Acta Mechanica最新文献

This paper studies multi-physical fields in a piezoelectric semiconductor (PS) fiber with consideration of heat conduction, pyroelectric, and thermoelectric effects. Based on the three-dimensional (3D) framework of piezoelectricity, drift–diffusion theory, Seebeck effect, and Peltier effect, we develop a highly nonlinear one-dimensional (1D) model that incorporates axial deformation, axial variations of the electric field, the redistribution of carriers, and temperature deviation. Combining the 1D nonlinear governing equations and the corresponding boundary conditions, the influence of the thermoelectric coefficients and axial forces on electrostatic potential, carrier redistribution, and temperature variation are solved numerically. Due to the nonlinearity of the model, these solutions are observed without symmetry or asymmetry. Our research shows that the temperature will increase near the action point of the axial force. Therefore, the temperature deviation in the fiber can be controlled by applying axial force at different points. Finally, we examine how the axial forces applied in the fiber affect the current–voltage relation. The presented study provides a potential application for mechanical switches, sensors, or thermal control for PSs.

In this article, an exact analytical method for the free vibration analysis of functionally graded (FG) graphene platelet (GPL)-reinforced composite (GPLRC) sector cylindrical shells is presented by considering Levy-type boundary conditions for the first time. The analysis relies on the use of the Halpin–Tsai micro-mechanical model for evaluating the material properties of the graded layers of the shell with three different grading patterns. Mathematical modeling of the Levy-type cylindrical shell is based on the Hamilton principle and the Sanders first-order shear deformation theory (FSDT). The governing equations of the composite shell are analytically solved using the state-space method. The validity of the proposed analytical method is demonstrated by the excellent agreement between the obtained results of the exact analytical solution and the results available in the literature. Furthermore, some parametric studies are conducted to reveal the effects of variations in boundary conditions, GPL distribution patterns, GPL weight fraction, and geometrical parameters such as shallowness angle, length-to-radius ratio, and thickness on the free vibration behavior of the shell structure. Natural frequencies and mode switching are reported for different mode numbers.

This paper deals with the local bifurcation analysis of a nanotube with a nanostring passing through it. Eringen’s two-phase local/nonlocal model and Eringen’s differential model are employed as constitutive equations. The governing equations are derived as two nonlinear first-order systems of ordinary differential equations. Nonlinear analysis is performed by using the Lyapunov–Schmidt method. The influence of the small length scale parameter and the phase parameter on critical buckling load, type of bifurcation and post-buckling shape of the nanotube is examined for both types of constitutive equations. Depending on the values of the small length scale parameter and the phase parameter, the critical buckling load corresponding to Eringen’s two-phase local/nonlocal model can be greater or less than that corresponding to Eringen’s differential model. It is shown that for both models supercritical pitchfork bifurcation occurs. The post-buckling shapes of nanotube, obtained by numerical integration, exhibit a qualitative difference between the two models.

Flexible piezoelectric materials have gained considerable attention due to their remarkable properties, including electromechanical coupling and high stretchability. These characteristics make them valuable in the realm of flexible electronic devices. However, the issue of fracture in these materials cannot be ignored. In general, these flexible/stretchable materials experience fractures when subjected to significant deformation, unlike brittle piezoelectric materials with low failure strain which have been extensively studied. There is a pressing need to investigate the fracture behavior of flexible piezoelectrics under finite deformation conditions. Within the framework of the phase field method, this work addresses the fracture of flexible piezoelectrics utilizing a nonlinear electromechanical material model. To investigate the influence of electrical boundary conditions on fracture behavior, a function related to the electric permittivity ratio and phase field variable is employed to degrade the electric energy density. By adjusting the electric permittivity ratio, the analysis encompasses the fracture behavior of flexible piezoelectric materials under the assumptions of electrically impermeable, semi-permeable, and permeable conditions, respectively. In order to solve the coupled governing equations, a residual controlled staggered algorithm (RCSA) is employed in the user element subroutine of commercial software ABAQUS. The simulation results indicate that fracture behavior in flexible piezoelectric materials is influenced by several factors, including material parameters, geometry, polarization direction, and the external electric field. Notably, when the poling direction is perpendicular to the electric field direction, variations in the external electric field have a minimal impact on fracture behavior. In contrast, when the poling direction is parallel to the electric field direction, the influence on fracture behavior is pronounced. These findings provide valuable insights for developing strategies to enhance the fracture resistance and durability of flexible piezoelectric materials in practical applications.

Steady viscous flow past a circular cylinder with velocity slip boundary condition is numerically solved. The Navier–Stokes equations are solved using the vorticity-stream function formulation for two-dimensional incompressible flows. A time-accurate solver is developed which can be used for accurate solution of time-dependent flows. However, only steady results for Reynolds numbers up to 40 are presented in this paper. Most of the emphasis is dedicated to the validation of the solver and the results, something which is more or less missing in previous studies of slip flows. There has been a controversy regarding the computation of the drag coefficient and its various contributions in the past. As reviewed in the text, some papers did not present the formulation of the drag coefficient and only presented the results, some papers used the no-slip formulae and some papers presented formulae for the slip case but did not validate them. Due to this controversy, we derived formulae for the various contributions to the drag coefficient and validated them by comparison to existing data, especially using an analytical solution of Oseen’s equation for creeping flow around a cylinder with slip condition. At the end, some results are presneted including wall vorticity and slip velocity distribution, streamlines, vorticity contours and various contributions to the drag coefficient.

