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A constitutive model for compressible elastomeric solids


A non-linear thermo-elastic constitutive model for the large deformations of isotropic materials is formulated. This model is specialized to account for the physics and thermodynamics of the elastic deformation of rubber-like materials, and based on these molecular considerations a constitutive model for compressible elastomeric solids is proposed. The new constitutive model generalizes the incompressible and isothermal model of Arruda and Boyce (1993) to include the compressibility and thermal expansion of these materials. The model is fit to existing experimental data on vulcanized natural rubbers to determine the material parameters for the rubbers examined. The fit between the simple model and the data is found to be very good for large stretches and moderate volume changes.

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Deformation function


Material point of a body in a reference configuration


Place occupied by material point p in the current configuration

F(p)\eq(\t6/\t6p) f(p):

Deformation gradient

J\s=det F\s>0:

Determinant of F


Polar decompositions of F

U, V:

Right and left stretch tensors; positive definite and symmetric


Rotation tensor; proper orthogonal

U=Σ 1−1 3 λ 1 2 r1⊗r1 :

Spectral representation of U

V=Σ 1=1 3 λ t 2 1t⊗11 :

Spectral representation of V

λt > 0:

Principal stretches


Right principal basis


Left principal basis

C\s=FTF, B\s=FFT :

Right and left Cauchy-Green strain tensors


Absolute temperature


Internal energy density/unit reference volume


Entropy density/unit reference volume


Helmholtz free energy/unit reference volume


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Communicated by S. N. Atluri, 27 March 1996

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Anand, L. A constitutive model for compressible elastomeric solids. Computational Mechanics 18, 339–355 (1996).

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  • Experimental Data
  • Rubber
  • Thermal Expansion
  • Simple Model
  • Information Theory