International Journal of Applied Mechanics

The wave propagation in an inhomogeneous half space with a semi-cylindrical surface bump is investigated by the means of complex function method. With the origin of the coordinate system as the center, the density of the medium changes radially. To solve the Helmholtz equation with variable coefficients caused by the inhomogeneous of the medium, a conformal transformation technique based on the theory of complex variable functions is adopted. Then, by adjusting the inhomogeneous parameters and comparing with the published analytical results, the correctness of the method in this paper is verified. Finally, the displacement amplitudes of typical observation points on the surface and inside are given, and the effects of incident wave angle, wave number and inhomogeneous parameters on wave energy distribution are analyzed.

This paper presents the formulation of a new efficient and conforming rectangular finite element for analysis of thin plates with any arbitrary variation of thickness along both edges. Shape functions of this new element are derived from multiplying shape functions of non-prismatic Euler–Bernoulli beam extracted from basic displacement functions. To provide $C^1$ consistency along the edges of elements, twist is added to conventional degrees of freedom, namely deflection and slopes resulting in an element with 16 degrees of freedom. The proposed element is used to solve various static and dynamic problems, and it is seen that the convergence of a new formulation occurs with much fewer elements compared to existing finite elements as a direct result of considering the variation of geometry in the derivation of shape functions, which renders the formulation competitive in both exactness and economy.

In this study, three-dimensional (3D) braided composites are integrated into the substructure of the energy harvester and a 3D braided piezoelectric composite energy harvester (BPCEH) with good performance is proposed. A theoretical model of the 3D BPCEH under the force–electricity–thermal coupling is established, and the output response, which is affected by excitation frequency, load resistance, external excitation and temperature, is simulated. The results illustrate that the braided elastic layer can greatly enhance the mechanical performance of the 3D BPCEH. With the increase in temperature and braided angle, the inherent frequency of the 3D BPCEH migrates into the low-frequency direction and can make the inherent frequency of the 3D BPCEH closer to environmental frequencies.

This paper analyzed a simple joint with the Goland–Reissner (G-R) theory. The study’s primary purpose is to define specific boundary conditions that depend on several factors to minimize the use of complex finite element analysis in the well-known applications. The problem depends on the length of the adhesions area and the magnitude of axial load P. The joint was first considered rigid to evaluate the stresses at its extremes, after which the theory of G-R was applied, considering the cases of equal and different adhesions. A mathematical approach was carried out starting from the equilibrium of the infinitesimal element. The results were finally compared with the Finite Element Method using FEM code.

The interaction of non-Newtonian grease with patterned surfaces was considered as a promising approach to find an effective method for reducing friction and wear in rolling contacts. Longitudinal and transverse patterns can retain the lubricant in the contact area and prevent it from escaping under high loads. In this paper, a model has been developed for grease elastohydrodynamic lubrication of surfaces with different patterns to estimate the lubrication parameters such as lubricant film thickness, pressure distribution, and viscous friction. Then several experimental tests are rolled out for different loads, velocities, and surface patterns. Because the friction model estimates only viscous friction, a correlation is recommended for considering the friction due to asperity interaction. This relation is based on average lubricant film thickness results which are calculated from the model. The calculated friction and experimental results have a good agreement. According to the experimental tests, transverse, longitudinal, and isotropic pattern had a lower friction coefficient, respectively. While the isotropic viscous friction coefficient estimated by the model is lower than others. Higher loads and lower velocities cause a higher friction coefficient in all surface patterns.

Lunar dust significantly impacts spacecraft and spacesuits during lunar exploration. The mechanical properties of lunar dust, including adhesion, contact, and wear, are investigated using new mechanical models proposed herein. First, the main contribution for mechanics of this paper was implementing the conical Johnson, Kendall, and Roberts (JKR) model using the energy method for investigating the normal and tangential mechanical characteristics of lunar dust. Additionally, the mechanical properties of lunar dust, such as adhesion, contact, and wear are proposed considering the adhesion effect using the mechanical model. The validity and accuracy of the conical JKR model were verified by comparing the results with experimental data and existing spherical and cylindrical JKR models. Furthermore, a new wear mechanical model for typical lunar dust is proposed considering the adhesion effect. The wear width and coefficients based on the wear model fit well with the existing experiment; therefore, the proposed model can be used to calculate the wear coefficient. Additionally, it can be used to estimate the contact force using an atomic force microscope (AFM) probe and analyze the adhesion between rough particles. The mechanical properties of lunar dust based on our models can be valuable for the characteristic research of in situ resource development and manned lunar landings.

