International Journal of Applied Mechanics

In technical practice, problems associated with material fatigue often arise. These problems can be caused by errors in the stages of design, production or use of the structure, e.g., by incorrect determination of service life, incorrect dimensioning of construction details, incorrect welds, etc. In the case of welds, such issues may be caused due to the fact that the base material is not welded through or due to the presence of a fistula inside the weld, the presence of slags or cracks inside the weld, etc. The task of the designer is to design a technological unit that meets all the requirements of future users. Components have to be designed for fatigue so that there is an acceptable level of probability that their operation will be satisfactory during their operation life. One of the most common causes of failure of welded joints is fatigue. Fatigue design life is understood to be the reference period of time during which the structure is required to serve safely and not to fail with an acceptable probability. This article deals with the assessment of service life of a welded supporting structure of technological equipment. The structure was subjected to strength analysis. The obtained FEA results were needed to plot the extreme amplitudes of the stresses. Based on the obtained stress vibrations and the welds used, the service life of the structure was assessed by means of the standard.

A hybrid finite element method is proposed for the heat conduction analysis with variable thermal conductivities. A linear combination of fundamental solutions is employed to approximate the intra-element temperature field while standard one-dimensional shape functions are utilized to independently define the frame temperature field along the element boundary. The influence of variable thermal conductivities embeds in the intra-element temperature field via the fundamental solution. A hybrid variational functional, which involves integrals along the element boundary only, is developed to link the two assumed fields to produce the thermal stiffness equation. The advantage of the proposed method lies that the changes in the thermal conductivity are captured inside the element domain. Numerical examples demonstrate the accuracy and efficiency of the proposed method and also the insensitivity to mesh distortion.

This study investigates the influence of large amplitude vibration on geometrically imperfect sandwich curved panels embedded with gradient metallic cellular (GMC) core using an efficient nonlinear finite element formulation based on higher-order shear deformation theory (HSDT). The cores of the sandwich curved panels are assumed to have three distinct porosity distributions. The material properties of the sandwich curved panel’s GMC core layer vary in the thickness direction as a function of porosity coefficient and mass density. The present nonlinear finite element model is validated with limited results available in the open literature, and few new results are also computed that can be used as a benchmark solution. The influence of porosity coefficient, porosity distribution type, amplitude ratio, imperfection amplitude, and curvature ratio on the free vibration characteristics of the geometrically imperfect sandwich curved panels with the GMC core are studied in detail.

In this paper, nonlinear resonance characteristics of a dielectric elastomer actuator are investigated with special consideration on the thermal effects. A finite thermo-elasticity model based on the Gent model is constructed to analyze the vibrational response of the system. The equation of motion is derived via the Euler–Lagrange method. The multiple scales method and the Taylor series expansion are used to solve the governing equation. Nonlinear resonant responses of the system such softening/hardening and jump are explored. Furthermore, the influences of different system parameters including temperature, limiting stretch, damping, mechanical load, relative permittivity and voltage on the frequency response curves are explored. The results are compared with those obtained in the isothermal state, and those solved by numerical methods. It is found that both softening and hardening-type nonlinearities occur in the system in both non-thermal and thermal conditions.

Computational models provide a powerful tool for pre-clinical assessment of medical devices and early evaluation of potential risks to the patient in terms of plaque fragmentation and in-stent restenosis (ISR). Using a suitable constitutive model for arterial tissue is key for the development of a reliable computational model. Although some inelastic phenomena such as stress softening and permanent deformation likely occur due to the supra-physiological loading of arterial tissue during the stenting procedure, hyperelastic constitutive models have been employed in most of the previously developed computational models. This study presents a finite element model for stent deployment into a patient-specific stenosed artery while inelastic arterial behaviors due to supra-physiological loading of the tissue have been considered. Specifically, the maximum stress in the plaque and the arterial layers which is the main cause of plaque fracture during stent deployment and the surgically-induced injury (damage) in the arterial wall, as the main cause of ISR, are presented. The results are compared with the commonly-used hyperelastic behavior for arterial layers. Furthermore, the effects of arterial material parameter variation, analogues to different patients, are investigated. A higher amount of damage is predicted for the artery which shows a higher stress in a specific strain.

The transient deflections of the functionally graded structure considering various types of patterns (power-law, sigmoid and exponential) are computed in this paper numerically using a higher-order shear deformation model. Also, the model includes variable distribution of porosity, i.e., the even and the uneven types, through the thickness direction ($z$-axis) of the graded panel. The transient deflection data are obtained computationally via a customized computer code prepared in MATLAB in association with Newmark’s constant acceleration-type time-integration technique. The model accuracy is checked by comparing the present time-dependent data with the published transient deflection values and the simulated results (modeled through a commercial package, ANSYS). Further, the effects of several design parameters (aspect ratio, thickness ratio, power exponent, porosity index, type of porosity, geometry and end-support conditions) on the transient deflection responses of the graded structure are computed through the derived numerical model.

