The choice between the Tresca yield criterion and the von Mises yield criterion

The choice between the Tresca yield criterion and the von Mises yield criterion depends on the specific characteristics of the material being analyzed and the nature of the deformation it undergoes. Here are some considerations for when the Tresca yield criterion is preferred over the von Mises yield criterion:

1. Materials with distinct yield strength in tension and compression: The Tresca yield criterion is often used for materials that exhibit a significant difference in their yield strengths under tension and compression. It assumes that failure occurs when the maximum shear stress in the material exceeds a certain critical value. This criterion is applicable to materials with yield behavior that is strongly influenced by the direction of applied stresses, such as brittle materials or some non-ferrous metals.
2. Dominance of shear failure: The Tresca yield criterion is suitable when the dominant mode of failure in a material is related to shear stress. It assumes that yielding occurs when the material experiences excessive shear stress without considering the hydrostatic stress component. This makes it particularly relevant for materials that are prone to shear failure, such as brittle materials or materials with weak intergranular bonds.
3. Consideration of stress concentrations: The Tresca yield criterion is often used in situations where stress concentrations play a significant role. This criterion allows for the assessment of localized stress concentrations, which can occur around notches, cracks, or geometric discontinuities. It provides a conservative estimate of failure by focusing on the maximum shear stress, which can be particularly important in designs where avoiding local failure is critical.

On the other hand, the von Mises yield criterion is commonly preferred in the following situations:

1. Materials with isotropic plastic behavior: The von Mises yield criterion assumes that yielding occurs when the von Mises equivalent stress (also known as the deviatoric or shear stress) exceeds a critical value. It is suitable for materials that exhibit isotropic plastic behavior, meaning their yield strength is not influenced by the direction of applied stresses. Many ductile materials, such as metals, tend to display isotropic plastic behavior.
2. General applications: The von Mises yield criterion is widely used in various engineering applications, as it provides a good approximation of the yielding behavior for many ductile materials. It simplifies the analysis by considering only the deviatoric stresses and disregarding the influence of hydrostatic stress. This criterion is commonly applied in plasticity theories, finite element simulations, and structural analysis.

In summary, the Tresca yield criterion is preferred over the von Mises yield criterion when dealing with materials that have distinct yield strengths in tension and compression, when shear failure dominates, or when stress concentrations are of concern. Conversely, the von Mises yield criterion is more suitable for materials with isotropic plastic behavior or general engineering applications. The choice depends on the specific material properties, failure mechanisms, and design requirements.