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EquivalentStrain[vars,pars,strain]

yields the equivalent strain from the strain matrix strain.

Details
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Examples  
Basic Examples  
Scope  
Applications  
Hyperelastic Stationary Analysis  
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EquivalentStrain

EquivalentStrain[vars,pars,strain]

yields the equivalent strain from the strain matrix strain.

Details

  • The equivalent strain measure is typically used to have a scalar strain measure similar to the von Mises stress measure.
  • The equivalent strain is also known as the von Mises equivalent strain.
  • EquivalentStrain computes a scalar strain measure given by:
  • The represent normal strains and the represent shear strains.
  • The equivalent strain is unitless.
  • EquivalentStrain uses the same variables vars specification as SolidMechanicsPDEComponent.
  • EquivalentStrain uses the same parameter pars specification as SolidMechanicsPDEComponent.
  • The strain matrix has to be a symmetric matrix. Either it is a 3×3 matrix or a 2×2 matrix, in which case all the components are assumed to be zero in the corresponding 3×3 matrix.

Examples

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Basic Examples  (1)

Compute the equivalent strain of a strain tensor:

Wolfram Language code: EquivalentStrain[{{u[x, y, z], v[x, y, z], w[x, y, z]}, {x, y, z}}, <|"YoungModulus" -> , "PoissonRatio" -> |>, SymmetrizedArray[{{Subscript[ϵ, xx], Subscript[γ, xy], Subscript[γ, xz]}, {Subscript[γ, xy], Subscript[ϵ, yy], Subscript[γ, yz]}, {Subscript[γ, xz], Subscript[γ, yz], Subscript[ϵ, zz]}}]]

Scope  (2)

Express the equivalent strain in terms of displacement. Compute strain from a displacement:

Wolfram Language code: SolidMechanicsStrain[{{u[x, y, z], v[x, y, z], w[x, y, z]}, {x, y, z}}, <|"YoungModulus" -> , "PoissonRatio" -> |>, {u[x, y, z], v[x, y, z], w[x, y, z]}]

Compute the equivalent strain:

Wolfram Language code: EquivalentStrain[{{u[x, y, z], v[x, y, z], w[x, y, z]}, {x, y, z}}, <|"YoungModulus" -> , "PoissonRatio" -> |>, %]

Explore equivalent strain for a titanium beam-like structure.

Set up the geometry of the beam:

Wolfram Language code: beam = \!\(\*Graphics3DBox[«4»]\);

Set up variables and material parameters:

Wolfram Language code: vars = {{u[x, y, z], v[x, y, z], w[x, y, z]}, {x, y, z}}; pars = <|"Material" -> Entity["Element", "Titanium"]|>;

Set up and solve the PDE:

Wolfram Language code: displacement = NDSolveValue[{SolidMechanicsPDEComponent[vars, pars] == SolidBoundaryLoadValue[x == 10, vars, pars, <|"Force" -> {0, 0, -2 * 10^7}|>], SolidFixedCondition[x == 0, vars, pars]}, {u[x, y, z], v[x, y, z], w[x, y, z]}, {x, y, z}∈beam];

Compute the strain tensor from the displacement:

Wolfram Language code: strains = SolidMechanicsStrain[vars, pars, displacement]

Compute the equivalent strain from the strain tensor:

Wolfram Language code: equivalentStrain = EquivalentStrain[vars, pars, strains]

Visualize the equivalent strain over the deformed body:

Wolfram Language code: VectorDisplacementPlot3D[{displacement, equivalentStrain}, {x, y, z}∈beam, VectorSizes -> 2, PlotPoints -> 40]

Applications  (2)

Compute the equivalent strain of a load on a beam. Create the beam and set up variables and material parameters:

Wolfram Language code: beam = [image]; vars = {{u[x, y, z], v[x, y, z], w[x, y, z]}, {x, y, z}}; pars = <|"Material" -> Entity["Element", "Titanium"]|>;

The beam is held fixed at the left, and a load of 100 newtons in the downward direction is applied at the right end of the beam. Compute the displacement of the beam under a load:

Wolfram Language code: displacement = NDSolveValue[{SolidMechanicsPDEComponent[vars, pars] == SolidBoundaryLoadValue[x == 0.2, vars, pars, <|"Force" -> {0, 0, Quantity[-100, "Newtons"]}|>], SolidFixedCondition[x == 0, vars, pars]}, {u[x, y, z], v[x, y, z], w[x, y, z]}, {x, y, z}∈beam];

Compute the strain tensor from the displacement and the equivalent strain:

Wolfram Language code: strains = SolidMechanicsStrain[vars, pars, displacement]; equivalentStrain = EquivalentStrain[vars, pars, strains]

Visualize the equivalent strain:

Wolfram Language code: SliceContourPlot3D[equivalentStrain, beam, {x, y, z}∈beam, ...]

Find the maximal equivalent strain value:

Wolfram Language code: MaxValue[equivalentStrain, {x, y, z}∈beam]

Hyperelastic Stationary Analysis  (1)

Compute the equivalent strain in an object with a hyperelastic material. Set up variables and material properties:

Wolfram Language code: vars = {{u[x, y], v[x, y]}, {x, y}}; pars = <|"SolidMechanicsMaterialModel" -> "NeoHookean", "ShearModulus" -> 100, "Thickness" -> 0.01|>;

Specify a geometry:

Wolfram Language code: Ω = [image];

The geometry is held fixed on the left edge and pulled to the right on the right edge. Solve the PDE for the displacement:

Wolfram Language code: displacement = NDSolveValue[{SolidMechanicsPDEComponent[vars, pars] == SolidBoundaryLoadValue[x == 1, vars, pars, <|"Force" -> {Quantity[1, "Newtons"], 0}|>], SolidFixedCondition[x == 0, vars, pars]}, {u[x, y], v[x, y]}, {x, y}∈Ω];

Compute the strains from the displacement:

Wolfram Language code: strains = SolidMechanicsStrain[vars, pars, displacement];

Compute the equivalent strain from the strain tensor:

Wolfram Language code: equivalentStrain = EquivalentStrain[vars, pars, strains];

Visualize the von Mises stress in the to-scale deformed object:

Wolfram Language code: VectorDisplacementPlot[{displacement, equivalentStrain}, {x, y}∈Ω, VectorSizes -> Full]
Wolfram Research (2026), EquivalentStrain, Wolfram Language function, https://reference.wolfram.com/language/ref/EquivalentStrain.html.

Text

Wolfram Research (2026), EquivalentStrain, Wolfram Language function, https://reference.wolfram.com/language/ref/EquivalentStrain.html.

CMS

Wolfram Language. 2026. "EquivalentStrain." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/EquivalentStrain.html.

APA

Wolfram Language. (2026). EquivalentStrain. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EquivalentStrain.html

BibTeX

@misc{reference.wolfram_2026_equivalentstrain, author="Wolfram Research", title="{EquivalentStrain}", year="2026", howpublished="\url{https://reference.wolfram.com/language/ref/EquivalentStrain.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_equivalentstrain, organization={Wolfram Research}, title={EquivalentStrain}, year={2026}, url={https://reference.wolfram.com/language/ref/EquivalentStrain.html}, note=[Accessed: 12-June-2026]}