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Memory response on generalized thermoelastic medium in context of dual phase lag thermoelasticity with non-local effect

Tiwari R., Saeed A. M., Kumar R., Kumar A., Singhal A.

Archives of Mechanics

2022

Vol. 74, nr 2-3

69--88

Theory of non-local continuum is contemporary appraised and is found to be supplementary coherent to capture the impacts of each and every point of the material at its single point. The conviction of memory dependent derivative is also newly appraised and is observed to be more intuitionistic for predicting the realistic character of the real-world obstacles. Attractiveness of the belief of a memory dependent derivative lies in its unique properties such as its significant constituents – a kernel function and time-delay are freely selected according to the requirement of a problem. The present study comprises a new meticulous thermoelastic heat conduction model for the homogeneous, isotropic, thermoelastic half space medium concerning memory effects and non-local effects. Governing equations are constructed on the basis of the newly appraised non-local generalized theory of thermoelasticity with two phase lags in the frame of a memory dependent derivative. Exact analytical solutions of the physical fields such as dimensionless temperature, displacement as well as thermal stress are evaluated by using a suitable technique of the Laplace transform. Quantitative results are determined in a time-domain for different values of time by taking the numerical inversion of the Laplace transform. Noteworthy role of the constituents of the memory dependent derivative such as kernel function as well as time-delay factor has been scrutinized on the crucial field variables of the medium through computational outcomes. Moreover, the impact of non-local parameter is examined on the variations of field quantities through the quantitative results.

From Euclid's elements to cosserat continua

Povstenko J.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2008

Vol. 13

33-42

The classical continuum theory is based on the assumption that each small particle behaves like a simple material point and ignores the relative motions of constituent parts of this particle. The development of the notion of a point and the development of non-Eeuclidean geometry is considered. The Cosserat continuum is an example of medium with microstructure, in which "a ponit" has an internal structure. Its motion is determined by the displacement and rotation fields.