Fractional order of refined Lord–Shulman model for a 1D thermoelastic response of skin tissue due to ramp-type heating

IF 2.2 3区工程技术 Q2 MECHANICS Archive of Applied Mechanics Pub Date : 2024-03-11 DOI:10.1007/s00419-024-02561-1

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Abstract

This manuscript introduces a novel mathematical formulation employing fractional-order principles to analyze the response of skin tissue exposed to ramp-type heating within the framework of the refined Lord–Shulman generalized thermoelasticity model. The classical, simple Lord–Shulman, and refined Lord–Shulman models are each examined. The governing equations for these three models are derived, and a general solution for the initial and boundary condition problem is obtained using the Laplace transform approach and its inverse. Numerical results are illustrated through figures, providing a comparative analysis across various theories and fractional-order values to elucidate the impact on temperature, displacement, and dilatation distributions. The numerical and graphical exploration of the influence of ramp-type heat on temperature, displacement, and dilatation distributions is conducted, considering different theoretical frameworks. The reduction in the conductivity caused by the fractional parameter and its ensuing effects on temperature, displacement, and stress are determined.

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细化 Lord-Shulman 模型的分数阶，用于测量斜坡式加热引起的皮肤组织一维热弹性响应

摘要本手稿介绍了一种新颖的数学公式，它采用分数阶原则，在改进的 Lord-Shulman 广义热弹性模型框架内分析暴露于斜坡型加热的皮肤组织的响应。对经典模型、简单 Lord-Shulman 模型和改进 Lord-Shulman 模型分别进行了研究。推导出了这三种模型的控制方程，并利用拉普拉斯变换及其逆变换方法获得了初始条件和边界条件问题的一般解。数值结果通过图表说明，提供了各种理论和分数阶值的比较分析，以阐明对温度、位移和膨胀分布的影响。考虑到不同的理论框架，对斜坡型热量对温度、位移和扩张分布的影响进行了数值和图形探索。确定了分数参数导致的电导率降低及其对温度、位移和应力的影响。

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来源期刊

Archive of Applied Mechanics 物理-力学

CiteScore

4.40

自引率

10.70%

发文量

234

审稿时长

4-8 weeks

期刊介绍： Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.