Materials-by-design to develop high performance composite materials is often computational intractable due to the tremendous design space. Here, a deep operator network (DeepONet) is presented to bridge the gap between the material design space and mechanical behaviors. The mechanical response such as stress or strain can be predicted directly from material makeup efficiently, and a good accuracy is observed on unseen data even with a small amount of training data. Furthermore, the proposed approach can predict mechanical response of complex materials regardless of geometry, constitutive relations, and boundary conditions. Combined with optimization algorithms, the network offers an efficient tool to solve inverse design problems of composite materials.

The nonlinear aeroelastic flutter characteristics of laminated composite curved (flat and cylindrical) panels are reported in this paper by obtaining the finite element (FE) solutions under the supersonic flow. The panel model has been derived from the third-order shear deformation theory framework including full geometrical nonlinearity via Green–Lagrange strain. In contrast, the flutter due to aerodynamic loading is included via the first-order piston theory. The current predicted solution accuracy and their validations have been demonstrated by relating the free vibration frequency, coalescence frequency, and critical aerodynamic pressure with the available numerical data. The initial free vibration eigenvalue responses are compared with in-house experimental values. Finally, a few numerical examples are presented by varying parameters like the effect of fiber orientation, flow angle, end boundary conditions, aspect ratio, modular ratio, thickness ratio, and amplitude ratio on the supersonic flutter boundaries of shell panels. The critical aerodyanamic pressure for simply supported cross-ply flat panels increases by 42.85% when the amplitude ratio increases from 0 to 0.75.

The coupled transient chemo-mechanical behavior as well as the large deformation behavior under various complex load conditions must be taken into account when designing a functional responsive polymer actuator or sensor. One sort of deformation that can be used to characterize the properties of materials with complicated behavior, like soft hydrogels, is coupled extension and torsion with internal pressure. It is important to thoroughly research the complex kinetics of pH-hydrogels with coupled diffusion and massive deformation behavior. The transient behavior of cylindrical hydrogels under coupled extension–torsion with internal pressure under indifferent conditions is proposed in this work using a reliable semi-analytical method. In this regard, an analytical solution is offered to inspect this problem, which is used as a common experimental methodology for the characterization and modeling of polymeric materials. The results show that the rate of deformation and the physical characteristics of the material have a substantial impact on the cylindrical hydrogel’s transient behavior under coupled extension–torsion and internal pressure. For the same problem, a 3D finite element study was done to assess the analytical solution. The accuracy of our method is supported by the results’ agreement in both the FE analysis and the proposed approach. However, offering such a solution for this complex problem is of tremendous relevance given the significantly cheaper computational cost of analytical methods when compared to FEM. Additionally, the calculations indicate a complex reaction force and moment because the hydrogel experiences nonlinear Poynting-type effects in this deformation domain. The suggested semi-analytical procedure’s resilience behavior is demonstrated by the visualization of the effects of various material properties. This method can be used to calibrate constitutive models and to develop and improve hydrogel structures.

Shape memory polymers (SMPs) as a class of smart material have provided diverse attributes recently used in different applications. Raising the usage of SMPs, especially in more sensitive environments, such as the human body or similar high-risk circumstances, highlights the necessity of more accurate simulations. Suitable constitutive modeling is the foundation of an accurate simulation. Not only should such modeling consider precise details to diminish errors, but also it must provide a robust and powerful procedure to calibrate the material parameters. To achieve these goals, in this paper a modified constitutive model for SMPs based on the concept of internal state variables and rational thermodynamics is proposed in large deformation. Taking its basis from the nonlinear hyperelasticity and viscoelasticity, the model can provide a more accurate prediction of SMPs response. In comparison to other available constitutive models based on viscoelastic approach, the number of material parameters is smaller. Furthermore, performing a new approach for material parameters extraction, two different SMP materials were calibrated. The proposed model’s capability was assessed by comparing the model outputs with experimental results in diverse conditions such as different temperature rates and applied stretch ratios. The user-friendly implementation process of this model in multi-physics software based on the finite element method can be counted as another advantage of the proposed model. Hence, to simulate smart systems containing SMP elements, three multi-physics analyses in various fields and conditions were performed, and the importance of conducting such multi-physics phenomena has been discussed.