Abstract
A spring/rod model is presented that describes one-dimensional behaviour of solids susceptible to large or small viscoelastic deformation. Derivation of its constitutive equation is underpinned by the fact that the internal energy, which the elastic part of deformation stores in the spring, changes in time with the observed strain as well as with some, unknown part of the strain-rate. The latter emerges through the action of a viscous flow potential and is the source of inelastic deformation. Thus, unlike its conventional viscoelasticity counterparts, the model does not postulate a priori a rule that relates strain with viscous flow formation. Instead, it considers that such a rule, as well as other important features of combined elastic and inelastic material response, should become known a posteriori through the solution of a relevant, well-posed boundary value problem. This paper begins with considerations compatible with large viscoelastic deformations and gradually progresses through simpler modelling situations. The latter also include the case of small viscoelastic strain that underpins formulation of classical, spring-dashpot viscoelastic models. In an example application, a relevant closed-form solution is obtained for a spring undergoing small viscoelastic deformation under the influence of a viscous flow potential which is quadratic in the stress.
Highlights
The subjects of Elasticity, Plasticity and Viscoelasticity are generally considered as parts of continuum solid mechanics that deal with different kinds of solid material behaviour
This is a case in which the internal energy function and the viscous flow potential of that geometrically linear viscoelastic spring are both quadratic functions of their arguments
The generalised viscoelastic spring model presented in this communication is directly relevant to the behaviour of one-dimensional solid components susceptible to large or small viscoelastic deformation
Summary
The subjects of Elasticity, Plasticity and Viscoelasticity are generally considered as parts of continuum solid mechanics that deal with different kinds of solid material behaviour. The present communication aims to demonstrate that the outlined new postulations [7] are relevant and applicable to classical viscoelasticity situations, and, to indicate that all three subjects of Hyperelasticity, Plasticity and Viscoelasticity share a common theoretical background With these aims in mind, attention here focuses onto one of the simplest possible models of one-dimensional deformable bodies, namely that of a cantilever viscoelastic cylindrical rod. This is a case in which the internal energy function and the viscous flow potential of that geometrically linear viscoelastic spring are both quadratic functions of their arguments.
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