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Nonlocal response of multi‐field coupling elastic medium based on fractional order strain
Author(s) -
Ma Yongbin,
Wang Le,
Huang Fei
Publication year - 2021
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201900284
Subject(s) - laplace transform , fourier transform , mathematical analysis , fractional calculus , field (mathematics) , mathematics , physics , pure mathematics
In this work, a three‐dimensional model of the generalized thermoelasticity with fractional order stain and nonlocal effect is established. Nonlocal effect is used to depict size‐dependence feature and fractional order strain is considered to describe memory‐dependence properties. The Laplace and double Fourier transform techniques are applied to the three‐dimensional half‐space model subjected to thermal shock and traction free surface. A complex inversion formula of the transform with the techniques of the Fourier expansion been applied to obtain the inverses of double Fourier transforms, and Laplace transforms. Numerical results for the temperature, stress, strain and displacement are represented graphically based on various values of the fractional order strain parameter and elastic nonlocal parameter. The fractional order strain and nonlocal parameter has a limited effect on the thermal waves while it has significant effects on the mechanical waves.