A study of biothermoelastic interaction in viscoelastic biological tissue using the eigenvalues method

Thermoelasticity integrates thermal and mechanical responses in materials subjected to coupled loads, with classical models constrained by the assumption of infinite thermal wave speeds. Advanced frameworks, such as the Lord–Shulman, Green–Naghdi, and dual‐phase lag models, address this limitation by introducing finite wave speeds and relaxation times. The Moore–Gibson–Thomson (MGT) model further refines heat conduction through third‐order derivatives, ensuring more realistic wave behavior. Memory‐dependent derivatives (MDD) enhance modeling by capturing historical effects, offering superior computational efficiency compared to fractional derivatives in dynamic scenarios, such as thermal shock or material processing. When combined with Eringen's nonlocal continuum theory, MDD accounts for small‐scale interactions that are critical in nanostructures. This study develops an advanced thermoelastic model that integrates MDD with the MGT equation to analyze a semi‐infinite medium under a moving heat source. The governing equations are solved analytically in the Laplace domain using the eigenvalue method, and numerical inversion is performed to obtain time‐domain solutions. Results for a copper medium, presented through figures and tables, demonstrate the model's capability to predict temperature, displacement, and stress distributions. These findings highlight the significance of memory effects and nonlocal interactions for applications in nanotechnology and engineering design.

Functionally graded material (FGM) concept has been applied successfully in order to improve/design heat transfer, electric and electronic conductivity, static and dynamic strengths of adhesive joints by reliving stress distributions in both adhesive and adherend materials. This new approach relies on tailoring material composition of adhesive and adherends along one or more coordinate directions. Thermal residual stresses in adhesive joints are a vital issue in terms of the joint strength. FGM concept also allows to relieve/control thermal residual stresses encountered in adhesive joints due to mismatches between coefficients of thermal expansion of adhesive and adherend materials. Mathematical models and solutions on the thermal residual stress analysis have been continuously improved. This paper reviews the current status of mathematical models, and offers an improved mathematical model and numerical solution method by considering two-dimensional thermal stress and deformation states of adhesively bonded bi-directional functionally graded clamped plates subjected to an in-plane heat flux along one of the ceramic edges. This mathematical model assumes the material properties of the functionally graded plates to vary with a power law along two in-plane directions and not through the plate thickness direction, in particular, considers the spatial derivatives of thermal and mechanical properties of the material, and enables the investigation of the effects of the bi-directional composition variations and spatial derivative terms on the displacement, strain and stress distributions. The heat conduction and Navier equations describing the twodimensional thermo-elastic problem are discretized using finite-difference method, and the set of linear equations are solved using the pseudo singular value method. The functionally graded plates relieve both stress and strain distributions and levels in the adhesive layer and in the plates even though the adhesive layer is still ungraded. The spatial derivatives of mechanical and thermal properties of the local material become more effective on the strain and stress distributions of the plates and adhesive layer. The model, disregarding these derivative terms, exhibits sensitivity to small changes in the compositional gradients (n, m) by adjusting the variations of ceramic volume fraction along the x - and y-directions, respectively, and instability in the calculation of stress and strain distributions and levels. However, the improved model with material derivatives, which considers the effects of these derivative terms, predicts stress and strain distributions and levels complying with changes in the compositional gradient exponents.

Dimensionless solutions and general characteristics of bioheat transfer during thermal therapy

An explicit dynamic coupled thermal-mechanical Arbitrary Lagrangian Eulerian (ALE) model was established to simulate orthogonal cutting AISI 52100 bearing steel, and its temperature and stress distribution. Based on ABAQUS, The ALE approach effectively simulates plastic flow around round edge of the cutting tool without employing chip separation criteria. The calculation results reveal that cutting speed and cutting depth have great impact on chip morphology, stress and temperature distribution in the finished surface and subsurface, the predicted temperature agrees well with experiment data obtained under the similar cutting conditions as well as the change in chip morphology from continuous to sawtooth as the cutting speed increases.

Fundamental solution in generalized magneto-thermoelasticity with two relaxation times for perfect conductor cylindrical region

Three-dimensional surface-mount assemblies (SMA) (leaded chip carriers (LCC) and self-stretching flip chip (SSC)) are modeled in this study by an effective finite element method to analyze the thermal conduction and thermal stress during the power-cycling. In this method the solder joints and leads are modeled by a special element, called the solder joint element. Since the solder joints and leads have the same shape, the stiffness matrix or thermal conduction matrix can be given by a unitized matrix for every solder joint element. Based upon an influence function method, the stiffness matrix and thermal conduction matrix are determined by finite element analyses. And then with the solder joint elements, finite element analyses of the global model of the surface-mount assembly are carried out to investigate the whole-field temperature distributions and displacement distributions. As an example evaluation, power cycling (power on without ambient temperature change) simulation is carried out. The computed temperature distributions are utilized to analyze the displacement fields for every solder joint and the stress distribution in the printed circle board (PCB). The displacement fields are then used as the imposed displacement boundary conditions for computing the stress and the strain of every solder joint. It is shown that the proposed method can be used as a rapid estimating tool to investigate the temperature distribution of the SMAs and thermal stress-strain distribution in the solder joints.

