International Journal of Applied Mechanics

This paper presents the results of experimental analyses of the static and dynamic behavior of bio-sourced conventional and auxetic architectural materials. Three different configurations were studied. The specimens were made with the technology of additive manufacturing (3D printing) and were made of the same material which is polylactic acid reinforced with flax fibers (PFF). Several tensile tests were performed on four relative densities for each configuration of the composite to understand their influence on the static behavior of the material. Taking into account the insufficiency of the static tests to correctly predict the behavior of the composite, vibration tests were carried out on the same densities and composite configurations. The focus will be mainly on the study of the influence of the 2D lattice structures for each density on the evolution of the dynamic stiffness and damping properties.

Based on the idea of dimension splitting method, a dimension splitting interpolating element-free Galerkin (DSIEFG) method for 3D wave propagation problems is proposed. In the splitting direction, the 3D domain of a problem is divided into a series of related 2D subdomains. Using the improved interpolating moving least-squares (IMLS) method to acquire the shape function in the 2D subdomains, the discretized equations are formed based on Galerkin weak form of 2D problem. The discretized equations are coupled by using the difference method in the splitting direction. Then, the final equations of the DSIEFG method for 3D wave propagation problems are obtained. Numerical examples are given to study the effects of node distribution, number of split layers, influence domain parameters, splitting direction, and time step on the computational accuracy of the DSIEFG method. The results of numerical examples show that the DSIEFG method is more efficient and accurate compared with the improved EFG method for 3D wave equations.

Magnetorheological fluids (MRFs) exhibit variable mechanical properties in response to magnetic stimuli. Thanks to their rapid and reversible viscosity changes, MRFs can be utilized in a variety of applications including torque transmission devices such as clutches. In this work, the geometrical design of cylindrical MR clutches is investigated with the aim of optimizing the torque transmission capability. Effects of design parameters such as radius, gap size, effective length, and MRF volume are investigated in the presence of variable magnetic field. Magneto-mechanical behavior of some MR fluids with different particle content are investigated by means of two different constitutive models to simulate the clutch performance in a range of geometrical parameters. It is shown that the transmitted torque increases nonlinearly by inner radius of the clutch, for example, in the studied range, 150% higher torque is achieved for only 40% larger radius. The clutch’s gap size does not much affect the torque, however, since it significantly affects the required volume of MRF, a lower gap size is favorable. The torque is also calculated for constant volumes of the MRFs. At a certain volume, although a higher radius translates to a shorter length, it is still favorable. For example, a 40% increase in the design radius, almost doubles the transmitted torque for both the studied MRFs. Moreover, a clutch filled by an MRF with higher particle content can transmit higher torques. It is also concluded that increasing the clutch’s radii is an easier way to improve the mean torque while altering the applied magnetic field is a better way to adjust the range of achievable torques. The simulations also demonstrate the importance of an accurate and reliable constitutive model in the design of MR devices. It is shown that Bingham model is not reliable at high magnetic fields as it underestimates the transmitted torque though calibrated at each field intensity. However, the employed nonlinear model provides more reliable results by only being calibrated at an arbitrary field.

By introducing the dimension splitting (DS) method into the moving least-squares (MLS) approximation, a dimension splitting moving least-squares (DS-MLS) method is proposed in this paper. In the DS-MLS method, the operator splitting and independent variable splitting of the DS method are used to reduce the dimension, thereby reducing the computational complexity of the matrix. The shape function of the DS-MLS method has the advantages of simple derivation and high computational efficiency. Then, by coupling DS-MLS method and Galerkin weak form, and performing the coordinate transformation, an improved element-free Galerkin method (IEFGM) based on the DS-MLS method is proposed for two-dimensional (2D) potential problems on irregular domains. The effectiveness of the method in this paper is verified by some numerical examples. The numerical results show that, compared with the element-free Galerkin (EFG) method, the IEFGM based on the DS-MLS method in this paper consumes less CPU time and has higher computational accuracy for some 2D potential problems on irregular domains.

This work provides a general analysis method for the crack detection in shales. The acoustic emission (AE) testing with data recovery is proposed for determining the crack modes and positions in the test and analysis process of the shale fracturing experiment. A fracturing and in situ AE monitoring system is constructed to collect the experimental data in at least six channels for the crack detection, and the source positions output from AE testing represent the positions of cracks. Due to some uncontrollable reasons, such as the poor coupling between sensors and sample and the sudden failure of the sensors, some parts of experimental data are missing during the experiments. Therefore, a data recovery neural network algorithm based on wavenet model is introduced to reconstruct the missing parts of experimental data in the waveforms. Since the accuracy of data recovery is not satisfying based on the collected experimental data, the interpolation of experimental data is performed to refine the data which can obviously improve the accuracy of data recovery. After all the required experimental data have been recovered, the crack mode for each crack can be determined based on the moment tensor analysis. This analysis method can be extensively applied to the shale crack detection.

