# Showing papers in "International Journal of Non-linear Mechanics in 2012"

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TL;DR: Numerical results indicate that the combination of MSEBI and PSO can provide a reliable tool to accurately identify the multiple structural damage.

Abstract: A two-stage method is proposed here to properly identify the site and extent of multiple damage cases in structural systems. In the first stage, a modal strain energy based index (MSEBI) is presented to precisely locate the eventual damage of a structure. The modal strain energy is calculated using the modal analysis information extracted from a finite element modeling. In the second stage, the extent of actual damage is determined via a particle swarm optimization (PSO) using the first stage results. Two illustrative test examples are considered to assess the performance of the proposed method. Numerical results indicate that the combination of MSEBI and PSO can provide a reliable tool to accurately identify the multiple structural damage.

216 citations

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TL;DR: In this article, a spherical balloon made out of an electroactive polymer which is subjected to coupled mechanical and electrical excitations is determined, and it is found that for certain material behaviors instabilities that correspond to abrupt changes in the balloon size can be triggered.

Abstract: Solution to the problem of a spherical balloon made out of an electroactive polymer which is subjected to coupled mechanical and electrical excitations is determined. It is found that for certain material behaviors instabilities that correspond to abrupt changes in the balloon size can be triggered. This can be exploited to electrically control different actuation cycles as well as to use the balloon as a micro-pump.

112 citations

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TL;DR: In this article, a micro-scale non-linear Timoshenko beam model based on a general form of strain gradient elasticity theory is developed, where the von Karman strain tensor is used to capture the geometric nonlinearity.

Abstract: In this study, a micro scale non-linear Timoshenko beam model based on a general form of strain gradient elasticity theory is developed. The von Karman strain tensor is used to capture the geometric non-linearity. Governing equations of motion and boundary conditions are derived using Hamilton's principle. For some specific values of the gradient-based material parameters, the general beam formulation can be specialized to those based on simple forms of strain gradient elasticity. Accordingly, a simple form of the microbeam formulation is introduced. In order to investigate the behavior of the beam formulation, the problem of non-linear free vibration of a simply-supported microbeam is solved. It is shown that both strain gradient effect and that of geometric non-linearity increase the beam natural frequency. Numerical results reveal that for a microbeam with a thickness comparable to its material length scale parameter, the effect of strain gradient is higher than that of the geometric non-linearity. However, as the beam thickness increases, the difference between the results of the classical beam formulation and those of the gradient-based formulations become negligible. In other words, geometric non-linearity plays the essential role on increasing the natural frequency of a microbeam having a large thickness-to-length parameter ratio. In addition, it is shown that for some microbeams, both geometric non-linearity and size effect have significant contributions on increasing the natural frequency of non-linear vibrations.

87 citations

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TL;DR: In this article, the Harmonic Balance Method (HBM) is applied to investigate the performance of nonlinear passive vibration isolators with cubic nonlinear damping and linear damping.

Abstract: In the present study, Harmonic Balance Method (HBM) is applied to investigate the performance of passive vibration isolators with cubic nonlinear damping. The results reveal that introducing either cubic nonlinear damping or linear damping could significantly reduce both the displacement transmissibility and the force transmissibility of the isolators over the resonance region. However, at the non-resonance region where frequency is lower than the resonant frequency, both the linear damping and the cubic nonlinear damping have almost no effect on the isolators. At the non-resonance region with higher frequency, increasing the linear damping has almost no effects on the displacement transmissibility but could raise the force transmissibility. In addition, the influence of the cubic nonlinear damping on the isolators is dependent on the type of the disturbing force. If the strength of the disturbing force is constant and independent of the excitation frequency, then the effect of cubic nonlinear damping on both the force and displacement transmissibility would be negligible. But, when the strength of the disturbing force is dependent of the excitation frequency, increasing the cubic nonlinear damping could slightly reduce the relative displacement transmissibility and increase the absolute displacement transmissibility but could significantly increase the force transmissibility. These conclusions are of significant importance in the analysis and design of nonlinear passive vibration isolators.

