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[example] Add a demo scene showcasing mesh-induced anisotropy effects (sofa-framework#5982)
Add a demo scene showcasing mesh-induced anisotropy effects Co-authored-by: Frederick Roy <fredroy@users.noreply.github.com>
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‎examples/Demos/MeshInducedAnisotropy.scn‎

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<?xml version="1.0"?>
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<Node name="root" dt="0.01" gravity="0 -9.81 0">
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<!--
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If all tetrahedra in a mesh are oriented in the same way (for example, all diagonals in a structured grid are split
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consistently in one direction), the mesh itself introduces a preferred direction.
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Even if the material model is isotropic, the numerical solution behaves as if the material were anisotropic.
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If the diagonals were alternated or randomized, the effect would largely disappear. The alternation can be
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controlled by the Data 'swapping' in the component 'Hexa2TetrahedronTopologicalMapping'.
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This scene shows the effect of the mesh-induced anisotropy at equilibrium, compared to a mesh where the diagonals
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are alternated.
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-->
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<Node name="plugins">
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<RequiredPlugin name="Sofa.Component.Constraint.Projective"/> <!-- Needed to use components [FixedProjectiveConstraint] -->
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<RequiredPlugin name="Sofa.Component.Engine.Select"/> <!-- Needed to use components [BoxROI] -->
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<RequiredPlugin name="Sofa.Component.LinearSolver.Direct"/> <!-- Needed to use components [SparseLDLSolver] -->
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<RequiredPlugin name="Sofa.Component.Mass"/> <!-- Needed to use components [DiagonalMass] -->
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<RequiredPlugin name="Sofa.Component.ODESolver.Backward"/> <!-- Needed to use components [NewtonRaphsonSolver,StaticSolver] -->
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<RequiredPlugin name="Sofa.Component.SolidMechanics.FEM.Elastic"/> <!-- Needed to use components [TetrahedronFEMForceField] -->
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<RequiredPlugin name="Sofa.Component.StateContainer"/> <!-- Needed to use components [MechanicalObject] -->
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<RequiredPlugin name="Sofa.Component.Topology.Container.Dynamic"/> <!-- Needed to use components [TetrahedronSetGeometryAlgorithms,TetrahedronSetTopologyContainer,TetrahedronSetTopologyModifier] -->
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<RequiredPlugin name="Sofa.Component.Topology.Container.Grid"/> <!-- Needed to use components [RegularGridTopology] -->
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<RequiredPlugin name="Sofa.Component.Topology.Mapping"/> <!-- Needed to use components [Hexa2TetraTopologicalMapping] -->
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<RequiredPlugin name="Sofa.Component.Visual"/> <!-- Needed to use components [VisualMesh,VisualStyle] -->
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</Node>
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<DefaultAnimationLoop/>
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<VisualStyle displayFlags="showBehaviorModels" />
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<!-- Dimensions are in meters -->
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<RegularGridTopology name="grid" min="-0.01 -0.01 0" max="0.01 0.01 0.2" n="5 5 30"/>
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<Node name="beam_with_anisotropy">
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<NewtonRaphsonSolver name="non_linear_solver" maxNbIterationsNewton="100"
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maxNbIterationsLineSearch="1" warnWhenLineSearchFails="false"/>
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<StaticSolver name="static_solver" newtonSolver="@non_linear_solver"/>
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<SparseLDLSolver name="linear_solver" template="CompressedRowSparseMatrixMat3x3d"/>
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<MechanicalObject template="Vec3" name="state" position="@/grid.position"/>
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<Node name="tetrahedra">
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<TetrahedronSetTopologyContainer name="Tetra_topo" position="@/grid.position"/>
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<TetrahedronSetTopologyModifier name="Modifier" />
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<TetrahedronSetGeometryAlgorithms template="Vec3" name="GeomAlgo" />
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<Hexa2TetraTopologicalMapping input="@grid" output="@Tetra_topo" swapping="false"/>
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<!-- Density is in kg/m^3 -->
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<DiagonalMass massDensity="1100" />
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<!-- Young's modulus is in Pa -->
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<TetrahedronFEMForceField name="FEM" youngModulus="1e6" poissonRatio="0.48"/>
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<VisualMesh position="@state.position" topology="@Tetra_topo"/>
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</Node>
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<BoxROI template="Vec3" name="box_roi" box="-0.011 -0.011 -0.0001 0.011 0.011 0.0001" drawBoxes="1" />
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<FixedProjectiveConstraint template="Vec3" indices="@box_roi.indices" />
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</Node>
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<Node name="beam_without_anisotropy">
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<NewtonRaphsonSolver name="non_linear_solver" maxNbIterationsNewton="100"
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maxNbIterationsLineSearch="1" warnWhenLineSearchFails="false"/>
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<StaticSolver name="static_solver" newtonSolver="@non_linear_solver"/>
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<SparseLDLSolver name="linear_solver" template="CompressedRowSparseMatrixMat3x3d"/>
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<MechanicalObject template="Vec3" name="state" position="@/grid.position"/>
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<Node name="tetrahedra">
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<TetrahedronSetTopologyContainer name="Tetra_topo" position="@/grid.position"/>
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<TetrahedronSetTopologyModifier name="Modifier" />
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<TetrahedronSetGeometryAlgorithms template="Vec3" name="GeomAlgo" />
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<Hexa2TetraTopologicalMapping input="@grid" output="@Tetra_topo" swapping="true"/>
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<!-- Density is in kg/m^3 -->
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<DiagonalMass massDensity="1100" />
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<!-- Young's modulus is in Pa -->
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<TetrahedronFEMForceField name="FEM" youngModulus="1e6" poissonRatio="0.48"/>
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<VisualMesh position="@state.position" topology="@Tetra_topo"/>
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</Node>
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<BoxROI template="Vec3" name="box_roi" box="-0.011 -0.011 -0.0001 0.011 0.011 0.0001" drawBoxes="1" />
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<FixedProjectiveConstraint template="Vec3" indices="@box_roi.indices" />
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</Node>
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</Node>

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