International Journal of Applied Mechanics

This study develops a new phenomenological constitutive model to capture the unique, evolving cyclic elastoplastic behaviours of hexagonal close-packed (HCP) sheet metals under uniaxial loading condition. This new constitutive model is developed by adopting the concepts of multiple-yield surface approaches and a combined isotropic-kinematic hardening rule. Three phenomenological modes, including tension ($T$), compression ($C$), and untwining (UT), are considered to represent the hardening evolution of the materials, including twining/untwining behaviours. Three different hardening laws are applied, and a Cazacu-Barlat 2004 (CB2004) type yield surface is assigned to each deformation mode. The UT hardening parameters are defined as functions of plastic pre-strains to mitigate interpolation errors caused by parameter determination processes of existing models. The new constitutive model is numerically implemented for finite element analysis via the UMAT subroutine available in a commonly-used commercial finite element analysis (FEA) package — Abaqus and validated by experimental data available from literature. The obtained results show that the new constitutive model can precisely capture mechanical behaviours of HCP sheet metals, e.g., stress–strain curves, compared to those experimental results.

Accurate and quantitative characterization of friction behavior is of critical importance for material design and manufacture, especially for soft materials. It is mainly because the sliding-caused deformation of soft materials has always been neglected during characterization. Here, a modified model considering sliding-caused deformation was proposed to characterize the friction behavior between a spherical glass indenter and silicon rubber. A novel friction apparatus consisting of a transparent spherical indenter connected with a camera was used in real-time to measure the friction contact status. The contact shape and area during friction were then extracted by a proposed shape function. Experimental results show that shrinking and expanding of the contact area occur simultaneously when a spherical-rigid indenter slides on a soft substrate due to sliding-caused deformation of soft materials. Based on these results, this study built a modified model considering the shape change and the accompanying deformation component of friction, which is an effective method for evaluating the friction behavior of soft materials.

Influence of surface energy on an interaction problem between a flexible circular nanoplate and a nanolayer is examined by using a variational formulation and the GM surface theory. The nanoplate is resting in smooth contact on the supporting nanolayer, and subjected to axisymmetric vertical loadings. The normal traction at the plate–layer interface is written in terms of generalized coordinates obtained from the flexibility equations derived from Green’s function and Hankel integral transform technique. A numerical solution scheme is then implemented into a computer code, and the convergence and accuracy of the proposed solution are verified with existing solutions. A set of numerical solutions is illustrated to present an impact of the surface energy effects on this interaction problem. Both deflection and bending moment of the nanoplate show a considerable dependence on the relative plate stiffness and the surface material properties, and demonstrate the size-dependent behaviors.

Amorphous silica (a-SiO₂) is a widely used inorganic material. Interestingly, the relationship between the local atomic structures of a-SiO₂ and their effects on ductility and fracture is seldom explored. Here, we combine large-scale molecular dynamics simulations and machine learning methods to examine the molecular deformations and fracture mechanisms of a-SiO₂. By quenching at high pressures, we demonstrate that densifying a-SiO₂ increases the ductility and toughness. Through theoretical analysis and simulation results, we find that changes in local bonding topologies greatly facilitate energy dissipation during plastic deformation, particularly if the coordination numbers decrease. The appearance of fracture can then be accurately located based on the spatial distribution of the atoms. We further observe that the static unstrained structure encodes the propensity for local atomic coordination to change during applied strain, hence a distinct connection can be made between the initial atomic configurations before loading and the final far-from-equilibrium atomic configurations upon fracture. These results are essential for understanding how atomic arrangements strongly influence the mechanical properties and structural features in amorphous solids and will be useful in atomistic design of functional materials.