85 citations

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TL;DR: In this paper, a homogenization framework for electro-elastic composite materials at finite strains is presented, where the effective energy of the composite is written in terms of a purely mechanical component together with a purely electrostatic component, this last one dependent on the macroscopic deformation via appropriate kinematic variables such as the particle displacements and rotations, and the change in size and shape of the appropriate unit cell.

Abstract: This paper presents a homogenization framework for electro-elastic composite materials at finite strains. The framework is used to develop constitutive models for electro-active composites consisting of initially aligned, rigid dielectric particles distributed periodically in a dielectric elastomeric matrix. For this purpose, a novel strategy is proposed to partially decouple the mechanical and electrostatic effects in the composite. Thus, the effective electro-elastic energy of the composite is written in terms of a purely mechanical component together with a purely electrostatic component, this last one dependent on the macroscopic deformation via appropriate kinematic variables, such as the particle displacements and rotations, and the change in size and shape of the appropriate unit cell. The results show that the macroscopic stress includes contributions due to the changes in the effective dielectric permittivity of the composite with the deformation. For the special case of a periodic distribution of electrically isotropic, spherical particles, the extra stresses are due to changes with the deformation in the unit cell shape and size, and are of order volume fraction squared, while the corresponding extra stresses for the case of aligned, ellipsoidal particles can be of order volume fraction, when changes are induced by the deformation in the orientation of the particles.

84 citations

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TL;DR: In this article, a weakly compressible smoothed particle hydrodynamics (WCSPH) method is used along with a new no-slip boundary condition to simulate movement of rigid bodies in incompressible Newtonian fluid flows.

Abstract: A weakly compressible smoothed particle hydrodynamics (WCSPH) method is used along with a new no-slip boundary condition to simulate movement of rigid bodies in incompressible Newtonian fluid flows. It is shown that the new boundary treatment method helps to efficiently calculate the hydrodynamic interaction forces acting on moving bodies. To compensate the effect of truncated compact support near solid boundaries, the method needs specific consistent renormalized schemes for the first and second-order spatial derivatives. In order to resolve the problem of spurious pressure oscillations in the WCSPH method, a modification to the continuity equation is used which improves the stability of the numerical method. The performance of the proposed method is assessed by solving a number of two-dimensional low-Reynolds fluid flow problems containing circular solid bodies. Wherever possible, the results are compared with the available numerical data.

83 citations

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TL;DR: For homogeneous isotropic, nonlinearly elastic materials, the form of the homogeneous deformation consistent with the application of a Cauchy shear stress was derived in this paper for both compressible and incompressible materials.

Abstract: For homogeneous, isotropic, non-linearly elastic materials, the form of the homogeneous deformation consistent with the application of a Cauchy shear stress is derived here for both compressible and incompressible materials. It is shown that this deformation is not simple shear, in contrast to the situation in linear elasticity. Instead, it consists of a triaxial stretch superposed on a classical simple shear deformation, for which the amount of shear cannot be greater than 1. In other words, the faces of a cubic block cannot be slanted by an angle greater than 45° by the application of a pure shear stress alone. The results are illustrated for those materials for which the strain-energy function does not depend on the principal second invariant of strain. For the case of a block deformed into a parallelepiped, the tractions on the inclined faces necessary to maintain the derived deformation are calculated.

73 citations

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TL;DR: In this paper, the quintic non-linear equation of motion is derived based on Hamilton's principle and solved by means of an analytical technique, namely the Homotopy analysis method.

Abstract: non-linear vibration analysis of beam used in steel structures is of particular importance in mechanical and industrial applications. To achieve a proper design of the beam structures, it is essential to realize how the beam vibrates in its transverse mode which in turn yields the natural frequency of the system. Equation of transversal vibration of hinged–hinged flexible beam subjected to constant excitation at its free end is identified as a non-linear differential equation. The quintic non-linear equation of motion is derived based on Hamilton’s principle and solved by means of an analytical technique, namely the Homotopy analysis method. To verify the soundness of the results, a comparison between analytical and numerical solutions is developed. Finally, to express the impact of the quintic nonlinearity, the non-linear responses obtained by HAM are compared with the results from usual beam theory.

