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EquivalentStrain[vars,pars,strain]

从应变矩阵 strain 中得出等效应变.

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Details and Options Details and Options
范例  
基本范例  
范围  
应用  
超弹性静态分析  
参见
技术笔记
相关指南
历史
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EquivalentStrain

EquivalentStrain[vars,pars,strain]

从应变矩阵 strain 中得出等效应变.

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  • 等效应变度量通常用于构建类似于冯·米塞斯应力度量的标量应变度量.
  • 等效应变也称为冯·米塞斯等效应变.
  • EquivalentStrain 计算由以下公式给出的标量应变度量：
  • 表示正应变， 表示剪切应变.
  • 等效应变为无量纲量.
  • EquivalentStrain 使用与 SolidMechanicsPDEComponent 相同的变量 vars 规范.
  • EquivalentStrain 使用与 SolidMechanicsPDEComponent 相同的参数 pars 规范.
  • strain 矩阵必须为对称矩阵. 它可以是 3×3 矩阵或 2×2 矩阵；若为 2×2 矩阵，则在对应的 3×3 矩阵中所有 方向分量均假定为零.

范例

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基本范例  (1)

计算应变张量的等效应变：

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]}}]]

范围  (2)

用位移表示等效应变. 根据位移计算应变：

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]}]

计算等效应变：

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

探究钛合金梁式结构的等效应变.

设置梁的几何构型：

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

设置变量和材料参数：

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

设置并求解偏微分方程：

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];

根据位移计算应变：

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

从应变张量计算等效应变：

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

在变形体上可视化等效应变分布：

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

应用  (2)

计算梁上载荷的等效应变. 创建梁模型及设置变量与材料参数：：

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"]|>;

梁左端固定，右端施加一个方向向下的 100 牛顿载荷. 计算载荷作用下梁的位移：

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];

根据位移计算应变张量：

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

可视化等效应变：

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

找到最大等效应变值：

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

超弹性静态分析  (1)

计算超弹性材料物体的等效应变. 设置变量与材料属性：

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

指定几何体：

Wolfram Language code: Ω = [image];

几何体左端固定，右端受向右拉伸。求解位移的偏微分方程：

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];

根据位移计算应变：

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

从应变张量计算等效应变：

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

在按比例变形的物体中可视化冯·米塞斯应力分布：

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

文本

Wolfram Research (2026)，EquivalentStrain，Wolfram 语言函数，https://reference.wolfram.com/language/ref/EquivalentStrain.html.

CMS

Wolfram 语言. 2026. "EquivalentStrain." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/EquivalentStrain.html.

APA

Wolfram 语言. (2026). EquivalentStrain. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/EquivalentStrain.html 年

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: 07-September-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: 07-September-2026]}