Von Mises yield criterion

A ductile-material yield condition stating that yielding begins when the second invariant of deviatoric stress reaches the value calibrated by uniaxial yield stress.

Version

v1 · 2026-09-08 · History

Domain-specific #

7441

Origin domain

continuum mechanics and plasticity

Subdomain

continuum mechanics and plasticity

Core Idea

The criterion reduces a three-dimensional stress tensor to von Mises equivalent stress, ignores hydrostatic pressure, and defines a cylindrical yield surface in principal-stress space. Mean stress is removed, the deviatoric tensor's J2 invariant is computed, and its calibrated scalar equivalent is compared with a material threshold under the assumed isotropic plasticity model. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

Scope of Application

Von Mises yield criterion belongs to continuum mechanics and plasticity and is useful where the analyst can specify the typed continuum mechanics and plasticity carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the stress measure and sign convention, material and temperature, isotropy and pressure-insensitivity assumptions, deviatoric stress, J2 and equivalent-stress normalization, yield threshold, hardening rule, loading history, and validation range are explicit. The scope is broad within that domain but bounded by the need for the stress measure and sign convention, material and temperature, isotropy and pressure-insensitivity assumptions, deviatoric stress, J2 and equivalent-stress normalization, yield threshold, hardening rule, loading history, and validation range are explicit.

Clarity

The abstraction clarifies a crowded vocabulary by making the stress measure and sign convention, material and temperature, isotropy and pressure-insensitivity assumptions, deviatoric stress, J2 and equivalent-stress normalization, yield threshold, hardening rule, loading history, and validation range are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.

Manages Complexity

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Von Mises yield criterion. Von Mises yield criterion compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning

1. Identify the carrier. State what the elements, states, objects, or observations are: the typed continuum mechanics and plasticity carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the stress measure and sign convention, material and temperature, isotropy and pressure-insensitivity assumptions, deviatoric stress, J2 and equivalent-stress normalization, yield threshold, hardening rule, loading history, and validation range are explicit independently of one notation or implementation.

Knowledge Transfer

Knowledge transfers strongly among subfields of continuum mechanics and plasticity because they reuse the typed continuum mechanics and plasticity carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Mean stress is removed, the deviatoric tensor's J2 invariant is computed, and its calibrated scalar equivalent is compared with a material threshold under the assumed isotropic plasticity model., and type the carrier, state every parameter and convention in the definition, test that the stress measure and sign convention, material and temperature, isotropy and pressure-insensitivity assumptions, deviatoric stress, J2 and equivalent-stress normalization, yield threshold, hardening rule, loading history, and validation range are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions

Current abstraction Von Mises yield criterion Domain-specific

Parents (1) — more general patterns this builds on

• Von Mises yield criterion is a kind of Threshold Prime

  The proposed strict upward parent is prime:threshold.

Hierarchy path (1) — routes to 1 parentless root

• Von Mises yield criterion → Threshold

Neighborhood in Abstraction Space

Von Mises yield criterion sits in a moderately populated region (41^st percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Materials Testing & Mechanical Properties (19 abstractions)

Nearest neighbors

• Stress triaxiality — 0.90
• Stress space — 0.90
• Polynomial hyperelastic model — 0.90
• Cauchy elastic material — 0.89
• Ductility — 0.89

Computed from structural-signature embeddings · 2026-09-08