In this paper, a novel hybrid approach with complex and conformal mapping functions is proposed for the first time. This strain-based approach is based on the special trial functions and the assumed natural strain (ANS) theory, which provides a unified framework for solving fracture problems. In the utilized method, the proposed super-element is divided into perforated and solid domains. For the perforated domain, Muskhelishvili–Kolosov potential function is employed to simulate the perforated discontinuity. For the solid domain, the higher-order strain field is assumed as the enriched interpolation functions. Moreover, the rigid body terms are imposed into the kinematic variables to enhance the convergence ability and the element performance. Numerical examples demonstrate that the proposed element (PHSM20) produces high precision results for both displacement and stresses.

In this paper, the incremental equilibrium equations and corresponding boundary conditions for the isotropic, hyperelastic and incompressible shells are derived and then employed in order to analyze the behavior of spherical and cylindrical shells subjected to external pressure. The generalized differential quadrature (GDQ) method is utilized to solve the eigenvalue problem that results from a linear bifurcation analysis. The results are in full agreement with the previously obtained results and the effects of thickness and mode number are studied on the shell’s stability. For the spherical and cylindrical shells of arbitrary thickness which are subjected to external hydrostatic pressure, the symmetrical buckling takes place at a value of ${\alpha }_1$ which depends on the geometric parameter $A_1/A_2$ and the mode number $n$, where $A_1$ and $A_2$ are the undeformed inner and outer radii, respectively, and ${\alpha }_1$ is the ratio of the deformed inner radius to the undeformed inner radius.

With the development of 3D printing technology, programmable auxetic structures have attracted extensive attention due to their designable and abnormally mechanical properties. In this study, we design a 3D printed programmable auxetic star-like structures using number of layers $(n)$, per-layer dimension reduction ratio $(L_n/l_n)$ and spatial programming of unit cells to achieve a simultaneous optimization of load carrying capacity and auxetic property. Effects of layers $(n)$ and dimension reduction ratio $(L_n/l_n)$ on the mechanical and Poisson’s ratio behaviors of the 3D printed auxetic star-like structures are investigated by finite element method and verified by experiments. Finally, the unit cell spatial programming is designed and analyzed to avoid buckling and rotation, while increasing the load carrying capacity and auxetic property in a coordinated way. This study is expected to provide a design guideline for meta-star-like structure with both high load carrying capacity and auxetic property via a novel nonuniform stiffness structure design.

In this paper, an extended Hertz model is proposed to predict the mechanical responses of the incompressible Mooney–Rivlin half-space under finite spherical indentation. The contact behaviors are systematically investigated through the axisymmetric finite element (FE) model using various constitutive parameter ratios. Based on the numerical results, the radius of contact zone is first derived by adopting the exact function of the indenter shape. A reliable prediction of contact force, for the incompressible neo-Hookean model, is then obtained by substituting newly modified contact radius into the original Hertz model. From this base, a correction factor, which characterizes the effect of constitutive parameter ratio, is introduced to predict the contact force, and the contact pressure distribution of the original Hertz’ formula is also extended for the incompressible Mooney–Rivlin half-space under spherical indentation up to the indenter radius. The extended Hertz model related to constitutive parameters is validated effectively through FE simulations and experimental indentation results under finite spherical indentation. On the contrary, when the indentation depth exceeds 10% of the indenter radius, the original Hertz model is unable to predict the strong effect of constitutive parameter ratio on the contact behaviors for the incompressible Mooney–Rivlin half-space.

Piezoelectric semiconductor (PS) nanostructures have a huge application potential in flexible electronic devices. We study the nonlinear multi-field coupling mechanical behaviors of axially loaded PS rods by taking the von Kármán type of nonlinear strain–displacement relations into account. The one-dimensional equations for extensional PS rods with the geometric nonlinearity are presented. The analytical solutions for an axially loaded PS rod with open-circuit and electrically isolated boundary conditions at the two ends are obtained based on the classical perturbation method. The zeroth-order perturbation solution is exactly the same as the linearized solution. The influences of the first- and second-order solutions on the multi-field coupling responses of the PS rods under different axial loads are investigated.