This paper presents a model for microbars with variable cross-sections using the Kelvin–Voigt model for viscoelastic material, accounting for size-dependent effects based on strain gradient theory. The size-dependent dynamic equations for the rod, which consider the variable cross-sectional area, are obtained through the extended Hamilton’s principle. These equations are then reduced in order using the Galerkin method and solved in the steady state using the harmonic response form and the algebra of complex numbers. To solve the equations from the transient state to the steady state, a combined method is implemented using the Grünwald–Letnikov derivative technique and the Newmark method. Furthermore, a model and analysis based on the finite element method are presented to validate the results. In the results section, various factors such as size-dependent effects, the order of the fractional derivative, the amount of the viscoelastic coefficient, and the shape of the section area are examined through the time history graph, frequency response, and maximum displacement in terms of force. The results demonstrate that the transient response converges to the stable response after a certain period of time. Moreover, it is observed that decreasing the order of the fractional derivative in the pre-resonance range leads to a decrease in response sensitivity, while in the resonance frequency range, the sensitivity increases with the increase in order.

Adhesive joints are an increasingly important joining method, in part due to usually being lighter than the alternatives, which is very important in the search for more energy efficient transportation. However, the amount of studies focused on the free-vibration behavior of adhesive joints is currently very limited. Since this knowledge is important, to ensure that a joint is working outside its natural frequencies, this work sets out to perform a parametric study of a Double Lap Joint (DLJ) using the Radial Point Interpolation Method (RPIM), a meshless method. Using the RPIM in the free vibration of adhesive joints is the next step for this numerical method, after using it in the static analysis of adhesive joints. Considering that this is one of the first uses of this method in this type of problem it is also necessary to validate it. This task was performed in this work by comparing it with the Finite Element Method (FEM), which is the standard numerical method for this type of problem. The validation was successful, showing very small differences between the two numerical methods. The parametric study should aid future adhesive joint designers to develop safer joint. It showed that changes to the adhesive produce diminutive changes to the natural frequencies of the joints. On the other hand, changes to the adherents change the natural frequencies significantly. The overlap length had different effects on the different modes.

Damage initiation due to the interfacial debonding plays a vital role in the mechanical properties of graphene-reinforced concrete. In this research, multi-scale modeling is exploited to study the effect of volume fraction, aspect ratio, and interaction properties of the multi-layer graphene nanoplatelets (GNPs) on the mechanical properties of reinforced concrete, assuming perfectly bonded and cohesively bonded interaction between the contact surface of the matrix and the GNPs. The cohesive zone model has been used to observe the debonding behavior and damage initiation between the concrete matrix and nanocomposites for cohesively bonded interaction. The required cohesive zone parameters were estimated based on the previously calculated information on graphene–graphene interactions. The results show that by increasing the volume fraction and aspect ratio of GNP, nanofiller improves the mechanical properties of the nanocomposite. In addition, results reveal that interaction properties significantly affect the mechanical properties of graphene-reinforced concrete.

The nonlinear flow behavior of granite with a single fracture at different shear displacements is researched by using the high-precision non-pulse long-time permeability test system. The effects of fracture roughness and confining pressure are studied. Forchheimer’s law and the critical normalized transmissivity can describe fluids’ nonlinear flow behavior under shear displacement. During the shear process, the change process of fluid flow can be divided into two stages, namely the sensitive change stage and the stable change stage, and the hydraulic parameters also change accordingly. The shear displacement is in the sensitive stage of 0–1mm, at this point, the nonlinear flow characteristic parameters change significantly, accompanied by a decrease in linear and nonlinear coefficients. The critical Reynolds number decreases with the increasing shear displacement and decreasing confining pressure. The increasing shear displacement and confining pressure decrease the critical hydraulic gradient. The hydraulic aperture of the fractured granite initially increases with the increase of shear displacement. The shear displacement between 1mm and 4mm is a stable stage, the characteristic parameters of fluid, critical Reynolds number and critical hydraulic gradient tend to be relatively stable and fluctuate in a small range. This is induced by the changes in the hydraulic aperture under the effects of shear displacement and confining pressure, noteworthy the influence of displacement on the hydraulic aperture is greater than that of confining pressure.

