MODELING AND RESEARCH OF PROCESSES FOR CREEP COMPLIANCE AND RELAXATION BASED ON FADING MEMORY CONCEPT
DOI:
https://doi.org/10.26577/JMMCS.2023.v117.i1.05Keywords:
relaxation, bisection method, conditional instantaneous stress, relaxation stressAbstract
Using of rheonomic materials in engineering structures is one of the most important issues in determining strength and durability. The main task of the mechanics of a deformable solid is to simulate the processes of deformation of viscoelastic materials. Currently, there are quite well-developed theories and methods of viscoelasticity that allow to determine and describe the viscoelastic properties of materials. They differ between linear and nonlinear viscoelasticity. In the linear and nonlinear theory of viscoelasticity, such a task is reduced to finding creep and relaxation kernel. Creep and relaxation kernel are interconnected by a known integral relationship that establishes a relationship between stress, strain and time.
The work is devoted to modeling of stress relaxation and sttrain of hereditary materials. Stress relaxation is described by a nonlinear integral equation with an Abel’s kernel. New efficient method has been proposed for determining of parameters (α, δ). Bisection method is used for obtaining of parameter α. Algorithm have been developed for calculating of parameters of α and δ.
References
[2] Tschoegl N.N. "The phenomenological theory of linear viscoelastic behavior An introduction, Springer-Verlag, Berlin, Germany, 1989
[3] Iskakbayev A., Teltayev B., Rossi C.O., Yensebayeva G. "Determination of nonlinear creep parameters for hereditary materials Applied Sciences, 2018, p. 1-17.
[4] Iskakbayev A.I., Teltayev B.B., Yensebayeva G.M., Kutimov K.S. "Computer modeling of creep for hereditary materials by Abel’s kernel News of the National Academy of Sciences of the Republic of Kazakhstan. Series of Geology and technical sciences, 6(432), 2018, p. 66-76.
[5] Dergunov N.N., Napernik l.Kh., Rabotnov Yu.N. "Analysis of graphite behavior based on nonlinear hereditary theory pMTF, No.2, 1971.
[6] Maksimov R.D., Jirgens L., Jansons J., Plume E. "Mechanical properties of polyester polymer-concrete Mechanics of Composite Material, Vol. 35, No.2, 1999.
[7] Maksimov R.D., Plume E. "Long-term creep of hybrid aramid/glass-fiber-reinforced plastics Mechanics of Composite Materials, Vol. 37, No.4, 2001.
[8] Rabotnov Yu.N. "Balance of the elastic medium with a aftereffect Applied Mathematics and Mechanics, vol. 12, issue 1, pp. 53-62, 1948.
[9] Volterra V. "Lecons surles fonctions de lignes Paris. Gautheir-Villard, 1913.
[10] Rabotnov Yu.N. "Balance of the elastic medium with a aftereffect Applied Mathematics and Mechanics, vol. 12, issue 1, pp. 53-62, 1948.
[11] Rabotnov Yu.N. "Mechanics of a deformed solid body Moscow; Nauka, 1988. 712 p.
[12] Rabotnov Yu.N. "Elements of hereditary mechanics of solids Nauka, Moscow, Russia, 1977. (in Russ.)
