International Journal of Applied Mechanics

Clotting of blood elements or intraluminal thrombus (ILT) is known to develop within aortic aneurysm sacs, and is clinically associated with the dilation and rupturing of aneurysms. However, the underlying factors that generate ILT are still unclear. We hypothesize that ILT can form under the influence of unfavorable hemodynamic patterns. This paper presents evidence for one such type of flow dynamics that could give rise to ILT within the aneurysm sac. Image-based patient-specific fluid–structure-interaction modeling of three cases of thoracic aortic aneurysms was performed, using retrospective CT images to investigate the formation of ILT as a result of local hemodynamic of aneurysm. This study showed that the formation of the ILT was associated with a vortex observed near the aortic narrowing, upstream of the aneurysm sac. This vortex could subject the blood elements to elevated stresses before directing them into the sac. The recirculation flow within the aneurysm sac may trap these activated blood elements, thus, leading to the formation of ILT during early diastole. One primary cause for ILT, as indicated in this study, could be attributed to the sharp curvature at the aortic narrowing (or isthmus) that gives rise to the vortex. Our study also showed that the size and location of the aneurysm have a direct impact on the duration and location of the vortex, which could influence the formation of the ILT.

Internal cracks are a serious problem in pipelines conveying unsteady pressurized fluids like natural gas. To investigate and overcome this problem, this paper is motivated to highlight and study the response of gas pipes made of functionally graded materials (FGM) instead of the traditional carbon steel material. FGM is proposed as a composite material because of its advantages of minimizing the stress variation in the pipe. Ceramic is applied because of its durability against corrosion and its surface hardness against erosion. FGM properties are radially graded and a finite element model is developed and implemented into ABAQUS package, including FORTRAN subroutines which are adapted for the present case study. Coupled plane strain thermoelastic analysis is used to investigate the stresses and the stress intensity factor (SIF) at various crack depths under the actual thermomechanical loads. Both coupled and uncoupled thermomechanical approaches are introduced and compared to reveal the necessity of the coupled analysis for accurate FGMs’ investigation. The different influences of unsteady thermal and mechanical loads on the crack propagation are discussed.

An implicit coupling finite element and peridynamic (PD) method is developed in this paper for the dynamic problems of solid mechanics with crack propagation. In this method, an implicit PD formulation is derived from the bond-based pairwise force that is described as a linear function of the displacements by using the first-order Taylor’s expansion technique. The equivalent incremental equations of the PD method and the finite element method are obtained on the basis of the Newmark and the Newton–Raphson schemes. To combine these two methods, the system is partitioned into two subregions and a convenient and efficient coupling strategy is proposed to form the coupling equivalent equation. The coupling domain is achieved by considering that the nodes and material points share the common information. Furthermore, displacement and load control-based incremental-iterative methods are adopted to solve the nonlinear equations. Several representative numerical examples are carried out and the results demonstrate the effectiveness and accuracy of the proposed coupling method.

Low-velocity impact of elasto-plastic functionally graded material (FGM) plates is first investigated in this paper based on Mori–Tanaka model to underline micromechanics and locally determine the effective FGM properties and self-consistent method of Suquet for the homogenization of the stress-field. The elasto-plastic behavior of the particle reinforced metal matrix FGM plate is assumed to follow Ludwik hardening law. An incremental formulation of the elasto-plastic constitutive relation is developed to predict the tangent operator. The homogenization formulation and numerical algorithms are implemented into ABAQUS/Standard via a user material subroutine (UMAT) and USDFLD subroutine. The effect of the power-law index on low-velocity impact parameters like contact force, deflection, permanent indentation, velocity distribution and the kinetic energy are examined using the proposed method. With the aim of demonstrating the accuracy and efficiency of the present method, current numerical results are compared to experimental and theoretical results from the literature and show very good agreement.