Modal discretization is commonly applied for dynamic analysis of non-linear continuum system. Considering the possible coupling effect between modes is necessary to obtain accurate results. In this case, the system may become increasingly complex, as the number of adopted modes can be a lot. Such complexity will lead to the difficulty of solution finding. This paper proposes a generic technique to simplify the governing functions by making non-linear stiffness matrix symmetric. The symmetric non-linear stiffness matrix is constructed by utilizing the mode shape vectors. The proposed procedure can theoretically guarantee non-linear stiffness matrix symmetric. The incremental harmonic balance (IHB) method is served as the main tool for finding solutions of systems. Dynamic analysis of axially moving beam and generalized suspension bridge are presented in this study for illustration. Results proved that the neighboring modes are critical during the resonance of target mode, which suggests the necessity of including sufficient modes for non-linear dynamic analysis. By applying the proposed technique, it is found that calculating time of IHB method can greatly shortened, especially for the case included modes becomes large. Results show that the time consumption with using the proposed method can be half of that not using it, when more than 5 modes are considered in the calculation.

Time-dependent wave motion coupled with bottom disturbances and poroelastic plate in a viscous incompressible fluid of finite depth is studied here. The problem is framed as an initial value problem in terms of potential and stream functions by assuming linear water wave theory. Three objectives are met in this work: first, the behaviour of the root of the dispersion relation is analyzed for plane progressive waves; second, the effect of viscosity on the asymptotic form of the plate deflection is studied. Third, the effect of plate porosity and other crucial parameters on fluid velocity are examined through various contour plots. Using Laplace and Fourier transform techniques, the expression for plate deflection is derived in terms of a highly oscillatory infinite integral and then evaluated asymptotically by using the steepest descent method. Different numerical analyses are performed by varying physical parameters such as viscosity, porosity, flexural rigidity and frequency of the wave motion. It is observed that, with an increase in the value of viscosity, the values of the real and imaginary parts of the complex root of the dispersion relation increase for frequency above a cut-off value; the maximum amplitude of the plate deflection decreases, and the vertical velocity decreases.

A comprehensive model was presented using the finite element method to analyze the dynamics of cylindrical microparticles, considering non-linear and size effects. The governing equations of motion have been derived based on the weak form method. The stiffness and mass matrices, along with the force vectors, have been presented for non-classical non-linear models of both the Euler–Bernoulli and Timoshenko types. The manipulation dynamics of cylindrical gold microparticles was simulated using FEM. In the simulations, four models of Euler–Bernoulli and Timoshenko beams were utilized. A mesh independence study was investigated. In non-linear models, the stiffness matrix takes into account the effects of higher-order strain terms, leading to a decrease in the maximum bending of the microparticle. The examination of the effects of aspect ratio showed that decreasing it reduces the deflection. After investigating the effects of length scale parameter and aspect ratio, a gold microparticle was manipulated by 200 nm using various models, and the final position of the particle was recorded. To validate the results, the deformations of polystyrene microrods were compared with the available data. The results can be used to make accurate estimates for the positioning of cylindrical microparticles, such as nanowires, nanorods and nanotubes.

Research on the mechanical properties of shale has contributed to the success of shale exploitation. These studies have revealed a strong correlation between the complex mesoscale structure of shale, its pronounced heterogeneity, and the varying equivalent modulus. However, conventional numerical methods face efficiency challenges in investigating the equivalent modulus of mesoscale three-dimensional (3D) shale samples. This research proposes a data-driven workflow for stochastic generation and equivalent modulus prediction of 3D shale volume elements, utilizing a limited set of two-dimensional (2D) SEM images from shale samples. First, 3D volume elements of mesoscale shale, which maintain the distribution characteristics of the mineral constituents observed in the 2D samples, are generated based only on the 2D SEM images using SliceGAN. Second, a dataset comprising the 3D mesoscale shale volume elements and their corresponding equivalent moduli is constructed using the finite element method. Then, a prediction model based on ResNet-18 is developed to predict the equivalent moduli of the shale volume elements. The proposed workflow provides a practical method for generating stochastic 3D samples and efficiently evaluating their mechanical properties. Furthermore, it fosters a better understanding of the behavior of mesoscale shale and paves the way for exploring similar applications in materials with complex mesoscale components.