The force response of poroelastic materials including poroelastic gels to indentation is known to be time- and space-dependent (i.e., a function of indenter shape and size). Despite the complexity of the poroelastic response and in contrast to viscoelastic mechanics, poroelastic mechanics can be captured in terms of several intrinsic mechanical properties, such as elasticity, permeability, and Poisson ratio. While these intrinsic properties can be found from time-domain or frequency-domain master curves, indentation is usually conducted and analyzed only in the time domain using stress-relaxation or creep experiments. This paper advocates using frequency-domain analysis of poroelastic gels by reviewing and analyzing the relevant works of the literature. The analysis and methods, proposed here, enable researchers to characterize dynamic moduli of poroelastic gels in frequency domain using only a few experimental defining parameters. The authors have intentionally provided extensive details and background, to make this work useful for researchers who consider using frequency-domain analysis for the first time. This work reviews and explains the instantaneous elastic modulus, depicted over normalized time as a unifying and understandable set of master curves for time-domain stress relaxation tests on poroelastic gels for cylindrical, conical, and spherical indenters. The dynamic elastic modulus, depicted over normalized frequency, are derived symbolically and numerically and explained for the first time as master curves with simple transfer function in the frequency domain for presenting poroelastic mechanics of gels.

For the distribution prediction of fatigue life and residual strength of fiber reinforced polymer composites, the existing models have the disadvantages of imprecision, instability and single applicability. A novel S–N curve model and a residual strength degradation model were first developed, which are independent and uncorrelated. After verifying their reliability, the statistical distribution models of fatigue life and residual strength were further derived and verified by using experimental data from literature. Compared with the other models, the proposed models can perfectly predict the probability distribution of fatigue life and residual strength under different materials, stacking sequences and stress levels, showing excellent prediction accuracy, stability and applicability.

The strong coupling effect of two-phase flow and ice accompanies the ice accretion process of aircraft and wind turbine in damp and cold environment. A method based on the Eulerian two-phase flow, domain discretization of finite volume method (FVM) and finite element method (FEM), and fluid–solid coupling for numerical simulation of ice accretion is presented in this paper. In addition, the icing process of two-dimensional (2D) ice accretion on airfoils is investigated. It is found that the difference between simulation results and experimental data comes from the phase changes of local collection efficiency $\beta$, which is a function of local vortex strength and changes with time. Furthermore, with the ice accretion, it is easy to generate a negative or distortion grid because of the inappropriate mesh boundary merge and reconstruction, leading to an inaccurate ice prediction result. Based on the influence region of icing accretion and capturing the complex flow characteristics of the near-wall region, a dynamic and partition adaptive grid reconstruction strategy between macroscopic ice layer and microscopic ice crystal growth process is established. This is then used to build the ice accretion step adjustment strategy for multi-step simulation method under different icing conditions. The droplet collection efficiency distribution is modified by considering the vortex structure in the near-wall region. For verification purposes, multi-step simulation results for ice accretion of NACA0012 airfoil and large camber and strong separation airfoil under specified icing conditions are compared with the corresponding experimental data and some previously predicted results. The results of quantitative comparison of ice shape indicate that the current calculation method has better consistency with the experimental data, especially for glaze ice. The similarity of ice shape is more than 20% higher than the previous prediction results, showing that the time-space adaptive adjustment strategy has good robustness and accuracy for ice prediction.

In this study, a bubble complex finite strip method (BCFSM) with the higher-order zigzag theory is formulated for mechanical buckling and free vibration analysis of laminated composite plates, including cross-ply and angle-ply laminates. Few studies have been done to obtain the analytical solutions for clamped and free boundary conditions in the longitudinal and transverse edges. Therefore, this study, for the first time, investigates the effects of various boundary conditions on the stability and vibration results of laminated composite plates subjected to axial or pure shear forces with the use of higher-order zigzag theory and BCFSM. Following this, both the interlaminar continuity conditions of transverse shear stresses and the shear-free surface conditions are satisfied by applying a cubic displacement and a zigzag linear varying displacement with the same number of unknowns as the first-order shear deformation theories. Moreover, the effects of width-to-thickness ratio, fiber orientation, number of modes, different dimensional ratios of the plate, and finally, the number of layers are investigated through numerical examples. The bubble shape functions are exploited in the transverse direction to improve the convergence of the method. Finally, the shearing and axial interaction diagrams of composite laminated plates are presented for various types of boundary conditions.

This work proposes a gradient enhanced localized radial basis collocation method (GL-RBCM) for solving boundary value problems. In particular, the attention is paid to the solution of inverse Cauchy problems. It is known that the approximation by radial basis functions often leads to ill-conditioned systems due to the global nature. To this end, the reproducing kernel shape function and gradient reproducing kernel shape function are proposed to localize the radial basis function while the gradient approximation is aimed at reducing the computational intensity of carrying out the second derivatives of reproducing kernel shape function. In the proposed weighted collocation method, the weights on Neumann and Dirichlet boundary conditions are determined for both direct problems and inverse problems. From stability analysis, it is shown that the GL-RBCM can maintain high accuracy of approximating the first derivatives even under irregular perturbation added to boundary conditions. By comparing with the localized RBCM, the CPU saving of the GL-RBCM is manifested. The efficacy of the proposed method is therefore demonstrated.

The stress-softening phenomenon, named as the Mullins effect, can widely occur in filled rubbers after cyclic loading and unloading conditions. The reloading curve is typically below the initial loading curve unless the applied strain exceeds the previously applied maximum strain. Experimental observations have also shown that the Mullins effect can be recovered by annealing the pre-deformed filled rubbers at a high temperature while the recovery level strongly depends on the annealing time and temperature. In this work, we develop a theoretical model to describe the recovery of the Mullins effect by incorporating the dynamic scission and recovery of polymer chains into the eight-chain model. Experiments have also been performed on two types of filled rubbers to validate the theory. The results show that the model is able to capture the main features of the experimental observations including the Mullins effect of virgin specimens and the recovery of the Mullins effect of pre-deformed specimens subjected to different annealed conditions.