Mechanics of Time-Dependent Materials最新文献

This study examines the dynamics of the three different fluid types, mono-, di-, and trihybrid nanofluids, emphasizing the distinction between the three types of fluids. Also, the report highlights the significance of the microgravity environment: (g*(tau ) = g_{0}(1+acos (pi omega {t}))), and a gravitational field plus a temperature gradient typically produce buoyant convective flows in a variety of different situations, most likely in environments of low gravity or microgravity. One of the reasons for the growing interest in trihybrid nanofluids is their unique ability to improve thermal performance, which is really useful in various heat exchangers. The leading governing equations of linear momentum and energy of the developed problem are transmuted into nondimensional nonlinear coupled PDEs by using appropriate similarity modifications. The obtained systems of partial differential equations are solved via the finite-element method (FEM) in a MATLAB environment. The FEM is the most reliable, powerful, efficient, and fast convergence rate technique. The fluid velocity decreases as a function of the increasing strength of the magnetic ((M)) and Casson (beta ) parameters. However, the temperature distribution increases as a function of these parameters. It is observed that both temperature and velocity functions for trihybrid nanofluid flow obtain peak values as compared to mono- and bihybrid cases. The Nusselt number exhibits an increasing behavior by (15%) as compared to mono- and trihybrid nanofluids and (5%) when comparing bihybrid cases with trihybrid cases. Furthermore, the shear stress and Nusselt number are enhanced against increasing amplitude modulation.

The objective of this study is to analyze the thermo-mechanical interactions occurring in a nonlocal transversely isotropic functionally graded (nonhomogeneous) micropolar thermoelastic half-space when subjected to an inclined load, based on the Lord and Shulman (LS) theory. The material properties are assumed to be graded exponentially along the (z)-direction. Utilizing the normal mode technique, the exact expressions for physical fields such as normal displacement, normal stress, shear stress, temperature field, and couple stress are derived. Numerical computation of the derived results is performed for a material resembling a magnesium crystal, and graphical representations are presented to illustrate the impacts of nonhomogeneity parameter, material’s anisotropy, time, nonlocal parameter, microinertia, and the inclination angle of the applied load on the variations of different physical fields. Some specific cases of interest have been deduced from the present investigation.

Accurate outcome prediction in a thermal treatment of a biological tissue is challenging for the medical practitioners. This paper makes an attempt to predict the outcomes using fractional modelling of the heat transfer. The model has the capability to describe the characteristics in the transient heat transport in a biological tissue. A novel heat transfer model is established with two relaxation times in the Atangana and Baleanu fractional derivatives. A comparison of the thermo-mechanical waves originated inside the skin tissue was made for the ramp and harmonic heat. Laplace transform is performed to obtain the analytical solution of dimensionless temperature, dilation, displacement, and thermal stress. Effects of the fractional parameters and the time are evaluated through the graphical results for both types of heat input. Auspicious outcomes are noticed for the different thermal loadings. Results under sinusoidal heat are observed to be stable compared to the results under ramp heat. Moreover, graphical results of the physical quantities under Atangana–Baleanu fractional model are compared with the results for the conventional dual phase lag model having integer-order derivatives. Results under fractional theory provide compressed values of the physical fields and prevent the damage formation inside the tissue. The paper provides a technique suitable for outcome prediction by medical practitioners in thermal therapy for diseases such as cancer and hyperthermia.

This paper investigates the uniaxial compressive failure behavior of polymethacrylimide (PMI) foam across a range of temperatures (20 °C–200 °C), at both macro- and microscales. The investigation includes dynamic mechanical analysis and dimensional stability tests to evaluate the material’s heat resistance. The stress–strain curve of PMI foam under varying compressive failure mechanisms was analyzed, utilizing the Liu–Subhash model for accurate prediction of the material’s stress–strain constitutive relationship at different temperatures. The results indicate that between 20 °C and 180 °C, PMI foam behaves as an elastoplastic material, displaying a “three-stage” pattern in its stress–strain curve. At 200 °C, the material transitions to a hyperelastic incompressible state, evidenced by a “two-stage” stress–strain pattern. The paper also determines how temperature affects yield strength and elastic modulus, as well as the influence of strain rate at different temperatures. A quasi-static compression constitutive model for PMI foam, considering temperature effects, was modified from the Liu–Subhash model. These findings offer crucial theoretical support and data for understanding the thermo-mechanical bearing mechanism in composite sandwich structures.

Triaxial creep tests of sandstone under different seepage pressures were carried out to research the effect of seepage on the rheological laws of sandstone. The effect of seepage pressure on the rheological properties of rocks is investigated by analyzing the creep deformation, creep rate and permeability of sandstones. The creep rate curve is related to the seepage pressure and the axial load level. At a constant load level, the change in the creep curve mainly shows a trend of rapid decline, followed by stability for a long time, and finally a rapid increase under the next load level, which is linked to the variables of axial strain, radial strain, and volumetric strain of the sandstone. Permeability, which can reflect the hydration effect of rocks, exhibits a typical three-phase characteristic under seepage pressure: decreasing phase, a steady phase, and an increasing phase. For the damage creep model, firstly, the traditional Nishihara model is modified based on the fractional order theory, and the coupling model reflecting the whole creep process of sandstone is obtained by connecting the acceleration elements describing the accelerating phase of the rock in series, and finally, it is shown through the validation that the model can describe the whole creep process of sandstone under the seepage pressure. This study can provide theoretical support for the stability analysis of slope engineering under seepage conditions.

