Failure theory identification: The maximum principal strain criterion for elastic failure is also known by which classical name?

Introduction / Context:
Multiple failure theories are used in design under multiaxial stress states. Each theory proposes a critical quantity (stress, strain, or energy) that governs yielding or failure. Recognizing their classical names is essential for exam and design problems.

Given Data / Assumptions:

• Elastic limit behavior is considered.
• Multiaxial stress state possible.
• Classical nomenclature is used.

Concept / Approach:

The maximum principal strain theory asserts failure when the largest tensile principal strain reaches the uniaxial failure strain. Historically, this has been attributed to St. Venant. In contrast, Rankine uses maximum principal stress; Tresca/Guest uses maximum shear stress; Haigh (Beltrami-Haigh) uses total strain energy; Von Mises uses distortion energy.

Step-by-Step Solution:

Verification / Alternative check:

Handbooks list: Rankine (max σ1), St. Venant (max ε1), Guest/Tresca (max τ_max), Beltrami-Haigh (total strain energy), Von Mises (distortion energy).

Why Other Options Are Wrong:

Each alternative refers to a different governing quantity and is not the “maximum principal strain” theory.

Common Pitfalls:

Confusing “maximum strain” with “maximum stress” (Rankine) or with “maximum shear stress” (Tresca/Guest).

Final Answer:

St. Venant's theory (maximum principal strain)