Abstract
This chapter contains a comprehensive discussion of the types of boundary-value problems encountered in linear viscoelasticity. The chapter presents detailed solution methods for compressible and incompressible solids, including materials with synchronous moduli, whose property functions are assumed to have the same time dependence. The method of separation of variables in the time domain and frequency domains is also described in full, as is the use of the Laplace and Fourier transformations. The elastic–viscoelastic correspondence principle, which allows viscoelastic solutions to be constructed from equivalent elastic ones and as a consequence of the applicability of integral transforms, is also developed and examined in detail.
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Notes
- 1.
The components of the displacement vector, the stress and strain tensors, the material density, the boundary values, and the normal to the surface, will in general depend on position. For clarity of exposition, however, dependence on position is omitted most of the time, but shall be understood.
- 2.
The reader is reminded that all boundary data as well as the displacement, stress and strain fields are dependent on position but that, sometimes, such dependence has been omitted for clarity.
- 3.
This limitation is implicit also in the methods presented in Sects. 9.6 and 9.7, for displacement-only boundary conditions. .
References
D.C. Leigh, Nonlinear Continuum Mechanics, (McGraw-Hill, NY, 1968) pp. 117–138
E. Volterra, J.H. Gaines, Advanced Strength of Materials, (Prentice-Hall, NJ, 1971), pp. 12–19, pp. 177–186
R.M. Christensen, Theory of Viscoelasticity, 2nd Ed. (Dover, 1982), pp. 37–41
Y.C. Fung, Foundations of Solid Mechanics, (Prentice Hall, NJ, 1965) pp. 99–103
I.S. Sokolnikoff, Mathematical Theory of Elasticity, (McGraw-Hill, US, 1956), pp. 71–79
A.C. Pipkin, Lectures on Viscoelasticity theory, (Springer, Berlin, 1956), 2nd Ed. pp. 77–79
T.L. Anderson, Fracture Mechanics, Fundamentals and Applications, 2nd Ed. CRC, CS, 1956), pp. 51–55
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Gutierrez-Lemini, D. (2014). Isothermal Boundary-Value Problems. In: Engineering Viscoelasticity. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-8139-3_9
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DOI: https://doi.org/10.1007/978-1-4614-8139-3_9
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