Archive of Applied Mechanics ( IF 2.8 ) Pub Date : 2024-03-11 , DOI: 10.1007/s00419-024-02561-1 A. M. Zenkour , T. Saeed , A. A. Al-Raezah
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.
中文翻译:
斜坡式加热引起的皮肤组织一维热弹性响应的精致 Lord–Shulman 模型的分数阶
摘要
本手稿介绍了一种新颖的数学公式,采用分数阶原理来分析皮肤组织在精炼的洛德-舒尔曼广义热弹性模型框架内对斜坡式加热的响应。经典的、简单的洛德-舒尔曼模型和精致的洛德-舒尔曼模型都被检验。推导了这三个模型的控制方程,并使用拉普拉斯变换方法及其逆方法获得了初始和边界条件问题的通解。数值结果通过图形进行说明,提供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。考虑不同的理论框架,对斜坡型热量对温度、位移和膨胀分布的影响进行了数值和图形探索。确定了分数参数引起的电导率降低及其对温度、位移和应力的影响。