International Journal of Applied Mechanics

This study aims to estimate elastic properties as well as voids interaction energy within the context of 3D nano-porous materials exhibiting spherical or cylindrical voids, with or without the effect of surface energy. For this purpose, numerical homogenization is applied, based on the finite element method (FEM) in combination with the level-set technique. Surface energy is approximated by explicitly taking into account its contribution to overall stiffness in the variational formulation. Several cases are then investigated to appreciate the interaction energy between multiple 3D nanovoids on the actual behavior of nanomaterials. As expected, and like surface energy, the results show that interaction energy keeps affecting the effective behavior by increasing the size of RVE as well as the number of voids inside. This influence is more marked the more cylindrical the voids and the more closely they are adjacent to each other.

This study proposes an innovative computational strategy to predict the initiation of elastoplastic buckling in shell structures. This strategy is developed in connection with ABAQUS/Standard Finite Element (FE) code. Toward this objective, two constitutive frameworks are implemented as User MATerial subroutines (UMATs) into this FE code; namely, the incremental flow theory of plasticity and the total deformation theory. These frameworks are formulated under the plane-stress condition, which is particularly suitable for modeling sheet structures and which enhances computational efficiency. Elastoplastic buckling is detected by the Hill loss of uniqueness criterion, which establishes that buckling occurs when the global stiffness matrix, derived from the finite element computations, becomes singular. To determine this matrix and investigate its singularity, a Python script is developed and combined to the ABAQUS computations. The reliability and accuracy of this computational strategy are assessed through various representative numerical examples. The effect of some geometric and material parameters on the onset of elastoplastic buckling in both thin and thick plates, as well as cruciform columns, is investigated and compared to reference results from the literature. The findings of the present contribution can serve as useful reference guidelines for ABAQUS/Standard users, offering valuable insights for predicting the occurrence of elastoplastic buckling, even in metallic structures characterized by complex mechanical behavior and geometric configurations.

Airfoil-type cracks with curved surfaces and sharp tips are frequently encountered in modern engineering applications and the aerospace industry. However, such cracks significantly threaten structures due to stress concentration and further cause damage. This study investigates the theoretical analysis and failure prediction of airfoil-type cracks within thermoelectric coupling materials under the interaction of remote mechanical loads, heat flux and electric current density. By employing complex variable theory, conformal mapping methods, and the analytic continuation theorem, the full-field stress and stress intensity factors of an airfoil-type crack were determined under three different loading conditions. The results indicate that when the airfoil-shaped crack tip is subjected to horizontal compression, vertical tensile mechanical load, and both heat flux and current density parallel to the crack, the crack tip would reach a dangerous state. Additionally, the full-field stress distribution reveals stress concentration around the crack tip, which explains variations in SIFs under different external forces and shape factors. Four critical situations suppressing crack propagation under mixed loading conditions are proposed. Furthermore, using an acrylic plate and bismuth telluride alloy as examples, the critical values of external loading for the mixed-mode fracture are determined based on the strain energy density criterion. These critical values can be used to predict failure initiation, thus reducing the risk of structural failure due to airfoil cracks within thermoelectric coupling materials.

An autonomous surface manipulator system (ASMS) is a novel intelligent system consisting of a robotic manipulator and an unmanned surface vehicle (USV). Due to the waves and the motions of the manipulators, ASMSs experience rolling while performing tasks, reducing their stability and working accuracy. Hence, two methods are proposed for improving the anti-rolling abilities of ASMSs based on their mathematical models. The first method is to solve the inverse kinematics issues of the manipulator with the objective of minimizing the moment between the manipulator and its base, and to design angle-time curves for each joint using seven-order polynomials. Experiment results demonstrate that the motion optimization of manipulators can reduce the maximum and stable roll angles of the USV by over 40%. The second method involves assembling a moving-mass system into the ASMS and controlling the motion of the moving mass using a dual-loop PID controller. The moving-mass system can significantly reduce the roll angle of USV caused by waves and the operations of manipulators, as validated by simulation on a proposed accurate dynamic model. The research work can greatly enhance the operation stability of ASMSs.

