Archive of Applied Mechanics最新文献

This study presents a comprehensive mathematical framework for modeling thermoelastic and thermodiffusive processes in fractal spherical tumor media, integrating the Moore–Gibson–Thompson (MGT) heat conduction theory with nonlocal elasticity and memory-dependent derivatives. The biological complexity of tumor tissue is captured via non-integer dimensional geometry, allowing for precise representation of radial transport phenomena. By incorporating kernel-based memory effects and Eringen’s nonlocal stress model, the coupled bioheat diffusion equations address the limitations of classical Fourier and Fick laws. The formulation includes generalized vector operators and Laplace-transformed governing equations to determine the distributions of displacement, temperature, concentration, stress, and chemical potential. Numerical inversion using the Gaver–Stehfest algorithm enables time-domain simulations, which elucidate the interplay between memory effects, nonlocal interactions, and fractal structure in biological systems. This work introduces a unified fractal–fractional framework for modeling thermoelastic diffusion in spherical tumor shells, offering methodological novelty and biomedical relevance to hyperthermia, cryotherapy, and drug delivery.

The electrodeposition method is among the various methods to produce metal foams by coating open-cell polymeric foams with a metallic layer. This process is governed by strong mechanical and electrical interactions which arise due to different factors such as presence of ions in the electrolyte, applied external current, charged solid surface and ionic concentration gradient. Hence, the related physical effects result in a nonlinear coupled process at the macroscale, which introduces a complex challenge for modelling and computational treatment. This work proposes a model to describe the electrocoating of polyurethane foams with nickel ions at macroscale, in an isothermal process and under the simplifying assumptions such as rigidity of the foam and incompressibility of the electrolyte. To do so, the multi-phase flow through the porous medium has to be modelled on a macroscopic scale. The governing equations describing the coating process are developed from the fundamental balance equations of mixture theory. By reasonable physical assumptions, different processes contributing to ionic transport, i.e. diffusion, convection and migration, are considered, and finally, the influence of different parameters in each transport mechanism is investigated. First 1D simulations show that the presented model is able to describe the experimentally observed effects, at least in a qualitative way.

This paper introduces a novel algorithmic model that simulates cracks in various materials, loadings, and boundary conditions. The new model can complete fracture simulations in just 1 s for 2D scenarios and 22 s for 3D scenarios. The highly efficient algorithm is based on an innovative computational framework of the peridynamic method, featuring reformulated peridynamics equations and a new scheme for bond shape and arrangement. Beyond its remarkable speed, the new model also improves the stability of peridynamics by removing divergence problems, since it is independent of horizon size or radius. The algorithm has been rigorously tested, validated against experimental data, and benchmarked against other numerical models across a range of problems. Furthermore, its high efficiency is clearly demonstrated when benchmarked against other methods.

This study presents a sophisticated thermoelastic model that integrates dual-phase-lag theory, memory-dependent kernel operators, and two distinct temperature fields—thermodynamic and conductive. The framework accounts for microstructural effects and temperature-dependent internal heat sources within a spherical cavity, modeled using a non-Fourier heat conduction approach grounded in energy conservation. The resulting system of coupled partial differential equations captures the evolution of thermal and mechanical fields under nonequilibrium conditions. Exact analytical solutions are obtained via Laplace transformations, and the Dubner–Abate technique is employed for accurate numerical inversion to recover time-domain behavior. The model offers enhanced physical realism compared to classical and fractional approaches, effectively representing the delayed and spatially distributed propagation of heat. Numerical simulations highlight the influence of kernel structure, hysteresis, and temperature discrepancy on stress and temperature profiles. These findings demonstrate the model’s predictive capability for advanced applications in microelectronics, nano-engineered materials, biomedical systems, and smart structures. An appendix detailing the numerical scheme is included to support reproducibility.

This paper deals with the development and assessment of 1D micropolar beam models of different lattice core structures according to micropolar continuum theory. The deformation kinematics of the lattice beams are based on the equivalent single-layer Timoshenko beam theory. The discrete-to-continuum transformation, through strain energy equivalence of discrete unit cells and corresponding micropolar continuum, is applied to deduce the constitutive law. The strain energy of the discrete unit cell is written by treating each element as Euler–Bernoulli beam element. The four different types of lattice cores are considered in the present study. The principle of minimum potential energy is used to derive the equilibrium equation for the webcore 1D micropolar Timoshenko beam model. Furthermore, the successive approximations are employed in the micropolar continuum model to deduce the governing equations for the couple stress Timoshenko beam model and classical Timoshenko and Euler–Bernoulli beam models. The couple stress Timoshenko beam models are obtained by assuming the internal antisymmetric shear force (S_a) equal to zero and microrotation (ψ) equal to macrorotation (Ω) for all lattice cores. Fourier series-based analytical solutions are obtained for the static behaviour of the different beams under uniformly distributed, sinusoidal and point loads. The present analytical solutions are compared with those obtained through the finite element method (ABAQUS) using plane frame element and it has been found that the accuracy of the different beam models is highly sensitive to the geometric properties of lattice. Among different theories, the micropolar continuum Timoshenko beam theory yields promising results.

