Linear viscoelastic solids three-parameter model

A three-parameter model, the Zener element or standard linear solid (SLS), has been used to represent viscoelastic behavior in certain solids. Two equivalent forms of the SLS are ... 

The viscoelastic properties of the human intervertebral disc have been modeled [36, 37] using the three-parameter solid. The parameters were obtained by fitting experimentally obtained creep curves to analytical equations using linear regression (Table B2.9). 

Two test cases are used to validate the linear viscoelastic analysis capability implemented in the present finite-element program named NOVA. In the first case, the tensile creep strain in a single eight-noded quadrilateral element was computed for both the plane-stress and plane-strain cases using the program NOVA. The results were then compared to the analytical solution for the plane-strain case presented in Reference 49. A uniform uniaxial tensile load of 13.79 MPa was applied on the test specimen. A three-parameter solid model was used to represent the tensile compliance of the adhesive. The Poisson s ratio was assumed to remain constant with time. The following time-dependent functions were used in Reference 49 to represent the tensile compliance for FM-73M at 72 °C ... 

Spring and damper elements can be combined in a variety of arrangements to produce a simulated viscoelastic response. Early models due to Maxwell and Kelvin combine a linear spring in series or in parallel with a Newtonian damper as shown in Fig. 3.21. Other basic arrangements include the three-parameter solid and the four-parameter fluid as shown in Fig. 3.22. 

We have shown (Section 5.2.7) tliat the standard linear solid, a three-component spring and dashpot model, provides to a first approximation a description of linear viscoelastic behaviour. Eyring and his colleagues [52] assumed that the deformation of a polymer was a thermally activated rate process involving the motion of segments of chain molecules over potential barriers, and modified the standard linear solid so that the movement of the dashpot was governed by the activated process. The model, which now represents non-linear viscoelastic behaviour, is useful because its parameters include an activation energy and... 

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