70 citations

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TL;DR: A novel computational model for skin to characterize its constitutive behavior when stretched within and beyond its physiological limits is established and the spatio-temporal evolution of stress, strain, and area gain for four commonly available tissue expander geometries is compared.

Abstract: The goal of this manuscript is to establish a novel computational model for skin to characterize its constitutive behavior when stretched within and beyond its physiological limits. Within the physiological regime, skin displays a reversible, highly nonlinear, stretch locking, and anisotropic behavior. We model these characteristics using a transversely isotropic chain network model composed of eight wormlike chains. Beyond the physiological limit, skin undergoes an irreversible area growth triggered through mechanical stretch. We model skin growth as a transversely isotropic process characterized through a single internal variable, the scalar-valued growth multiplier. To discretize the evolution of growth in time, we apply an unconditionally stable, implicit Euler backward scheme. To discretize it in space, we utilize the finite element method. For maximum algorithmic efficiency and optimal convergence, we suggest an inner Newton iteration to locally update the growth multiplier at each integration point. This iteration is embedded within an outer Newton iteration to globally update the deformation at each finite element node. To illustrate the characteristic features of skin growth, we first compare the two simple model problems of displacement- and force-driven growth. Then, we model the process of stretch-induced skin growth during tissue expansion. In particular, we compare the spatio-temporal evolution of stress, strain, and area gain for four commonly available tissue expander geometries. We believe that the proposed model has the potential to open new avenues in reconstructive surgery and rationalize critical process parameters in tissue expansion, such as expander geometry, expander size, expander placement, and inflation timing.

68 citations

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TL;DR: In this article, a phenomenological framework for an electro-viscoelastic material model was developed for modeling and simulation of applications for electroactive polymers (EAPs) within a continuum mechanics setting.

Abstract: A common usage for electroactive polymers (EAPs) is in different types of actuators, where advantage is taken of the deformation of the polymer due to an electric field It turns out that time-dependent effects are present in these applications One of these effects is the viscoelastic behavior of the polymer material In view of the modeling and simulation of applications for EAP within a continuum mechanics setting, a phenomenological framework for an electro-viscoelastic material model is elaborated in this work The different specific models are fitted to experimental data available in the literature While the experimental data used for inherent electrostriction is restricted to small strains, a large strain setting is used for the model in order to account for possible applications where the polymers undergo large deformations, such as in pre-strained actuators

68 citations

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TL;DR: In this article, the primary resonance of a Duffing oscillator with two kinds of fractional-order derivatives is investigated analytically based on the averaging method, the approximately analytical solution and the amplitude-frequency equation are obtained.

Abstract: In this paper, the primary resonance of Duffing oscillator with two kinds of fractional-order derivatives is investigated analytically. Based on the averaging method, the approximately analytical solution and the amplitude–frequency equation are obtained. The effects of the two kinds of fractional-order derivatives on the system dynamics are analyzed, and it is found that these two kinds of fractional-order derivatives could affect not only the linear viscous damping, but also the linear stiffness, which could be characterized by the equivalent damping coefficient and the equivalent stiffness coefficient. The different effects are analyzed based on these two deduced equivalent parameters, when the two fractional orders are limited in the typical intervals, i.e. p1∈[0 1] and p2∈[1 2]. Moreover, the comparisons of the amplitude–frequency curves obtained by the approximately analytical solution and the numerical integration are fulfilled, and the results certify the correctness and satisfactory precision of the approximately analytical solution. Especially, the effects of the parameters in the second kind of fractional-order derivative are studied when the coefficient of the first kind of fractional-order derivative is zero or not. At last, two special cases for the coefficient of the second kind of fractional-order derivative are analyzed, which could make engineers obtain satisfactory vibration control performance and keep the frequency characteristic almost unchanged. These results are very useful in vibration control engineering.