This paper introduces an analytical framework for examining the coupled bidirectional bending and torsional vibrations of non-symmetric, axially loaded thin-walled Timoshenko–Ehrenfest beams. By integrating axial loads, shear deformation, rotational inertia, and warping stiffness into the traditional Timoshenko–Ehrenfest beam theory, we enhance its ability to address complex bending-torsion interactions. Utilizing Hamilton’s principle, we derive five coupled differential equations and twelve boundary conditions to accurately describe the beam’s dynamic behavior. The normal mode method is used to derive closed-form expressions of frequency responses under arbitrary harmonic loads, and orthogonality conditions are established to obtain precise modal impulse and frequency response functions. Our framework provides accurate and computationally efficient solutions and examines the impact of axial loads on natural frequencies, offering practical guidance for engineering design. These findings contribute to the dynamic analysis of thin-walled Timoshenko–Ehrenfest beams, providing useful insights for engineers in designing and optimizing structures under complex loading conditions.

This study presents a semi-analytical method for analyzing the buckling behavior of nonlocal Timoshenko beams using Eringen’s nonlocal elasticity theory. The method combines the initial value method (IVM) with a segment-wise approximate transfer matrix (ATM) approach, enabling accurate and efficient computation of critical buckling loads under various boundary conditions. The IVM calculates displacements and stress resultants from initial conditions, while the ATM constructs the principal matrix required by the IVM through segment-wise integration, ensuring numerical stability. The IVM–ATM framework offers a practical alternative to traditional analytical and numerical methods, especially for size-dependent problems. The results show excellent agreement with existing solutions, validating the method’s accuracy. The method’s accuracy is further supported by detailed convergence analyses. Parametric studies highlight the effects of length-to-diameter ratio, nonlocal parameter, and boundary conditions on buckling behavior. The proposed method provides a reliable and efficient tool for nanoscale beam structures.

The cerebral microvasculature plays a key role in determining the blood perfusion and oxygen diffusion to surrounding tissue. Multiscale models have thus been developed to incorporate the effect of the microvasculature into overall brain function. Moreover, brain tissue poroelastic properties are also influenced by the microvasculature. This study aims to determine the pororelastic properties of brain tissue using multiscale modeling on microvasculature networks described by the following effective parametric tensors: blood flow permeability ({varvec{K}}), interstitial fluid flow permeability ({varvec{G}}), Biot’s coefficients for blood ({alpha }_{c}) and interstitial fluid ({alpha }_{t}), Young’s modulus (overline{E }), and Poisson’s ratio (overline{v }). The microvasculature networks are built from a morphometric data of brain capillary distribution, which is represented using 1D lines. To allow for solving the microscale cell equations using finite element method, the microvasculature is modified into 3D shapes. The modifications resulted in 15% increment of the microvasculature volume. Validation is then performed by comparing the permeability tensor ({varvec{K}}) obtained using Poiseuille’s and Stokes’ equations, which resulted in the value of ({varvec{K}}) obtained through solving Stokes’ equation to be about 70% less than through solving Poiseuille’s equation. Based on these results, the other effective parameters have been estimated by considering the microvasculature volume increment due to the geometry modification. The volume increment significantly affects the parameter ({alpha }_{c}) but not the other parameters. The effective parameters are then used in a benchmark simulation, which further demonstrates the model value in describing the effects of brain capillary morphology in cerebrovascular diseases.

This paper reports on a comprehensive nonlinear transient dynamic analysis of nanocomposite beams reinforced with graphene oxide powders (GOPs) dispersed in a functionally graded (FG) manner within the polymer matrix (PM). The Bernoulli–Euler beam structural model, incorporating von Kármán-type geometric nonlinearities, is adopted for modeling composite beams. The nanocomposite beams’ effective mechanical properties are determined using the modified Halpin–Tsai micromechanical model and the rule of mixture. The nonlinear governing equations of motion are derived using Hamilton’s principle and solved within a numerical framework that combines the finite element method for spatial discretization, the Newton–Raphson method for nonlinear resolution, and the Newmark time integration scheme for temporal discretization. After validating the results by ABAQUS software, parametric investigations are conducted to examine the influence of the GOPs diameter-to-thickness ratio, GOPs weight fraction, and various functionally graded distribution patterns on the nonlinear transient dynamic response of composite beams. The results reveal that an increase in the nanofillers’ geometric dimensions and content significantly enhances stiffness, leading to reduced deflection amplitudes and shorter oscillation periods of the beams. Additionally, among the distribution patterns, the FG-X configuration demonstrates the most favorable dynamic performance, followed by UD, FG-V, and FG-O. These findings offer valuable insights into the nonlinear dynamic characteristics of advanced nanocomposite beams and highlight the potential of FG-GOPs-reinforced PM nanocomposite structures for vibration-critical applications, such as aerospace and mechatronics. This work makes a substantial contribution to the ongoing development of smart materials and nonlinear structural dynamics in engineered systems.