Tresca

Tresca refers primarily to the Tresca yield criterion in plasticity, named after the French engineer Henri Tresca who introduced it in the late 19th century. In materials science, it provides a criterion for predicting the onset of yielding in ductile metals under complex, multiaxial loading. The criterion states that yielding begins when the maximum shear stress in any plane reaches the yield stress observed in simple tension. Equivalently, with principal stresses σ1 ≥ σ2 ≥ σ3, yielding occurs when max(|σ1 − σ2|, |σ2 − σ3|, |σ3 − σ1|) = σ_y, where σ_y is the uniaxial yield stress.

Geometrically, the Tresca yield surface in principal-stress space is a regular hexagonal prism, reflecting the piecewise-linear nature of the criterion. This contrasts with the von Mises criterion, whose yield surface is a smooth ellipsoid. Because of its simplicity, the Tresca criterion is often used in metal forming analyses and in situations where a computationally inexpensive criterion is desirable, though von Mises is more commonly adopted for its closer empirical correlation with ductile-metal yielding in many applications.

Limitations include its piecewise linear boundary, which can lead to non-smooth responses in numerical simulations, and its sometimes conservative predictions compared with more refined criteria.

The term Tresca is also the surname of various individuals; in engineering contexts, it most often refers to this yield criterion.