This paper presents a fractional approach as a substitute to the integer-order model, describing the magnetohydrodynamics (MHD) effect of blood flow in a stenosed artery. We not only obtain an analytical solution for the fractional governing equation but also present an expression for the wall-shear stress. After the successful verification of our model with established models, we carry out a two-step validation with the experimental data existing in literature. Then, we analyze the obtained plots by using the analytic expression. We exhibit how fractional model (FM) is helpful for controlling the blood flow through a stenosed artery. This study also indicates that magnetic field intensity significantly controls the flow velocity and wall-shear stress to a great extent. We also show that the external magnetic field, along with the fractional order of the governing equation, plays a pivotal role in the solution of the problem involving the treatment of stenosis. Finally, we conduct some experimental data approximation by the solution to establish the credibility of the proposed fractional-order model.

The shape memory effect (SME) under multiaxial pre-deformation has become a significant problem restricting the development of thermo-induced shape memory polyurethane (TSMPU) in complex service conditions. This study experimentally investigates the multiaxial SME of TSMPU under proportionally and non-proportionally multiaxial loadings. The effects of different loading directions and paths with combined tension/compression–torsion pre-deformations on the multiaxial SME are discussed. The results indicate that the SME exhibits significant anisotropic characteristics under different loading angles. Additionally, the multiaxial SME shows considerable dependence on the loading path and loading sequence. The conditions under compression and torsion loadings can promote more deformation recovery than that under tension loading. The functional degradation of the multiaxial SME under various loading paths is revealed through cyclic thermomechanical experiments. Based on these experimental results, the deformation mechanism for the multiaxial SME based on the motivation of molecular chains is proposed, which is crucial for constructing a thermomechanical constitutive model of TSMPU under proportionally and non-proportionally multiaxial pre-deformations.

The polymer chain network within the dielectric elastomers (DEs) contains numerous entanglements, crosslinks and finite extensibility, all of which play a substantial role in the nonlinear finite deformation behavior of the DE-based phononic crystals. In this study, a theoretical model is proposed to investigate the intricate interplay between internal polymer chain entanglements, crosslinks and finite extensibility, and their influence on the tunable band gap properties of soft dielectric elastomer phononic crystals. To capture the inherent characteristics of the polymer chain network, a physics-based nonaffine material model is employed. By incorporating nonlinear electro-elasticity theory and the linearized incremental theory, the equations governing the voltage-induced finite deformation and superimposed incremental anti-plane shear waves are formulated. Employing the finite element method and Bloch’s theorem, the band structure of an infinite periodic DE phononic crystal is extracted. The numerical results reveal that under higher electric fields, the intrinsic properties of the polymer network significantly impact the band gap characteristics of DE phononic crystals. The outcomes of the numerical simulations and the insights derived from this study offer valuable guidance for the design and manufacturing of soft electro-statically tunable phononic structures.

The Poncelet equation can effectively characterize the resistance of a granular medium to a projectile. However, the determination of the drag coefficient remains challenging. This study aims to explore the potential effects of granular medium parameters on the drag coefficient and to identify key granular medium parameters. Horizontal ballistic tests and quasi-static penetrometer tests were conducted on dry silica sand of four different grain sizes (0.3–0.6 mm, 0.6–2.0 mm, 2.0–4.0 mm and 4.0–8.0 mm). During the ballistic tests, the bulk density of the sand targets was kept consistent, and the entering velocities and the penetration depth of the projectiles were recorded. The bearing strength of the sand targets with different relative densities (30%, 50% and 70%) was measured in the quasi-static tests. Furthermore, two methods were employed to determine the drag coefficients, namely, (1) single-parameter fitting (SF), where the static resistance term was defined as the average bearing strength and the drag coefficients were fitted using the ballistic test data, and (2) two-parameter fitting (TF), where the optimal drag coefficients and bearing strengths were derived from ballistic data. The results showed that the TF method was susceptible to the size effect, differing significantly from the SF method when the projectile diameter was less than 21 times the grain size. The relative density was identified by the SF method as a critical factor affecting the drag coefficient of the granular medium.

Lattice structures with negative Poisson’s ratios (NPR) can integrate advanced functionalities in various engineering applications, including biomedical, aerospace and protective systems. This study explores the mechanical properties of auxetic double arrowhead honeycomb composites, a novel geometric functionally graded auxetic double arrowhead composite with NPR. Analytical expressions for Young’s modulus in both longitudinal and lateral directions are derived and validated using finite element simulations. To this aim, the Euler–Bernoulli beam theory and the free body diagram were used to investigate the elastic response on two different types of arrowhead composite structures. Two types of structures are investigated: uniform (constant forming angle) and geometrically functionally graded (varying forming angle with height). For experimental validation, chopped carbon fiber-reinforced polylactic acid (PLA) composite lattice structures were fabricated via fused filament fabrication. Results indicate that increasing the forming angle enhances lateral stiffness (Young’s modulus) while decreasing longitudinal stiffness. The rate of change of Young’s modulus in the lateral direction is higher than that in the longitudinal direction based on the variations of the forming angles. It was concluded that geometric functionally graded structures could simultaneously have a better elastic response with a more significant Young’s modulus for both longitudinal and lateral directions.

