International Journal of Applied Mechanics

A model is reported for the mechanical response of a cationic polyelectrolyte gel subjected to swelling in a water bath with an arbitrary pH and an arbitrary concentration of a monovalent salt. A gel is treated as a three-phase medium consisting of a polymer network, solvent (water), and solute (mobile ions). Transport of solvent and solute is thought of as their diffusion through the network accelerated by the electric field formed by mobile ions and bound charges and accompanied by chemical reactions (self-ionization of water molecules, protonation of functional groups, and formation of ion pairs between fixed cations and mobile anions). Material constants in the governing equations are determined by fitting equilibrium swelling diagrams on several copolymer gels with vinylimidazole component. Simulation demonstrates that the anti-polyelectrolyte effect (nonmonotonic changes in degree of swelling with molar fraction of salt) can be observed in cationic gels and core-shell microgels.

In this work, we present a new rate type formulation of large deformation generalized plasticity which is based on the consistent use of the logarithmic rate concept. For this purpose, the basic constitutive equations are initially established in a local rotationally neutralized configuration which is defined by the logarithmic spin. These are then rephrased in their spatial form, by employing some standard concepts from the tensor analysis on manifolds. Such an approach, besides being compatible with the notion of (hyper)elasticity, offers three basic advantages, namely:

(i) The principle of material frame-indifference is trivially satisfied.

(ii) The structure of the infinitesimal theory remains essentially unaltered.

(iii) The formulation does not preclude anisotropic response.

A general integration scheme for the computational implementation of generalized plasticity models which are based on the logarithmic rate is also discussed. The performance of the scheme is tested by two representative numerical examples.

Nonlinear behavior is present in the operating conditions of many mechanical systems, especially if nonsmall oscillations are considered. In these cases, in order to improve vibration control performance, a common engineering practice is to design the control system on a set of linearized models, for given operating conditions. The well-known gain-scheduling technique allows the parameters of the control law to be changed according to the current working condition, also increasing system stability. However, more recently new control logics directly applicable to the systems in nonlinear form have been developed. The aim of this paper is to study, both numerically and experimentally, the dynamic of a mechanical system (a 3-link flexible manipulator) comparing the performance of a fully nonlinear control (the sliding-mode control) and a standard linearized approach.

Air cushion is an important packaging material with admirable cushion property in protecting articles from damage. Polymer membrane in air cushion renders a highly nonlinear elastic and rate dependent mechanical behavior in experimental tensile test. A visco-hyperelastic constitutive model for a polymer membrane of an air cushion is developed by additively decomposing its mechanical response into a hyperelastic portion and a viscoelastic portion. Material parameters are consecutively obtained by matching experimental data of static and dynamic uni-axial tensile tests of the membrane, respectively. Compression test of a single air column of the air cushion is conducted as a means of validation on the proposed constitutive model. By comparing simulation results with experimental data, it is shown that the proposed visco-hyperelastic model can properly characterize the mechanical behavior of the air cushion packaging material. The model can be applied to evaluate cushion performance of air cushions and their optimum design.

In this paper, the predictions of different beam theories for the behavior of a shape memory polymer (SMP) beam in different steps of a thermomechanical cycle are compared. Employing the equilibrium equations, the governing equations of the deflection of a SMP beam in the different steps of a thermomechanical cycle, for higher order beam theories (Timoshenko Beam Theory and von-Kármán Beam Theory), are developed. For the Timoshenko Beam Theory, a closed form analytical solution for various steps of the thermomechanical cycle is presented. The nonlinear governing equations in von-Kármán Beam theory are numerically solved. Results reveal that in the various beam length to beam thickness ratios, one of the beam theories provides the most accurate results. In other words, employing the Euler–Bernoulli Beam Theory for developing the governing equations, especially in the large and small beam length to beam thickness ratios, leads to erroneous results.

Modal analysis of rotating tapered cantilevered Timoshenko beams undergoing in-plane vibration is investigated. The coupling effect of axial motion and transverse motion is considered. The Kane dynamic method is applied to deriving the governing eigenvalue equations. The displacement and rotational angle components are approximately described by the products of Chebyshev polynomials and corresponding boundary functions. Chebyshev polynomials guarantee the numerical robustness while the boundary functions guarantee the satisfaction of the geometric boundary conditions. The excellent convergence of the present solution is exhibited. The results are compared with those available in literature, good agreement is observed. The parametric studies on modal characteristics are presented in detail. The tuned rotational speed is examined and the eigenvalue loci veering phenomenon along with the corresponding mode shapes is investigated.

When blood flows in vessel curved portion, the presence of curvature generates a centrifugal force that acts in the same manner as a compressive load. Therefore, blood flow velocity has an important effect on the stability of vessels. In this study, the blood vessel is simulated as a flexible beam conveying fluid base on Euler–Bernoulli beam theory, and various boundary conditions are represented for the modeled vessels. Then, analytical and numerical methods are deployed to extract desired parameters. The effects of blood flow, hematocrit and stiffness of surrounding tissues on the buckling critical pressure are investigated. The results show that the mentioned parameters have considerable effects on blood vessels stability. Several numerical findings illustrate a reduction in critical buckling pressure with increasing hematocrit and blood flow velocity. In addition, the size of red blood cell has a significant effect on critical buckling pressure in low hematocrits. As increasing red blood cell diameter decreases critical buckling pressure. Furthermore, because of blood viscosity, the non-uniformity effects of the blood flow on blood vessels stability are investigated by considering a modification factor. These results improve our understanding of blood vessels instability.