Cavitation intensity variations in fluid lubrication may alter the mechanical and lubrication properties of the fluid. In this paper, a compressible cavitation model is presented to study the effect of fluid cavitation intensity on zero-leakage flow of upstream-pumping spiral grooves face seals (UPSGLFS). The pressure variation in cavities can be calculated considering the compressibility of the lubricating medium, the ratio of minimum pressure to cavitation pressure is further defined to characterize the cavitation intensity. A numerical analysis of the zero-leakage behavior of UPSGLFS is then performed based on its effect. Results show that cavitation plays a negative role in sealing performances. However, the groove’s configuration and working conditions have substantial effects on controlling the cavitation intensity. Meanwhile, whether a circumferential continuous pressure ring above the seal pressure can be formed is the design basis for judging the strict zero leakage of the medium, rather than only depending on the change of leakage rate parameter value. With suitable spiral groove parameter design, zero-leakage design for upstream-pumping seals may be achieved under multi-speed and multi-seal-pressure conditions. Here, a zero-leakage map is presented for working conditions with multi-speed ranging from 500 to 20,000rpm and multi-seal pressure ranging from 0.1 to 3.0MPa.

Morphing wings covered with elastomeric skin have emerged as a promising technique for enhancing the performance and efficiency of unmanned aerial vehicles (UAVs). These morphing wings can change shape in flight, enabling UAVs to adapt to evolving aerodynamic conditions, fly more efficiently, maneuver more effectively and perform a broader range of missions. The durability of such elastomeric skins that cover the wings, on the other hand, is a critical issue that requires careful consideration. During the flight, elastomeric skins are subjected to a variety of mechanical stresses, including tear and fracture, which can significantly impact the performance and reliability of elastomeric morphing wings. To ensure the long-term durability of the morphing wings, a comprehensive understanding of the tear fracture of elastomeric skins is essential. This study employs a multi-faceted approach of experimental and computational research to investigate the tear fracture of elastomeric skins in morphing wings. Initially, the fracture properties of three materials — Latex, Oppo and Ecoflex — are evaluated experimentally for various cut positions. Subsequently, a continuum physics-based tear fracture model is derived to numerically simulate the mechanical behavior of elastomeric skins. The Griffith criterion, a well-established method, is adopted to investigate mode-III fracture tests, specifically the trousers test, which involves pulling two legs of a cut specimen horizontally apart. Finally, the derived tear fracture model is validated by comparing model solutions to tear test data obtained experimentally. The study suggests that adjusting the stretch ratio and cut position can significantly impact the stress distribution of elastomeric skins, the ability to resist fracture and the stretching behavior of elastomeric morphing wings.

The rate form constitutive expression plays an important role in finite deformation theory and is widely used in the finite element method (FEM) software. However, the choice of objective stress and strain rates in constitutive expressions has caused many controversies. This paper aims to clarify these controversies by distinguishing the related concepts: constitutive behavior, constitutive model and constitutive expression, and discuss the influence of constitutive model choices and constitutive expression choices separately. As a certain constitutive model may correspond to many different rate form constitutive expressions, the conversion relationships among them are derived, which can help clarify many controversies. First, it is proven that three different stress–strain curves in the controversial simple shear example actually correspond to three constitutive models. For each constitutive model, the corresponding different rate form constitutive expressions yield consistent calculation results. We also demonstrate that the applicability of a constitutive model is completely independent of the choice of objective stress rates in the constitutive expressions. Second, we find that for FEM simulation, the element tangent stiffness matrix can serve as an indicator to evaluate the validity of different constitutive expressions and their corresponding FEM formulations. Moreover, even though non-work-conjugate stress-strain rates are adopted, such as the Jaumann stress rate/deformation rate, different rate form constitutive expressions can correctly reflect the constitutive model with the proper tangent modulus tensors. All these conclusions have been verified by examples. For convenience, we recommend using the constitutive expressions in terms of the second Piola–Kirchhoff stress versus Green’s strain tensor and Truesdell stress rate versus deformation rate for experimental measurements and FEM simulations. Of course, other objective stress rates are all applicable and have no effect on the calculation results as long as the correct conversion relationships are used.