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TL;DR: In this paper, the thermal buckling and postbuckling analysis of laminated composite beams with temperature-dependent material properties is presented, where the governing equations are based on first-order shear deformation beam theory (FSDT) and the geometrical nonlinearity is modeled using Green's strain tensor in conjunction with the von Karman assumptions.

Abstract: The thermal buckling and postbuckling analysis of laminated composite beams with temperature-dependent material properties is presented. The governing equations are based on the first-order shear deformation beam theory (FSDT) and the geometrical nonlinearity is modeled using Green's strain tensor in conjunction with the von Karman assumptions. The differential quadrature method (DQM) as an accurate, simple and computationally efficient numerical tool is adopted to discretize the governing equations and the related boundary conditions. A direct iterative method is employed to obtain the critical temperature (bifurcation point) as well as the nonlinear equilibrium path (the postbuckling behavior) of symmetrically laminated beams. The applicability, rapid rate of convergence and high accuracy of the method are established via different examples and by comparing the results with those of existing in literature. Then, the effects of temperature dependence of the material properties, boundary conditions, length-to-thickness ratios, number of layers and ply angle on the thermal buckling and postbuckling characteristic of symmetrically laminated beams are investigated.

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TL;DR: In this paper, a biological tissue is represented by a multi-constituent, fiber-reinforced material, in which two phases: fluid, and a fiber reinforced solid.

Abstract: We represent a biological tissue by a multi-constituent, fiber-reinforced material, in which we consider two phases: fluid, and a fiber-reinforced solid. Among the various processes that may occur in such a system, we study growth, mass transfer, and remodeling. To us, mass transfer is the reciprocal exchange of constituents between the phases, growth is the variation of mass of the system in response to interactions with the surrounding environment, and remodeling is the evolution of its internal structure. We embrace the theory according to which these events, which lead to a structural reorganization of the system and anelastic deformations, require the introduction of balance laws, which complete the physical picture offered by the standard ones. The former are said to be non-standard. Our purposes are to determine the rates of anelastic deformation related to mass transfer and growth, and to study fiber reorientation in the case of a statistical distribution of fibers. In particular, we discuss the use of the non-standard balance laws in modeling transfer of mass, and compare our results with a formulation in which such balance laws are not introduced.

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TL;DR: In this paper, a linearization method for the Foppl-von-karman equations is presented, which preserves much of the structure of the original equations and enables to construct qualitatively meaningful perturbation solutions in relatively few terms.

Abstract: We discuss the method of linearization and construction of perturbation solutions for the Foppl–von Karman equations, a set of non-linear partial differential equations describing the large deflections of thin flat plates. In particular, we present a linearization method for the Foppl–von Karman equations which preserves much of the structure of the original equations, which in turn enables us to construct qualitatively meaningful perturbation solutions in relatively few terms. Interestingly, the perturbation solutions do not rely on any small parameters, as an auxiliary parameter is introduced and later taken to unity. The obtained solutions are given recursively, and a method of error analysis is provided to ensure convergence of the solutions. Hence, with appropriate general boundary data, we show that one may construct solutions to a desired accuracy over the finite bounded domain. We show that our solutions agree with the exact solutions in the limit as the thickness of the plate is made arbitrarily small.

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TL;DR: In this paper, the dynamic stability of a symmetric sandwich beam with magnetorheological elastomer (MRE) embedded viscoelastic core and conductive skins subjected to time varying axial force and magnetic field was investigated.

Abstract: The present work deals with the dynamic stability of a symmetric sandwich beam with magnetorheological elastomer (MRE) embedded viscoelastic core and conductive skins subjected to time varying axial force and magnetic field. The conductive skins induce magnetic loads and moments under the application of magnetic field during vibration. The MRE part works in shear mode and hence the dynamic properties of the sandwich beam can be controlled by magnetic fields due to the field dependent shear modulus of MRE material. Considering the core to be incompressible in transverse direction, classical sandwich beam theory has been used along with extended Hamilton's principle and Galarkin's method to derive the governing equation of motion. The resulting equation reduces to that of a multi-frequency parametrically excited system. Second order method of multiple scales has been used to study the stability of the system for simply supported and clamped free sandwich beams. Here the experimentally obtained properties of magnetorheological elastomers based on natural rubber have been considered in the numerical simulation. The results suggest that the stability of the MRE embedded sandwich beam can be improved by using magnetic field.

