    lroot.addObject('RequiredPlugin', name="Sofa.Component.LinearSolver.Iterative")
    lroot.addObject('RequiredPlugin', name="Sofa.Component.Mapping.Linear")
    lroot.addObject('RequiredPlugin', name="Sofa.Component.Mass")
    lroot.addObject('RequiredPlugin', name="Sofa.Component.ODESolver.Backward")
    lroot.addObject('RequiredPlugin', name="Sofa.Component.SolidMechanics.FEM.Elastic")
    lroot.addObject('RequiredPlugin', name="Sofa.Component.SolidMechanics.Spring")
    lroot.addObject('RequiredPlugin', name="Sofa.Component.StateContainer")
    lroot.addObject('RequiredPlugin', name="Sofa.Component.Topology.Container.Dynamic")
    lroot.addObject('RequiredPlugin', name="Sofa.Component.Visual")
    lroot.addObject('RequiredPlugin', name="Sofa.GL.Component.Rendering3D")
    lroot.addObject('VisualStyle', displayFlags="showInteractionForceFields")
    lroot.addObject('DefaultAnimationLoop')
    lroot.addObject('MeshOBJLoader', name="LiverSurface", filename="mesh/liver-smooth.obj")

    Liver = lroot.addChild('Liver')
    Liver.addObject('EulerImplicitSolver', name="cg_odesolver", rayleighStiffness="0.1", rayleighMass="0.1")
    Liver.addObject('CGLinearSolver', name="linear solver", iterations="25", tolerance="1e-09", threshold="1e-09")
    Liver.addObject('MeshGmshLoader', name="meshLoader", filename="mesh/liver.msh")
    Liver.addObject('TetrahedronSetTopologyContainer', name="topo", src="@meshLoader")
    Liver.addObject('MechanicalObject', name="dofs", src="@meshLoader")
    Liver.addObject('TetrahedronSetGeometryAlgorithms', template="Vec3", name="GeomAlgo")
    Liver.addObject('DiagonalMass', name="computed using mass density", massDensity="1")
    Liver.addObject('TetrahedralCorotationalFEMForceField', template="Vec3", name="FEM", method="large", poissonRatio="0.3", youngModulus="3000", computeGlobalMatrix="0")
    Liver.addObject('FixedProjectiveConstraint', name="FixedProjectiveConstraint", indices="3 39 64")

    Visu = Liver.addChild('Visu', tags="Visual", gravity="0 -9.81 0")
    Visu.addObject('OglModel', name="VisualModel", src="@../../LiverSurface")
    Visu.addObject('BarycentricMapping', name="visual mapping", input="@../dofs", output="@VisualModel")

    Weight = Liver.addChild('Weight')
    Weight.addObject('MechanicalObject', template="Vec3", name="myParticle", rest_position="0 0 0", position="0 0 0")
    Weight.addObject('UniformMass', totalMass="30")
    Weight.addObject('PolynomialSpringsForceField', polynomialDegree="3", polynomialStiffness="20 10 50", object1="@.", firstObjectPoints="0", object2="@../dofs", secondObjectPoints="15", drawMode="0", showIndicesScale="1")