A new nonlinear viscoelastic model and mathematical solution of solids for improving prediction accuracy

Abstract

We developed an innovative material nonlinear viscoelastic model with physical mechanism and mathematical solution to improve existing ones. the relaxation modulus transits from the glassy stage to the rubbery stage through a time-dependent viscosity in a continuous spectrum considering the nonlinear strain hardening. Experimental results of differential solid materials including asphalt concrete, agarose gel, vaginal tissue, polymer, agar, bone, spider silk, and hydrogel demonstrate that the developed model is superior to generalized Maxwell model or Prony series for more accurate prediction outside of the range for data fitting while using much less model parameters. Numerical simulation results indicate that the new model has improved accuracy. It is stable numerically, and does not reduce computation speed. Therefore, the model may be used to simulate a broad range of viscoelastic solids for predicting experimental data and responses with improved accuracy.

Viscoelasticity Acts as a Marker for Tumor Extracellular Matrix Characteristics

“…Alterations of the free volume or relaxation time are employed to explore this transition characteristics (Q. Xu et al, 2020 ). The viscoelastic deformation has been explained in terms of two atomistic phenomena ( Roylance et al, 2001 ): on the one hand, the distortion of the lengths and angles of chemical bonds linking atoms in a small and fast agitation, and on the other hand, the large-scale redistributions of atoms and molecules.…”

“…But the physical explanation of this large spring and dashpot arrangement turns out to be less obvious and more complicated (Q. Xu et al, 2020 ). These inadequacies of available models are the motivation to strive for the creation of a new viscoelastic material model that more precisely depicts a broad spectrum of materials (Q.…”

“…These inadequacies of available models are the motivation to strive for the creation of a new viscoelastic material model that more precisely depicts a broad spectrum of materials (Q. Xu et al, 2020 ). In specific detail, a theoretical model and a mathematical solve have been formulated.…”

“…Hence, the novel Xu’s model (Q. Xu et al, 2020 ) is debated in the following. An innovative nonlinear viscoelastic model for describing the glass transition of solid matter has been introduced to surmount the inadequacies of available models.…”

Fast-Acquiring High-Quality Prony Series Parameters of Asphalt Concrete through Viscoelastic Continuous Spectral Models

“…In the LVE theory, the generalized Maxwell model and generalized Kelvin model appear to be the most commonly used models for describing both time-and frequency-domain material functions, and they have been implemented into many commercial numerical simulation programs, e.g., ABAQUS, ANSYS and COMSOL Multiphysics [7][8][9][10][11]. This can be primarily attributed to their high computational efficiency and wide applicability [3,12,13].…”