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TL;DR: In this article, a model of a 3D rigid body with a rectangular base, able to rock around a side or a vertex of the base is developed, and the equations of motion are obtained through the general balance principle.

Abstract: A model of 3D rigid body with a rectangular base, able to rock around a side or a vertex of the base is developed. Eccentricity of the center of mass with respect to the geometrical center of the body is also considered. The equations of motion are obtained through the general balance principle. A one-sine pulse base excitation is applied to the body in different directions. The analyses are conducted with the aim to highlight the role of the period, the amplitude and the direction of the external excitation. In significant ranges of the previous parameters, the results obtained with a bi-dimensional model, that does not consider the 3D rocking motions on a vertex of the base, are not in favor of safety. It is found, in fact, that in several conditions the overturning of the 3D block takes place for amplitudes of excitation smaller than those able to overturn the 3D block.

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TL;DR: In this paper, the axisymmetric flow of a non-Newtonian fluid over a radially stretching sheet is analyzed using the homotopy analysis method (HAM).

Abstract: This study presents an analysis of the axisymmetric flow of a non-Newtonian fluid over a radially stretching sheet. The momentum equations for two-dimensional flow are first modeled for Sisko fluid constitutive model, which is a combination of power-law and Newtonian fluids. The general momentum equations are then simplified by invoking the boundary layer analysis. Then a non-linear ordinary differential equation governing the axisymmetric boundary layer flow of Sisko fluid over a radially stretching sheet is obtained by introducing new suitable similarity transformations. The resulting non-linear ordinary differential equation is solved analytically via the homotopy analysis method (HAM). Closed form exact solution is then also obtained for the cases n=0 and 1. Analytical results are presented for the velocity profiles for some values of governing parameters such as power-law index, material parameter and stretching parameter. In addition, the local skin friction coefficient for several sets of the values of physical parameter is tabulated and analyzed. It is shown that the results presented in this study for the axisymmetric flow over a radially non-linear stretching sheet of Sisko fluid are quite general so that the corresponding results for the Newtonian fluid and the power-law fluid can be obtained as two limiting cases.

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TL;DR: In this article, a three dimensional formulation for the rocking motion of a rigid rectangular prism on a deformable base is introduced, where sliding and uplift are taken into account and the fully non-linear equations of the problem are developed and solved numerically.

Abstract: The rocking motion of a rigid rectangular prism on a moving base is a complex three dimensional phenomenon. Although, with very few exceptions, the previous models in the literature make the simplified assumption that this motion is planar, this is usually not true since a body will probably not be aligned with the direction of the ground motion. Thus, even in the case where the body is fully symmetric, the rocking motion involves three dimensional rotations and displacements. In this work, a three dimensional formulation is introduced for the rocking motion of a rigid rectangular prism on a deformable base. Two models are developed: the Concentrated Springs Model and the Winkler Model. Both sliding and uplift are taken into account and the fully non-linear equations of the problem are developed and solved numerically. The models developed are later used to examine the behavior of bodies subjected to general ground excitations. The contribution of phenomena neglected in previous models, such as twist, is stressed.

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TL;DR: In this article, a weak nonlinear stability problem of magneto-convection in an electrically conducting Newtonian fluid, confined between two horizontal surfaces, under a constant vertical magnetic field, and subjected to an imposed time-periodic boundary temperature (ITBT) or gravity modulation (ITGM), is considered.