Rubber-like materials as many soft tissues can be described as incompressible and hyper-elastic materials. Their comparable elastic behavior, up to a certain extent, has been exploited to develop and test experimental methodologies to be then applied to soft biological tissues such as aortic wall. Hence, theoretical and experimental simulation of aortic tissue, and more generally blood vessel tissue, has been often conducted using rubbers. Despite all the efforts in characterizing such materials, a clear and comprehensive testing procedure is still missing. In particular, the influence of pre-conditioning in the mechanical response of hyper-elastic materials has been often neglected. In this paper, the importance of pre-conditioning is demonstrated by: (i) exploring the effect of stretching frequency applied before the uniaxial tensile test; (ii) recognizing the role of specimen geometry and strain amplitude; (iii) verifying the impact of experimental data acquisition on finite element predictions. It was found that stress–strain relationship shows a statistical difference between some frequencies of pre-conditioning and its absence. Only certain pre-conditioning frequencies were able to generate repeatable experimental data for strip or dumb-bell shapes. This feature corresponds to a consistent reduction in the scatter of critical pressures obtained by numerical simulations.

In many instances, marine vessel may suffer unexpected flexural–longitudinal vibrations as the consequences of the unevenly distribution of the inner structures and equipment. In order to study the dynamic behaviors of the marine vessel with the involvement of the mass unevenness, the whole vessel is modeled as a discretely connected double-beam system in this paper. In this model, the misalignment between geometric and gravitational center are considered as the simplification of the mass unevenness. The governing equations of coupled flexural–longitudinal vibrations of Timoshenko beam due to mass eccentricity are derived. Extending to the double-beam model, the natural frequencies, modal shapes and forced response of the system are obtained analytically by using the modified transfer matrix method. The comparison between the present method and the conventional finite element method shows a great match. The result indicates that the existence of mass eccentricity can cause significant coupled flexural–longitudinal vibrations, thus, even only vertical force is applied, the vibration in longitudinal direction can be excited and controlled by the natural frequencies of the flexural vibration.

In this paper, the damping properties of flax fiber reinforced composites were investigated. Throughout a series of resonance vibration tests, the natural frequencies and the modal damping were evaluated. A numerical modelling was also produced by using a finite element model to determine the energies dissipated in each layer of the laminate structure in order to calculate the damping factors. The results obtained for the dynamic properties of flax fiber reinforced composites from experimental data and numerical analysis method show close agreement. The effect of fiber orientations on the damping behavior for this material was investigated. Another part of our work was to insert a thin viscoelastic layer within the flax fiber laminate. The interposition of this viscoelastic layer had a significant influence on the vibration behavior, bending stiffness and damping factors.

Based on the meshless local natural neighbor interpolation method (MLNNI), a novel solution procedure is developed for the analysis of nonlinear steady and transient heat transfer of two-dimensional structures in this paper. Nonlinearities arising from temperature dependence of material properties and nonlinear boundary conditions have been taken into account. The present method is developed based on the natural neighbor interpolation (NNI) for constructing shape functions at scattered nodes. The three-node triangular FEM shape function is employed as the test function, which reduces the orders of integrands involved in domain integrals. Due to the delta function property of the natural neighbor shape functions, there is no need to employ special techniques to enforce the essential boundary conditions. The backward difference method is employed for the time integration scheme in transient analysis and the Newton–Raphson iterative procedure is required at each time step. Three numerical examples with different geometries and boundary conditions are presented at the end to demonstrate the validity and accuracy of the proposed method for the solution of a wide class of nonlinear steady and transient heat transfer problems.

An efficient and accurate elastic analysis based on boundary integral methods is presented for crack problems in inhomogeneous elastic media consisting of a set of individually uniform strata. The method combines the direct boundary integral method (DM) and the displacement discontinuity method (DDM) so that it shares both the efficiency of the DDM and the broad applicability of the DM. The DDM is implemented to construct the stiffness matrix in each layer, while the DM is used to characterize the effects of the interfaces. All the variables on the interfaces can then be eliminated through the continuity conditions, leading to the final system of equations consisting of variables on crack surfaces only. The concept of the crack tip element is also adopted for a better treatment of the crack tip singularity. The examples demonstrate that the combined method has comparable accuracy of DM but is more efficient, especially for the scaled thin layers in the application of practical hydraulic fracturing simulations.

This paper provides a general solution for confocally elliptic layers in antiplane elasticity. The studied medium is composed of many layers with different shear moduli. The remote stresses are applied at infinity. Complex variable method is used to study the problem. The continuity conditions for the displacement and the resultant force along the interfaces are suggested. By using the complex variable, the matrix transfer technique, and the boundary condition, the final solution is obtainable. Numerical examples are carried out to show the influence of the different shear moduli defined on different layers to the stress distribution.

The aim of this paper is to provide an overview of the existing industrial practices used for cabin noise control in various industries such as automotive, marine, aerospace, and defense. However, emphasis is placed on automobiles and armored vehicles. Generally, automobile cabins usually constitute of thin structural panels, where the fundamental frequency typically falls below 200Hz. If a specific structural mode couples with a specific acoustic mode of the cabin, booming noise occurs. As such, discomfort may be felt by the occupants. Fundamentally, vibroacoustics problems may be minimized if the acoustic modes and the structural modes are decoupled, which is achieved usually by structural modifications or acoustical treatments. However, if excessively performed, the weight limitation of an automobile design will be exceeded; not to mention the adverse effect of increased weight on several factors such as fuel efficiency, mileage life of tires and acceleration of the vehicle. Moreover, current solutions have several drawbacks in low frequency noise control. In light of this, it is of great interest to explore the feasibility of acoustic metamaterials as an alternative with hope to improve cabin noise.