In this paper, we consider the frictional contact model between a piezoelectric body and an electrically conductive foundation. This contact is described by a reduced normal compliance law. To address this problem, we establish a mixed variational formulation and prove the existence of a unique solution. Moreover, we present an efficient algorithm for approximating the weak solution for the contact problem, taking into account both friction and electrical contact conditions. We conclude with numerical examples that demonstrate the practicality of the model.

Film boiling has practical applications in the current technology including steam power plants, cooling of electronic devices and emergency cooling systems. A finite difference/front tracking method is used to simulate film boiling at high density ratios on a horizontal plate subject to a constant wall heat flux. The grid resolution is relatively high (768 grids per width of the domain). The flow is dominated by Rayleigh–Taylor instability as well as Kelvin–Helmholtz instability. The flow structure includes the roll up of the interface between the gas and liquid. This happens at high density ratio (1000) where the difference between the gas and the liquid velocities across the interface is large. The jump in tangential velocity is an order of magnitude smaller at a lower density ratio (100). Hence, there is no roll up at a lower density ratio. The flow is also influenced by vortex development as a result of the baroclinic term in the vorticity transport equation. The density gradient is large at the interface at high density ratio which tends to amplify the baroclinic term. The plot of pressure gradient and density gradient shows that they are not parallel in the roll up regions. As a result, vortices in small scales develop that shed in the gas phase. The plot of the enstrophy with time shows that it is smooth and match for two grid resolutions, however at a specific time enstrophies become spiky, and they depart from each other at two grid resolutions. The spiky behavior of enstrophy is due to vortex shedding in the roll up region.

In this paper, the free and forced vibration behaviors of a piezoelectric semiconductor (PS) cylindrical shell are investigated based on the first order shear deformation theory. According to the constitutive equation as well as geometric relationship, the kinetic energy, strain energy and virtual work of the PS cylindrical shell are obtained. Furthermore, the vibration governing equations of the system are derived by means of Hamilton’s principle, and the analytical solutions are acquired for the simply supported PS cylindrical shell. Through numerical examples, the effects of the initial electron concentration, circumferential wave number, geometric parameter and excitation frequency on the natural frequency, damping characteristic, vibration amplitude and induced electric potential of the PS cylindrical shell are discussed. The multi-field coupling characteristic among deformation, polarization and carrier is revealed. The main innovation of the manuscript is that the maximum radial displacement and induced electric potential of the PS cylindrical shell can be effectively controlled by doping different initial electron concentrations, and the damping characteristic of the system is obviously size-dependent.

The elastic–plastic infinitesimal deformation of a solid is considered within the framework of the incremental flow theory using the constitutive relation in the general rate form. The appropriate initial boundary value problem is formulated for the displacement in the form of the evolutionary-variational problem (EVP), i.e., as the abstract Cauchy problem in the Hilbert space which coincides with a weak form of the equilibrium equation, known as the principle of possible displacements in mechanics. The general existence and uniqueness theorem for the EVP is discussed. The main sufficient condition has a simple algebraic form and does not coincide with the classical Drucker and similar thermodynamical postulates; therefore, it must be independently verified. Its independence is illustrated for the non-associated plastic model of linear isotropic-kinematic hardening with dilatation and internal friction. The classical and endochronic models are analyzed too. The initial EVP is reduced by a spatial finite element approximation to the Cauchy problem for an implicit system of essentially nonlinear ordinary differential equations which can be stiff. Therefore, for the numerical solution the implicit Euler scheme is proposed. All theoretical results are illustrated by means of original numerical experiments.

Two-dimensional (plane) elasticity equations in solid mechanics are solved numerically with the use of an ensemble of physics-informed neural networks (PINNs). The system of equations consists of the kinematic definitions, i.e. the strain–displacement relations, the equilibrium equations connecting a stress tensor with external loading forces and the isotropic constitutive relations for stress and strain tensors. Different boundary conditions for the strain tensor and displacements are considered. The proposed computational approach is based on principles of artificial intelligence and uses a developed open-source machine learning platform, scientific software Tensorflow, written in Python and Keras library, an application programming interface, intended for a deep learning. A deep learning is performed through training the physics-informed neural network model in order to fit the plain elasticity equations and given boundary conditions at collocation points. The numerical technique is tested on an example, where the exact solution is given. Two examples with plane stress problems are calculated with the proposed multi-PINN model. The numerical solution is compared with results obtained after using commercial finite element software. The numerical results have shown that an application of a multi-network approach is more beneficial in comparison with using a single PINN with many outputs. The derived results confirmed the efficiency of the introduced methodology. The proposed technique can be extended and applied to the structures with nonlinear material properties.