Cellular materials, such as lattices and honeycombs, were widely used for structural protection owing to their excellent mechanical properties. By combining the excellent characteristics of lattice and honeycomb curved surface structures, this study designed a cell called Cubic Spherical Hollow (CSH), which had the advantages of orthogonal isotropy and better spatial connectivity. Inspired by the micro-structural arrangement of bamboo fiber and conch shell, we designed the new CSH cellular materials through the interlayer offset strategy. Then, the effects of interlayer offset on the mechanical properties and compression deformation behavior were explored experimentally and simulatively. Compared with other cellular materials, CSH cellular materials exhibited excellent mechanical properties with higher specific strength and specific modulus. The arrangement offsets of the CSH cells between different layers led to a change in the deformation mechanism from a rod’s compressive mode to a combination of a rod’s compressive mode and curved surface’s bending mode. The initial peak stress and plateau stress decreased with the increased arrangement offsets of the CSH since the extruded protrusions of the structure filled the holes and reduced the lateral expansion behavior of the material in the pressurized environment. This phenomenon also reduced the transverse expansion and prevented the sudden change in stress in the constrained space, indicating that the structural deformation was stable and had excellent cushioning and energy absorption properties. In this study, the cellular material design strategy opens a new avenue for energy absorption.

In addressing the viscoelastic behavior of biological soft tissues, the precise and expeditious measurement methodologies hold paramount significance, given the intrinsic softness and heightened aqueous content of such substrates. We have introduced an expeditious modality for the characterization of viscoelasticity in biological soft tissues, hinged upon a power-law model. This method has been rigorously validated through ramp–hold tests conducted on mechanically stable hydrogels. Notably, during the Ramp phase, the viscoelastic parameters of the material can be readily extracted. Furthermore, we applied unconfined compression stress-relaxation/creep tests with three different ramp–strain rates, namely $\dot{𝜀}=0.01{\mathrm{\text{s}}}^{-1},0.1{\mathrm{\text{s}}}^{-1},1{\mathrm{\text{s}}}^{-1}$, on both white and gray matter to enable rapid quantification. The results indicate that the predicted curves during the Hold phase exhibit notable consistency with experimental data. Moreover, under quasi-static loading conditions, an increase in strain rate significantly enhances the predictive adaptability. Nonetheless, it is crucial to be mindful of the sensitivity to initial stress conditions. This study offers a promising avenue for the expeditious characterization of soft tissue viscoelasticity. It underscores the feasibility of mechanical characterization metrics from a phenomenological model for the assessment of physiological variations and pathological mechanisms in tissue states.

When employing numerical methods to simulate the behavior of saturated porous media under impact load, the Gibbs phenomenon often occurs, significantly compromising the accuracy of numerical calculations. To improve the accuracy of numerical solutions, this study introduces a fast time-discontinuous peridynamic (TDPD) method for simulating the propagation of fluid pressure and solid stress waves within saturated porous media. In this method, the classical u–p and u–U models are reformulated from spatial differential equations into integral equations to facilitate the simulation of fracture problems. Subsequently, the basic field variables are independently interpolated in the temporal domain, with the introduction of jump terms representing the discontinuities of variables between adjacent time steps. Then an integral weak form in the temporal domain of the spatially discrete governing equations is constructed and the basic formula of the TDPD is derived. Additionally, an efficient approximation method that directly uses the internal force to calculate its time derivative is further proposed. These characteristics ensure that the TDPD can effectively and efficiently capture the inherent sharp gradient features of wave propagation in solid phase and fluid while controlling spurious numerical oscillations. Several representative numerical examples demonstrate that the TDPD can obtain more accurate results compared with conventional peridynamic solution schemes. Moreover, the TDPD can also be viewed as a novel time integration technique, holding substantial potential for high-precision numerical solutions of hyperbolic equations in diverse physical contexts.