The wave finite element method (WFEM) is developed to simulate the wave propagation in one-dimensional problem of nonhomogeneous linear micropolar rod of variable cross-section. For this purpose, two kinds of waves with fast and slow velocities are detected. For micropolar medium, an additional rotational degree of freedom (DOF) is considered besides the classical elasticity’s DOF. The proposed method is implemented to solve the wave propagation, reflection and transmission of two distinct waves and impact problems in micropolar rods with different layers. Along with new solutions, results of the micropolar wave finite element method (MWFEM) are compared with some numerical and/or analytical solutions available in the literature, which indicate excellent agreements between the results.

Training of a shape memory alloy (SMA) is a process in which the mechanical response is stabilized. Since in real-world applications of an SMA, stress is variable and different from the training stress, in this paper we study NiTi-based SMAs’ response in higher and lower stresses than the training stress. In this work, six SMA wire samples were trained at stresses $30,50,100,150,200$ and 250MPa. Then, their recoverable strains were evaluated at a stress range of zero to 250MPa. Regarding the results, SMA wires which trained at 30, 150 and 200MPa exhibited a two-way shape memory effect (TWSME) behavior. Moreover, experimental tests showed that in stresses higher than 100MPa, recoverable strains are independent of the training stress, and to arrive at a better performance, training stresses higher than 100MPa are required. An unstable behavior was observed for SMA wires which were trained at 180MPa and 200MPa.

In the paper, a novel model of fluid-conveying nanotubes made of bi-directional functionally graded materials is presented for investigating the dynamic behaviors and stability. For the first time, the material properties of the nanotubes along both radical and axial directions are under consideration. Based on Euler–Bernoulli beam and Eringen’s nonlocal elasticity theories, the governing equation of the nanotubes and associated boundary conditions are developed using Hamilton’s principle. Differential quadrature method (DQM) is applied for discretizing the equation to determine the numerical solutions of the nanotubes with different boundary conditions. Numerical examples are presented to examine the effects of the material gradation, nonlocal parameter, and mode order on the dynamics and stability. It is shown that the two-directional materials distribution can significantly change the critical flow velocity, fundamental frequencies and stability. Comparing with traditional one-directional distribution, such 2D is more flexible to tune overall dynamic behaviors, this may provide new avenues for smart pipes.

In this paper, the analytical homogenization method of Periodic Discrete Media (HPDM) and the numerical Condensed Wave Finite Element Method (CWFEM) are employed to study the wave propagation in two-dimensional periodic beam lattices. The validity of the HPDM is re-evaluated using the wave propagation feature identified by the CWFEM. Particular attention is paid to the polarization direction of the waves. The wave propagation in two directions is investigated while characteristic wave propagation features such as local resonance, veering and locking phenomena are observed. Complementary results are deduced from the two methods.

In this paper, employing a thermomechanical small strain constitutive model for shape memory polymers (SMP), a beam element made of SMPs is presented based on the kinematic assumptions of Timoshenko beam theory. Considering the low stiffness of SMPs, the necessity for developing a Timoshenko beam element becomes more prominent. This is due to the fact that relatively thicker beams are required in the design procedure of smart structures. Furthermore, in the design and optimization process of these structures which involves a large number of simulations, we cannot rely only on the time consuming 3D finite element analyses. In order to properly validate the developed formulations, the numeric results of the present work are compared with those of 3D finite element results of the authors, previously available in the literature. The parametric study on the material parameters, e.g., hard segment volume fracture, viscosity coefficient of different phases, and the external force applied on the structure (during the recovery stage) are conducted on the thermomechanical response of a short I-shape SMP beam. For instance, the maximum beam deflection error in one of the studied examples for the Euler–Bernoulli beam theory is 7.3%, while for the Timoshenko beam theory, is 1.5% with respect to the 3D FE solution. It is noted that for thicker or shorter beams, the error of the Euler–Bernoulli beam theory even more increases. The proposed beam element in this work could be a fast and reliable alternative tool for modeling 3D computationally expensive simulations.

