Acta Mechanica最新文献

An enhancement of the MITC3+ flat shell element using curvature corrections is proposed. Herein, the corrected curvature field is established through the utilization of corrected nodal derivatives that satisfy the discrete divergence consistency (DCC). The concept of DDC in this study is derived from the orthogonality condition between resultant bending stress (bending moments) and curvature (bending strain) differences within the Hu-Washizu three-field variational principle. In the context of membrane behavior, we employ the Allman-like triangular element with drilling degrees of freedom (DOFs), ensuring both the true rotation of drilling DOFs within elasticity and the effective elimination of spurious energy modes. Through numerical results, the proposed method exhibits exceptional performance in addressing plate and shell structural problems, outperforming the MITC3+. Remarkably, using the constant base demonstrates the highest level of robustness.

We have studied the transmission of a wave packet through finite discontinuous media with dissipation using analytical methods. The focus is on the behavior of an electromagnetic pulse moving from air to a finite conducting slab. The wave equation governs the pulse’s evolution in the free medium, while the telegrapher’s equation is applied in the slab. The presence of the Joule effect in the slab affects the wave packet’s propagation. By solving three discontinuous partial differential equations analytically using Fourier representation and the attenuated spatial wave packet formalism, we derive reflection and transmission coefficients as functions of the telegrapher’s equation parameters. Experimental results for the transmission coefficient varying the absorption energy are presented, utilizing a demineralized water tank with different salt concentrations as the slab. The results are consistent with our theoretical model.

We investigate objective corotational rates satisfying an additional, physically plausible assumption. More precisely, we require for

that the characteristic stiffness tensor (mathbb {A}^{circ }(B)) is positive-definite. Here, (B = F , F^T) is the left Cauchy–Green tensor, (frac{textrm{D}^{circ }}{textrm{D}t}) is a specific objective corotational rate, (D = {{,textrm{sym},}}, D_xi v) is the Eulerian stretching and (mathbb {A}^{circ }(B)) is the corresponding induced characteristic fourth-order stiffness tensor. Well-known corotational rates like the Zaremba–Jaumann rate, the Green–Naghdi rate and the logarithmic rate belong to this family of “positive” corotational rates. For general objective corotational rates (frac{textrm{D}^{circ }}{textrm{D}t}), we determine several conditions characterizing positivity. Among them is an explicit condition on the material spin-functions of Xiao, Bruhns and Meyers [84]. We also give a geometrical motivation for invertibility and positivity of ( mathbb {A}^{circ }(B)) and highlight the structure-preserving properties of corotational rates that distinguish them from more general objective stress rates. Applications of this novel concept are indicated.

Under an electric field, three types of polarization occur in dielectric elastomers. The phenomenon of linear polarization has been extensively studied. However, there is still a lack of in-depth studies on other types of polarization and their effects in the temperature field. In this paper, firstly, the constitutive equation of coupling temperature under polarization saturation is established. Secondly, the constitutive equation of coupling temperature and electrostrictive coefficient under polarization saturation is established, and the behavior of dielectric elastomer under polarization saturation is discussed respectively. Numerical analysis of dielectric elastomers shows that temperature and appropriate electrostriction coefficient can improve the stability of dielectric elastomers. It is hoped that this work will guide the development of dielectric elastomer materials and devices for applications operating at variable temperatures.

Ferromagnetic continuum robots, characterized by their remarkable flexibility, offer significant potential for advanced medical applications. However, the nonlinear behavior of these robots requires complex modeling, which incurs high computational costs, and presents significant challenges in developing precise, real-time controllers. Ensuring accuracy and computational efficiency in critical procedures, such as minimally invasive surgery, is challenging, as precise control of the robot is essential. Overcoming these challenges requires innovative modeling and control strategies that leverage the unique properties of these robots while maintaining stability and responsiveness in medical environments. To address these challenges and considering the nature of the system, including its low inertia and slow system behavior, the system is treated as quasi-static. Additionally, an artificial neural network approach is employed for modeling the ferromagnetic continuum robot. The data required for training the neural network are collected using the Cosserat theory. Additionally, considering the quasi-static nature of the system, a proportional-integral controller will be used to control the tip position of the robot. To evaluate the performance of the Cosserat theory for calculating the deformation of the robot and the proposed controller, the results obtained from the simulations of trajectory tracking for various paths are compared with experimental data, showing an acceptable agreement with the experimental results.