Alcoa to acquire Tital

Numerical analysis and experimental investigation of welding residual stresses and distortions in a T-joint fillet weld

The determination of the stress, strain, and displacement distribution around a horizontal tunnel is an important engineering problem. The initial solution was obtained assuming the rock to be linearly elastic. The stress distribution was obtained by analogy with the problem of stress distribution around holes made through elastic plates (see Habib (1973)). Thus the problem was assumed to be a plane stress problem. The first solution seems to have been obtained by G. Kirsch in 1898 (for the history of the problem, see Obert and Duvall (1967)).

Some model tests have shown that the H-V reinforcement system behaves more uniform, carries greater surcharge, and settles less than the equivalent strip one. However, the mechanism of the H-V reinforced soil foundation is still not well understood. FEM is a useful method to investigate the soil foundation. The different type of foundation can be multiple simulated by finite element. Through comparing the difference of stress and displacement distribution in strip and H-V reinforced soil foundation, the friction on the surface of strip and H-V reinforcement, and the stress distribution on a vertical inclusion of H-V reinforcement. It can be concluded that beside the tension membrane reinforcement mechanism, the H-V reinforcement of relatively small vertical inclusions height behaves as a shallow beam that deflects under the footing loading leading to higher contact pressure underneath. The H-V reinforced base acts as a mattress to restrain the soil from moving upward/downward outside the loading area, redistributes the footing load over a wider area, and reduces the settlement, which in turn principally improves the bearing capacity and reduce the settlement of foundation.

This paper investigates the stress and displacement distribution in a two-dimensional elastic hollow disk subjected to distributed diametric loading, extending our previous analysis of concentrated loading [Okamura et al. Strength Mater. 57 , 102–114 (2025)]. The study provides deeper insights into the mechanical behavior of materials such as concrete and rock by examining the effects of load distribution on stress localization and displacement patterns. Using elastodynamic theory, we derive the static stress distributions and identify key differences from the concentrated loading case, particularly in the locations and magnitudes of stress extrema. This work contributes to a more comprehensive understanding of stress behavior in elastic disks under realistic loading conditions.

Traditional jaw crusher has the problems of unreasonable structure, heavy weight, low utilization of material and high cost. This paper chooses the flywheel which has great influence on the total weight as the research object. Finite element method are used to anlysis stress and displacement distribution under the action of maximum crushing force. It shows weak link and surplus position of primary structure. Use the parametric design language APDL to establish and analyze finite element model, based on crusher structural features. Make lightweight design meeting the demands of intensity, stiffness and moment of inertia. The result indicates that modified flywheel is less than the original one by 5%, makes structure more reasonable and stress distribution more even.

Bio-heat transfer analysis during short pulse laser irradiation of tissues

The effect of blood velocity pulsations on bioheat transfer is studied. A simple model of a straight rigid blood vessel with unsteady periodic flow is considered. A numerical solution that considers the fully coupled Navier-Stokes and energy equations is used for the simulations. The influence of the pulsation rate on the temperature distribution and energy transport is studied for four typical vessel sizes: aorta, large arteries, terminal arterial branches, and arterioles. The results show that: the pulsating axial velocity produces a pulsating temperature distribution; reversal of flow occurs in the aorta and in large vessels, which produces significant time variation in the temperature profile. Change of the pulsation rate yields a change of the energy transport between the vessel wall and fluid for the large vessels. For the thermally important terminal arteries (0.04-1 mm), velocity pulsations have a small influence on temperature distribution and on the energy transport out of the vessels (8 percent for the Womersley number corresponding to a normal heart rate). Given that there is a small difference between the time-averaged unsteady heat flux due to a pulsating blood velocity and an assumed nonpulsating blood velocity, it is reasonable to assume a nonpulsating blood velocity for the purposes of estimating bioheat transfer.

The dynamical interactions caused by a line heat source moving inside a homogeneous isotropic thermo-microstretch viscoelastic half space, whose surface is subjected to a thermal load, are investigated. The formulation is in the context of generalized thermoelasticity theories proposed by Lord and Shulman (J. Mech. Phys. Solid, 15, 299 (1967)) and Green and Lindsay (Thermoelasticity, J. Elasticity, 2, 1 (1972)). The surface is assumed to be traction free. The solutions in terms of displacement components, mechanical stresses, temperature, couple stress, and microstress distribution are procured by employing the normal mode analysis. The numerical estimates of the considered variables are obtained for an aluminium–epoxy material. The results obtained are demonstrated graphically to show the effect of moving heat source and viscosity on the displacement, stresses, and temperature distribution.