Physical interpretation and essence of the standard linear solid model
Journal
International Journal of Mechanical Sciences
Journal Volume
310
Start Page
111139
ISSN
00207403
Date Issued
2026-01-15
Author(s)
Abstract
The standard linear solid model (SLSM) in the theory of viscoelasticity has a long history and has been widely applied in various fields, but its physical interpretation, essence, fundamentals and mathematical properties are still not completely understood. This paper uses a general, assumption-free frequency domain analysis and novel theories to demonstrate the physical meanings and numerical restrictions of the parameters of the Maxwell and Kelvin forms of the classical and a type of fractional-derivative SLSM. The findings demonstrate that each parameter of the Maxwell form has a significant and independent physical meaning associated with the mechanical properties of a constitutive part of a viscoelastic solid, and the model structure of the Maxwell form is also physically significant. The Kelvin form lacks physical significance. Hence, it is highly recommended to employ the Maxwell form if the SLSM is intended to be used (unless there is a reason that the Kelvin form is needed) based on the consideration of physical significance, although both forms are completely equivalent in terms of their mathematical and analytical properties. However, no matter which form is employed, consistent analysis results and accurate interpretations can always be obtained, as long as the parameters of both forms are accurately interpreted and transformed using the relationships between them. The numerical restrictions of the parameters of both forms of the SLSM are simple: each parameter must be positive. There do not exist other inequalities that define the numerical restrictions of the parameters of a form of the SLSM.
Subjects
Constitutive modeling
Frequency domain analysis
Rheology
Standard linear solid model
Thermodynamic consistency
Viscoelasticity
Publisher
Elsevier Ltd
Type
journal article