Yeoh hyperelastic model¶

The Yeoh hyperelastic material model is a phenomenological model for the deformation of nearly incompressible, nonlinear elastic materials such as rubber.

Version: v1 · 2026-09-28 · History
Domain-specific #: 12933
Domain group: Applied Sciences & Engineering
Origin domain: Engineering & Design (beyond software)
Subdomains: Solid Mechanics, Hyperelasticity → Engineering & Design (beyond software)

Core Idea¶

Yeoh hyperelastic model is treated here as the recurring naturalsciencesengineeringhealth identity summarized by this source-grounded definition: The Yeoh hyperelastic material model is a phenomenological model for the deformation of nearly incompressible, nonlinear elastic materials such as rubber. The Yeoh hyperelastic material model is a phenomenological model for the deformation of nearly incompressible, nonlinear elastic materials such as rubber. The model is based on Ronald Rivlin's observation that the elastic properties of rubber may be described using a strain energy density function which is a power series in the strain invariants I1, I2, I3 of the.

Scope of Application¶

Documented setting. Since a polynomial form of the strain energy density function is used but all the three invariants of the left Cauchy-Green deformation tensor are not, the Yeoh model is also called.
Strain energy density function. Today a slightly more generalized version of the Yeoh model is used.
Yeoh model for compressible rubbers. A version of the Yeoh model that includes I3 = J^2 dependence is used for compressible rubbers.
Yeoh model for compressible rubbers. The strain energy density function for this model is written as.
Documented setting. The model is based on Ronald Rivlin's observation that the elastic properties of rubber may be described using a strain energy density function which is a power series in the strain.

Clarity¶

A clear use of Yeoh hyperelastic model names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is The Yeoh hyperelastic material model is a phenomenological model for the deformation of nearly incompressible, nonlinear elastic materials such as rubber.

Manages Complexity¶

Yeoh hyperelastic model compresses multiple naturalsciencesengineeringhealth details into a stable diagnostic relation. The source shows both the central mechanism—the quantity 2 C1 can be interpreted as the initial shear modulus.—and the practical consequence—2~\cfrac{\partial W}{\partial I1}~\boldsymbol{B} _;~ \cfrac{\partial W}{\partial I1} = \sum{i=1}^n i_Ci(I1-3)^{i-1} ~. This compression makes cases comparable while leaving parameters, conventions, exceptions, and evidential quality explicit.

Abstract Reasoning¶

Type the carrier. Identify the naturalsciencesengineeringhealth entities to which the claim applies.
State the relation. Use the source-grounded identity: The Yeoh hyperelastic material model is a phenomenological model for the deformation of nearly incompressible, nonlinear elastic materials such as rubber.
Check operation and conditions. Today a slightly more generalized version of the Yeoh model is used.
Demand recognition evidence. When n=1 the Yeoh model reduces to the neo-Hookean model for incompressible materials.
Test variation.

Knowledge Transfer¶

Within the home domain. Knowledge about Yeoh hyperelastic model transfers literally when a new case preserves the same carrier type, relation, and recognition test. Since a polynomial form of the strain energy density function is used but all the three invariants of the left Cauchy-Green deformation tensor are not, the Yeoh model is also called the reduced polynomial model. Today a slightly more generalized version of the Yeoh model is used. Beyond the home domain. Transfer the broader Theory relation when the natural sciences engineering health-specific differentia cannot be filled.

Relationships to Other Abstractions¶

Current abstraction Yeoh hyperelastic model Domain-specific

Parents (1) — more general patterns this builds on

Yeoh hyperelastic model is a kind of Theory Prime

Yeoh hyperelastic model is a strict kind of Theory: The Yeoh hyperelastic material model is a phenomenological model for the deformation of nearly incompressible, nonlinear elastic materials such as rubber.

Hierarchy paths (2) — routes to 2 parentless roots

Yeoh hyperelastic model → Theory → Formalization → Representation → Abstraction

Show alternative path (1)

Neighborhood in Abstraction Space¶

Yeoh hyperelastic model sits in a sparse region of the domain-specific corpus (65^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Continuum Mechanics & Field Models (42 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08