Equivalences and Contrasts of Thermo-Elasticity and Thermo-Viscoelasticity: A Comprehensive Critique

Abstract

Similarities and differences between thermo-elasticity and thermo-viscoelas- ticity are critically examined and evaluated. Topics include, among others, constitutive relations, Poisson's ratio, energy dissipation, temperature effects on material properties, thermal expansions, loading histories, failure criteria, lifetimes, 1–D beams, torsion, columns, plates, motions in time of neutral axes and shear centers, computational issues, wave propagation, torsional divergence, control reversal, aerodynamic derivatives, flutter and experimental determinations of viscoelastic properties. The full, partial or no possible applications of the elastic/viscoelastic correspondence principle, including approximate approaches, are analyzed and discussed.

Keywords:

• Creep buckling
• Elastic-viscoelastic correspondence principle
• Failure probability
• Flutter
• Poisson's ratio
• Residual stresses
• Survival times
• Temperature induced non-homogeneities
• Thermal Euler–Bernoulli bending
• Thermal stresses
• Wave motion

Acknowledgments

This paper represents an invited lecture at the 9th International Congress in Thermal Stresses. Budapest, June 6–9, 2011.

Support by the Private Sector Program Division (PSP) of the National Center for Supercomputing Applications (NCSA) at the University of Illinois at Urbana-Champaign (UIUC) is gratefully acknowledged.

Notes

Civil and military airplanes, missiles, spacecraft, unmanned aerial vehicles (UAVs), micro aerial vehicles (MAVs), wind turbine and helicopter blades, etc.

Underlined indices indicate no summations.

Force (F), length (L), time (T).

Restrictions: no dynamic effects, no mixed or moving boundary conditions, isothermal, homogeneous materials, no thermal strains if BCs are non-zero. It is also required that the viscoelastic bulk modulus K(t) = ∞ and the Young's, which leads to the shear moduli relation E(t) = 3G(t).

Also see the next Section on FGM.

The time intervals need not be of equal size.

Due to any one or more of material distributions, FGMs and material dependence on thermal gradients.

The integral stress-strain relations (2) can be turned into differential equations by differentiating them N _ijkl number for times [24] with N _ijkl defined by Eqs. (6).

An extensive bibliography on this subject may be found in [24].

In general, I _μ(x) = ı^−μ J _μ(ıx), where J _μ is the Bessel function of the first kind.

Series multiplications, algebra, differentiations, integrations, etc.

See Section on Material Failure Criteria.

See [139] for an extensive bibliography.

In elastic materials any two of the following is sufficient: Young's, shear or bulk moduli or Poisson's ratio. In viscoelastic material PRs are not material properties. See previous Section on PRs.

See [60, 61] for comprehensive bibliographies.