Application of the memory-dependent derivative to a nonlocal thermoelastic problem with a new version of a nonlinear memory kernel

IF 3 4区工程技术 Q3 MECHANICS

Continuum Mechanics and Thermodynamics Pub Date : 2026-02-24 DOI:10.1007/s00161-026-01457-5

Subhadip Karmakar, Smita Pal Sarkar

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Abstract

This study formulates a new version of a nonlinear memory kernel within the framework of the memory-dependent derivative and applies it to a two-dimensional nonlocal thermoelastic problem subjected to a heat source, using the dual phase lag model. The rationale for introducing the new version of the memory kernel is underpinned by a comprehensive literature review that brings to light the established advantages of a nonlinear quadratic kernel. A semi-analytical method is used to determine the thermophysical quantities by bringing in suitable potential functions into the analysis. The governing equations are first transformed using Laplace and Fourier integral transforms, and numerical inversion techniques are then employed to retrieve the solutions in the physical domain. Recognizing the crucial influence that kernel functions exert in the structure of memory-dependent derivative, this work undertakes a comparative analysis of two distinct generalized thermoelastic models, focusing on how variations in kernel formulations impact the resulting thermophysical behavior. The results under nonlocal influences have been examined for two distinct thermoelastic models. The influence of the memory-dependent derivative is evaluated by presenting results obtained without it and comparing them with those that incorporate its effect.

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具有新版本非线性记忆核的记忆相关导数在非局部热弹性问题中的应用

本研究在记忆相关导数的框架内提出了一个新版本的非线性记忆核，并使用双相位滞后模型将其应用于受热源影响的二维非局部热弹性问题。介绍新版本内存内核的基本原理是通过全面的文献综述来支持的，该综述揭示了非线性二次核的既定优势。在分析中引入合适的势函数，采用半解析法确定热物理量。首先使用拉普拉斯和傅立叶积分变换对控制方程进行变换，然后使用数值反演技术在物理域中检索解。认识到核函数对记忆依赖导数结构的重要影响，本工作对两种不同的广义热弹性模型进行了比较分析，重点关注核公式的变化如何影响所产生的热物理行为。对两种不同的热弹性模型检验了非局部影响下的结果。通过展示没有记忆依赖导数的结果，并将它们与包含其影响的结果进行比较，来评估记忆依赖导数的影响。

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来源期刊

Continuum Mechanics and Thermodynamics 物理-力学

CiteScore

5.30

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： This interdisciplinary journal provides a forum for presenting new ideas in continuum and quasi-continuum modeling of systems with a large number of degrees of freedom and sufficient complexity to require thermodynamic closure. Major emphasis is placed on papers attempting to bridge the gap between discrete and continuum approaches as well as micro- and macro-scales, by means of homogenization, statistical averaging and other mathematical tools aimed at the judicial elimination of small time and length scales. The journal is particularly interested in contributions focusing on a simultaneous description of complex systems at several disparate scales. Papers presenting and explaining new experimental findings are highly encouraged. The journal welcomes numerical studies aimed at understanding the physical nature of the phenomena. Potential subjects range from boiling and turbulence to plasticity and earthquakes. Studies of fluids and solids with nonlinear and non-local interactions, multiple fields and multi-scale responses, nontrivial dissipative properties and complex dynamics are expected to have a strong presence in the pages of the journal. An incomplete list of featured topics includes: active solids and liquids, nano-scale effects and molecular structure of materials, singularities in fluid and solid mechanics, polymers, elastomers and liquid crystals, rheology, cavitation and fracture, hysteresis and friction, mechanics of solid and liquid phase transformations, composite, porous and granular media, scaling in statics and dynamics, large scale processes and geomechanics, stochastic aspects of mechanics. The journal would also like to attract papers addressing the very foundations of thermodynamics and kinetics of continuum processes. Of special interest are contributions to the emerging areas of biophysics and biomechanics of cells, bones and tissues leading to new continuum and thermodynamical models.