The proposed hyperbolic hygrothermal coupled model, which incorporates non-Fourier and non-Fick effects, is used to examine the fracture behavior of a nanocylinder with a circumferential crack through dual-phase-lag (DPL) theory. Analytical solutions for temperature distribution, moisture distribution, and hygrothermal stresses in an uncracked nanocylinder are obtained using Laplace transform and approximation methods in the Laplace domain. The mode-I crack problem is formulated by applying an opposite sign to the crack surface through the superposition method. The Numerical Inverse Laplace Transform (NILT) is then employed to derive solutions in the time domain. Results indicate that the hyperbolic hygrothermal model yields more conservative outcomes compared to the parabolic hygrothermal model for the safe design of structures with cracked surfaces. The phase lag effects of heat and moisture flux on transient temperature fields, moisture fields, hygrothermal stresses, stress intensity factors, and crack opening displacements are shown graphically.

This paper explores the influences of the external magnetic field, microstructural effects, and thermal effects on the reflection and transmission behaviors of macro–micro coupled waves. The microstructural effects are manifested by dipolar gradient elasticity. The heat conduction phenomenon is described using the non-Fourier law without energy dissipation (GN-II). The Lorentz force resulting from the external magnetic field is deduced based on the electromagnetic induction law and Maxwell’s equations. Numerical results are presented for the case of an incident CP1 wave. It is discovered that both the microstructural effect and the thermal effects give rise to the dispersive feature of elastic waves. Although the external magnetic field does not play a role in causing dispersion, it significantly affects the reflection and transmission amplitudes.

Autofrettage is a cold metal forming process that aims to improve the load-bearing capacity and delay the crack initiation for thick-walled annular disks/cylinders. The current study presents numerical solution of stress distribution during the loading and unloading stage subjected to rotational autofrettage for uniform and non-uniform annular disks. The analysis assumed the plane stress condition, von Mises yield criterion, and polynomial strain hardening behavior. The stress distribution during loading and after unloading has been demonstrated for a typical SS304 uniform disk and later validated the results using a 2D FEM model in ABAQUS software. A comparative analysis has been conducted to understand the pressure-bearing capacity in second-stage loading between numerical solutions based on the von Mises yield criterion incorporating perfectly plastic hardening behavior and the proposed model. Furthermore, the stress distribution has been evaluated for non-uniform thickness and density rotating annular disks, and numerical experimentation has been conducted to underscore the importance of profile-specific strategies to induce desired beneficial compressive residual stress in the inner region of the disk.

This paper presents a numerical approach for the dynamical response of geometrically imperfect multilayered beams subjected to a moving load. The multilayer beam with a porosity-dependent nanocomposite core and titanium alloy layers is analyzed based on a high-order shear deformation theory including hyperbolic functions. The large deflection assumptions are also included into the formulations. The core of the multilayer beam consists of six porous aluminum layers where each of them are reinforced by graphene platelets (GPLs) with different values of porosity. The equations of motion are determined using the Lagrange’s equation and are solved by the Ritz solution method for three different boundary conditions. The effects of porosity coefficient and graded pattern of aluminum constituents and their distributions on the forced vibrations are analyzed. Also, the effects of the length-to-thickness ratio and the weight fraction of GPLs are examined and compared. A good agreement is determined by comparing our formulation with other available works in the literature.

This paper seeks to address the size dependence of microstructure by defining a characteristic scale vector to characterize the size effect in materials. It introduces high-order stress moments and high-order momentum moment as foundational concepts. Based on these ideas, we propose a high-order stress theory for solids that integrates a complete second-order displacement gradient, as opposed to solely incorporating a rotation gradient or a strain gradient. This methodology enhances the high-order stress theory, rendering it a more comprehensive and generalized framework. Under certain conditions, this theory can be degenerated into other models that elucidate the size effect, indicating that the high-order stress theory has a wider applicability and is not limited by its own ideal assumptions or prerequisites, unlike other existing theories. The high-order stress theory presented in this paper is applicable not only in the field of micromechanics but also in multi-field analyses. To exemplify its utility, we investigate the flexoelectric effect in dielectric materials using the proposed high-order theory. We compute parameters such as electric field intensity and structural response under various deformation conditions, including tension, bending, shearing, and torsion. Furthermore, we conduct electromechanical coupling experiments on PZT plates within these deformation scenarios. The analysis of the experimental results substantiates the efficacy of the high-order theory.