The long-term stability of coal pillars affected by cyclic dry-saturation state faces serious challenge in the normal operation of underground reservoirs in coal mines. The time-dependent deformation of coal is often controlled by the combined effects of mining disturbance, pressure- relief, dry and saturated cycles, etc. Tri-axial creep tests of coal samples were performed under stepped deviatoric stress paths including increasing axial pressure (AP) and decreasing confining pressure (CP). In addition, a fractional derivative creep model considering long-term strength is proposed to describe multi-step creep deformation. It was found that the saturation state has little effect on the peak deviatoric stress in the CP-unloading creep. In analyzing the creep strain, the tangent method can accurately distinguish transition boundary between the deceleration creep and the constant-velocity creep, and the statistical averaging method provides a large time scale for grasping the whole behavior of creep deformation. Finally, the long-term strengths of dry-saturated coal are obtained by the isochronous deviatoric stress–circumferential strain curve cluster. The proposed fractional derivative creep model is suitable for the CP-unloading creep test and can describe the multi-step creep deformation and the transient deformation in stepped stages.

The classical Green–Naghdi (GN-II) model encounters challenges in accurately describing the thermo-mechanical behavior of electro-thermoelastic materials; in particular, the model does not consider the memory effect. To address this, a novel mathematical model of the Green–Naghdi (GN-II) theory is developed, incorporating a fractional order of heat transfer. This enhanced model offers a more comprehensive understanding by including several theories as limiting examples. Central to this approach is the use of the matrix exponential method, foundational to the state-space approach in modern theory. Additionally, the Laplace transform is employed to facilitate the model formulation. This formulation is applied to a specific half-space problem, which involves exposure to a uniform magnetic field and heating by a moving heat source at a constant speed. For the practical application of this model, a numerical method is utilized for the inverse Laplace transform. The roles of various factors on the solution are examined, including the figure-of-merit quantity, speed of the heat source, fractional parameter, magnetic number, and thermal shock parameter. By exploring these variables the model provides a thorough understanding of the interaction between heat transfer and magnetic fields in electro-thermoelastic materials. This research represents a significant advancement in the modeling of electro-thermoelastic materials, offering a more accurate and comprehensive tool for predicting their behavior under varying thermal and magnetic conditions.

This paper solves the dynamic contact problem when a rigid flat punch indents into an exponentially graded (FG) viscoelastic coated homogeneous half-plane. A harmonic vertical force is applied to the FG coating, and the solution is obtained for the stress and displacement for both the FG viscoelastic coating and the half-plane using the Helmholtz functions and the Fourier integral transform technique. By applying specific boundary conditions, the contact mechanics problem is converted into a singular integral equation of the first kind. This equation is then solved numerically using the Gauss-Chebyshev integration formulas. The analysis provides detailed insights into how various parameters—such as external excitation frequency, loss factor ratio, Young’s modulus ratio, density ratio, Poisson’s ratio, indentation load, and punch length—affect the dynamic contact stress and dynamic in-plane stress.

This paper introduces a size-dependent model for evaluating thermoelastic damping (TED) in small-scaled rectangular plates, incorporating three-dimensional (3D) heat transfer. Utilizing the modified couple stress theory (MCST) and Moore–Gibson–Thompson (MGT) heat equation, we enhance the thermomechanical analysis accuracy in micro/nano-structures. The model employs MCST to derive size-dependent constitutive relations for rectangular plates, coupled with the MGT model for formulating the 3D heat conduction equation. This approach facilitates the analysis of the 3D temperature field and aids in defining TED using the energy loss method. Consequently, an analytical expression is developed to predict 3D TED in rectangular plate resonators, integrating characteristic MCST length and nonclassical MGT parameters. Comparative analyses with existing studies and a series of simulated numerical results are presented. These simulations primarily focus on contrasting the 3D model with conventional 1D models and examining the effects of implementing MCST and MGT models. Findings reveal that the proposed formulation significantly alters outcomes for very small and relatively thick plates compared to simpler models. This advancement in modeling provides a more precise understanding of TED in micro/nano-plate structures, offering vital insights for their optimal design and application in advanced technological fields.

We propose a constitutive material model to describe the rheological (viscoelastic) mechanical response of timber. The viscoelastic model is based on the generalized Kelvin chain applied to the orthotropic material and is compared to the simple approach given by standards. The contribution of this study consists of the algorithmization of the viscoelastic material model of the material applied to the orthotropic constitutive law and implementation into the FEM solver. In the next step, the fitting of the input parameters of the Kelvin chain is described, and at least a material model benchmark and comparison to the approach given by standards were done. The standardized approach is based on the reduction of the material rigidity at the end of the loading period using a creep coefficient, whereas the loading history state variables are not considered when establishing the result for a specific time step. The paper presents the benefits of the rheological model. It also demonstrates the fitting algorithm based on particle swarm optimization and the least squares method, which are essential for the use of the generalized Kelvin chain model. The material model based on the orthotropic generalized Kelvin chain was implemented into the FEM solver for the shell elements. This material model was validated on the presented benchmark tasks, and the influence of the time step size on the accuracy of model results was analyzed.