JP Journal of Solids and Structures
Volume 3, Issue 1, Pages 43 - 69
(March 2009)
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EFFECT OF INTRINSIC LENGTH SCALE AND MULTI-SCALE INFORMATION MIGRATION FOR CALCULATING ELASTODYNAMIC GREEN’S FUNCTION USING NONLOCAL THEORY
Sourav Banerjee (U.S.A.)
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Abstract:
Continuum theory of elasticity fails to incorporate the effect of intrinsic length scales in wave propagation analysis. Real time wave field modeling needs better understanding of material behavior and its dispersion relation at intrinsic length scales. Conventional ab initio dynamics also fails to provide complete information of the system at the macro scale because the complete domain ab initio dynamics cannot be studied with present generation computers. Hence, the only viable alternative could be modifying the continuum theory considering intrinsic length scale effects in global form of analysis in a recognized fashion. Materials under fatigue loading continuously respond by adjusting their inherent microstructures and which can be simulated by a parametric variation. Such variations causes change is dispersion relation at much smaller length scale and can be predicted by ab initio dynamics. However, effect of such parameters at macro scale over a course of time needs to be studied for most elegant real time wave field modeling techniques. These techniques require elastodynamic Green’s function for the analysis and such Green’s functions must have the manifestation of the material level perturbation. In this paper, nonlocal theory has been employed to calculate the elastodynamic Green’s function in isotropic elastic solid for the first time in a perturbed sense. After having a better understanding of intrinsic length scale effects on the dispersion relation of elastic wave, suitable nonlocal parameter and nonlocal differential operator can be chosen to calculate the perturbed elastodynamic Green’s function. The methodology presented here takes into account the length scale effect in calculating the perturbed Green’s function for macro scale analysis. Later the calculated Green’s function can be also used to solve wave propagation problems in the material for modeling real time wave field. In this paper, effect of ten different length scale parameters on the elastodynamic Green’s function is shown. Green’s function with three dimensional forcing functions is also used to calculate the superposed Green’s function with parametric variation. It is found that small parametric variations can significantly affect the Green’s function and such parameters can be used as a migratory parameter for elastodynamic analysis in macro scale considering the intrinsic length scale effect. |
| Keywords and phrases: intrinsic length scale, nonlocal theory, elastodynamic Green’s function, material fatigue, multiscale model for SHM. |
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