冯·米塞斯屈服准则

冯·米塞斯屈服准则，也称为最大变形能准则，是一种广泛用于预测延性材料塑性变形开始的模型。该准则假定，当材料单位体积变形的弹性应变能达到临界值时，材料开始屈服。这与静水压力能（与体积变化相关）不同，静水压力能被认为对延性金属的屈服没有贡献。

Mathematically, this is equivalent to stating that the second invariant of the deviatoric stress tensor, [latex]J_2[/latex], reaches a constant value. The deviatoric stress tensor is the total stress tensor minus its hydrostatic component. The criterion is often expressed through the von Mises equivalent stress, [latex]\sigma_v[/latex], which is a scalar combination of the six components of the stress tensor. For a general 3D state of stress, it is calculated as: [latex]\sigma_v = \sqrt{\frac{1}{2}[(\sigma_{11}-\sigma_{22})^2 + (\sigma_{22}-\sigma_{33})^2 + (\sigma_{33}-\sigma_{11})^2 + 6(\sigma_{12}^2 + \sigma_{23}^2 + \sigma_{31}^2)]}[/latex].

Yielding is predicted to occur when [latex]\sigma_v[/latex] equals the material’s yield strength, [latex]\sigma_y[/latex], which is typically determined from a simple uniaxial tensile test. In principal stress space, the von Mises criterion defines a smooth, circular cylinder whose axis is the hydrostatic line ([latex]\sigma_1 = \sigma_2 = \sigma_3[/latex]). This contrasts with the Tresca criterion, which defines a hexagonal prism. The von Mises criterion generally provides a better fit with experimental data for most ductile metals and is continuously differentiable, which is advantageous in numerical computations.