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In classical continuum theory, Volterra's principle [1, 2] is a long-knownmethod to solve linear rheological (viscoelastic) problems derived from thecorresponding elastic ones. Here, we introduce and present another approachthat is simpler to apply (no operator inverse is required to compute but onlylinear ordinary differential equations to solve). Our method starts with theknown elastic solution, replaces the elasticity coefficients with timedependent functions, derives differential equations on them, and determines thesolution corresponding to the initial conditions. We present several examplessolved via this new method, like tunnels and spherical hollows opened invarious initial stress states, and pressurizing of thick-walled tubes andspherical tanks. These examples are useful for applications and, in parallel,are suitable for testing and validating numerical methods of various kinds.

Analytical solution method for rheological problems of solids