Alternative Form of Standard Linear Solid Model for Characterizing Stress Relaxation and Creep: Including a Novel Parameter for Quantifying the Ratio of Fluids to Solids of a Viscoelastic Solid

Abstract

The standard linear solid model (SLSM) is a typical and useful model for analyzing stress relaxation and creep behaviors of viscoelastic solids for obtaining the corresponding viscoelastic properties. However, the analysis results cannot be directly compared to the parameters commonly adopted for defining the mechanical properties of viscoelastic solids in the finite element simulation package such as the modulus of elasticity (E e) and the two parameters in the dimensionless form of the relaxation modulus (g and τ 1). The purpose of this paper is to introduce an alternative form of SLSM in terms of E e , g, and τ 1 for characterizing stress relaxation and creep behaviors. A series of stress relaxation and creep curves with different E e , g, and τ 1 was simulated by finite element simulation. The derived alternative form of SLSM was used to curve fit the simulated stress relaxation and creep curves to obtain the corresponding values of E e , g, and τ 1. The results showed that the values of E e , g, and τ 1 obtained from the simulation were approximately equal to the theoretical ones (i.e., those set in the simulation), showing that the alternative form of SLSM can accurately evaluate the corresponding E e , g, and τ 1. In conclusion, the alternative form is formulated in terms of the parameters used to define the mechanical properties in the finite element simulation package, so that the parameters obtained by curve fitting can be directly compared to those set in the finite element simulation package. It was also found that the physical meaning of g is associated with the ratio of viscous fluids to solids of a viscoelastic solid.

Ramp-Creep Ultrasound Viscoelastography for Measuring Viscoelastic Parameters of Materials

“…The error for becomes significant (higher than 5%) for the fourth case in the second group when is 0.9. In [ 35 ], it was found that the error of the estimation of viscoelastic time constants increased nonlinearly with increasing , and became larger and larger when was larger than 0.9 and approached 1. The possible reason for this phenomenon is that numerical divergence can occur and get larger when approaches its upper limit 1, causing the distortion of the simulated strain–time curve and resulting in a significant error.…”

“…It has been reported that [ 35 ], in the standard linear solid model, there is a physical parameter defined as: where is a real number between 0 and 1. The physical meaning of is associated with the ratio of viscous fluids to solids in a viscoelastic solid [ 35 ].…”

“…is the magnitude of the strain (hereafter referred to as "strain" for brevity) of that material element. It has been reported that [35], in the standard linear solid model, there is a physical parameter defined as:…”

“…where is a real number between 0 and 1. The physical meaning of is associated with the ratio of viscous fluids to solids in a viscoelastic solid [35].…”

“…where g is a real number between 0 and 1. The physical meaning of g is associated with the ratio of viscous fluids to solids in a viscoelastic solid [35]. The relaxation time constant τ R , creep time constant τ C , and g are three parameters relevant to the viscoelastic properties of the material.…”