Constitutive Relation of Engineering Material Based on SIR Model and HAM

Abstract

As an epidemic mathematical model, the SIR model represents the transition of the Susceptible, Infected, and Recovered. The profound implication of the SIR model is viewed as the propagation and dynamic evolutionary process of the different internal components and the characteristics in a complex system subject to external effect. The uniaxial stress-strain curve of engineering material represents the basic constitutive relation, which also represents the damage propagation in the units of the damaged member. Hence, a novel dynamic stress-strain model is established based on the SIR model. The analytical solution and the approximate solution for the proposed model are represented according to the homotopy analysis method (HAM), and the relationship of the solution and the size effect and the strain rate is discussed. In addition, an experiment on the size effect of confined concrete is carried out and the solution of SIR model is suitable for simulation. The results show that the mechanical mechanism of the parameters of the uniaxial stress-strain model proposed in this paper reflects the actual characteristics of the materials. The solution of the SIR model can fully and accurately show the change of the mechanical performance and the influence of the size effect and the strain rate.

Effect of Filling Interval Time on Mechanical Characteristics of Cemented Tailing Backfill

“…According to the literature, the energy required for the damage to develop to d S D damage is G normald S D = 1 2 S C σ d ε …”

Experimental Research on Uniaxial Compression Constitutive Model of Hybrid Fiber-Reinforced Cementitious Composites

“…In this article, a load-deformation constitutive model of HFRC is established by introducing SIR model of infectious disease transmission dynamics [19]. The SIR model divides the population in the epidemic area into three categories: the susceptible group S, referring to those who have not been infected; the infected group, I, referring to those who have been infected with infectious diseases, can spread to the members of class, S; and the Removed group, R, referring to those who have been isolated or immunized by the disease.…”

Experimental investigation and design method for the shear strength of self-piercing rivet connections in thin-walled steel structures

“…Based on the transmission dynamics model of infectious diseases (SIR model) [27,28], a stress-strain model for SPR specimens was established to account for SPR behaviors:…”

“…Therefore, the numerical calculation method is usually used to solve it. In this paper, based on the homotopy analysis method (HAM) [27][28][29], approximate analytic solution of Formula (4) is derived in Formula (5): According to characteristic of analytic solution, Formula (5) can be simplified:…”