The ultrafine-grained interstitial free (UFG-IF) steel was fabricated using the equal channel angular pressing (ECAP) method. Transmission electronic microscope (TEM) observations showed that the grains were refined to sub-micrometer scale and the average grain size was several hundred nanometers (nm). Uniaxial compression tests were conducted over a wide range of strain rates (up to 6000/s) and temperatures (from −196${}^{\circ }$C to 300${}^{\circ }$C) to understand the dependence of mechanical behaviors on the strain rate and temperature. It is found that the UFG-IF steel showed a weak strain rate sensitivity and displayed a strong temperature sensitivity only within a very narrow temperature range. Microstructural observations on the specimens deformed dynamically at temperatures below −20${}^{\circ }$C via scanning electronic microscopy (SEM) and TEM indicated the occurrence of adiabatic shear localization. In order to explain the reason why adiabatic shear localization formed at the low temperatures and high strain rates, the susceptibility factor to adiabatic shear band (ASB) was estimated. It is proposed that more heat generated during the adiabatic plastic deformation process due to the enhanced flow stress of the UFG-IF steel at lower temperatures may play a dominant role in the formation of ASB. Meanwhile, the experimental results also provide strong evidence that for the UFG-IF steel the dynamic recrystallization which results from the severe plastic deformation and high temperature rise only occurs at the later stage of ASB evolution. With regard to the formation of ASB in the UFG IF steel, the localized plastic flow at a lower stress level indicates that localized deformation happens firstly and the temperature rise in the localized shearing zone leads to the final plastic instability.

In order to satisfy the increasing computational demands of micromechanics, the Finite-Volume Direct Averaging Micromechanics (FVDAM) theory is developed in three-dimensional (3D) domain to simulate the multiphase heterogeneous materials whose microstructures are distributed periodically in the space. Parametric mapping, which endorses arbitrarily shaped and oriented hexahedral elements in the microstructure discretization, is employed in the unit cell solution. Unlike the finite-element (FE) technique, the expressions for local stiffness matrices are derived explicitly, enabling efficient global stiffness matrix assembly using an easily implementable algorithm. To demonstrate the accuracy and efficiency of the proposed theory, the homogenized moduli and localized stress distributions produced by the FE analyses are given for comparisons, where excellent agreement is always obtained for the 3D microstructures with different geometrical and material properties. Finally, a multi-scale stress analysis of functionally graded composite cylinders is conducted. This extension further increases the FVDAM’s range of applicability and opens new opportunities for pursuing other areas, providing an attractive alternative to the FE-based approaches that may be compared.

This paper is developed to characterize mechanical properties of multilayer coatings for different modulation periods. To that end, Dimensional Analysis Method (DAM) and Finite Element Method (FEM) are applied. Based on these methodologies, two dimensionless forms for the new model are expressed. Numerical nanoindentation tests are carried out for different set properties of multilayer coatings in order to validate the proposed model. Therefore, the mechanical properties of multilayer thin films are identified according to the reverse analysis algorithm. Hence, the input and the identified properties are consistent which ensure the effectiveness and the reliability of the proposed model. Moreover, a case study of Ti-TiN multilayer coating deposited on Zr-based metallic glasses was considered. As a result, the new model is useful for multilayer coatings for different modulation periods and can be used for technological applications.

In this paper, the interpolating moving least-squares (IMLS) method based on a nonsingular weight function is used to construct the approximation function, the weak form of the problem of inhomogeneous swelling of polymer gels is used to obtain the final discretized equations, and penalty method is applied to impose the displacement boundary condition, then an improved element-free Galerkin (IEFG) method for the problem of the inhomogeneous swelling of polymer gels is presented. Three selected examples of inhomogeneous swelling of polymer gels solved with the IEFG method are given in this paper. The accuracy of the numerical solutions of the IEFG method are discussed by using different weight functions, penalty factor, scale parameter of influence domain, node distribution and step number. Numerical results of the IEFG method for inhomogeneous swelling of polymer gels show that this method has great precision, and it can solve large deformation problems of polymer gels effectively.