Abstract: The present paper deals with a weak non-linear stability problem of magneto-convection in an electrically conducting Newtonian fluid, confined between two horizontal surfaces, under a constant vertical magnetic field, and subjected to an imposed time-periodic boundary temperature (ITBT) or gravity modulation (ITGM). In the case of ITBT, the temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent oscillatory part. The temperature of both walls is modulated in this case. In the problem involving ITGM, the gravity field has two parts: a constant part and an externally imposed time periodic part, which can be realized by oscillating the fluid layer. The disturbance is expanded in terms of power series of amplitude of convection, which is assumed to be small. Using Ginzburg–Landau equation, the effect of modulations on heat transport is analyzed. Effect of various parameters on the heat transport is also discussed.

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TL;DR: In this paper, a model of non-linearly elastic solids reinforced by continuously distributed embedded fibers is formulated in which elastic resistance of the fibers to extension, bending and twist is taken into account explicitly.

Abstract: A model of non-linearly elastic solids reinforced by continuously distributed embedded fibers is formulated in which elastic resistance of the fibers to extension, bending and twist is taken into account explicitly. This generalizes the conventional theory in which the solid is modeled as a transversely isotropic simple material.

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TL;DR: 3rd International Conference on Dynamics, Vibration and Control will be held in Hangzhou, China on May 12-14, 2010.

Abstract: Conference Name:3rd International Conference on Dynamics, Vibration and Control. Conference Address: Hangzhou, PEOPLES R CHINA. Time:MAY 12-14, 2010.

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TL;DR: In this paper, a canonical dual mixed finite element method for post-buckling analysis of planar beams with large elastic deformations is presented, which is governed by a fourth-order non-linear differential equation.

Abstract: This paper presents a canonical dual mixed finite element method for the post-buckling analysis of planar beams with large elastic deformations. The mathematical beam model employed in the present work was introduced by Gao in 1996, and is governed by a fourth-order non-linear differential equation. The total potential energy associated with this model is a non-convex functional and can be used to study both the pre- and the post-buckling responses of the beams. Using the so-called canonical duality theory, this non-convex primal variational problem is transformed into a dual problem. In a proper feasible space, the dual variational problem corresponds to a globally concave maximization problem. A mixed finite element method involving both the transverse displacement field and the stress field as approximate element functions is derived from the dual variational problem and used to compute global optimal solutions. Numerical applications are illustrated by several problems with different boundary conditions.

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TL;DR: In this article, the authors studied the relationship between eccentric and concentric annulus flows through catheterized stenosed arteries and showed that there is a significant deference between eccentric flows through concentric flows.

Abstract: This study is concerned with the surgical technique for the injection of catheter through stenotic arteries. The present theoretical model may be considered as mathematical representation to the movement of physiological fluid representing blood in the gap between two eccentric tubes (eccentric-annulus flows) where the inner tube is uniform rigid representing moving catheter while the other is a tapered cylindrical tube representing artery with overlapping stenosis. The nature of blood is analyzed mathematically by considering it as a Newtonian fluid. The analysis is carried out for an artery with a mild stenosis. The problem is formulated using a perturbation expansion in terms of a variant of the eccentricity parameter (the parameter that controls the eccentricity of the catheter position) to obtain explicit forms for the axial velocity, the stream function, the resistance impedance and the wall shear stress distribution also the results were studied for various values of the physical parameters, such as the eccentricity parameter ϵ , the radius of catheter σ , the velocity of catheter Vo, the angle of circumferential direction θ (azimuthal coordinate), the taper angle ϕ and the maximum height of stenosis δ ⁎ . The obtained results show that there is a significant deference between eccentric and concentric annulus flows through catheterized stenosed arteries.

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TL;DR: In this article, mixed variational principles are presented for problems involving electro-elastic interactions, whereby the electric field follows from a scalar potential, and a geometrically non-linear deformable body that is surrounded by free space is treated.

Abstract: Some mixed variational principles are presented for problems involving electro-elastic interactions, whereby the electric field follows from a scalar potential. Firstly, in order to set the stage, we consider the basic case of merely free space. Secondly, to increase the complexity, we immerse an electro-active but mechanically rigid body into vacuum. As our final goal we thirdly treat a geometrically non-linear deformable electro-elastic body that is surrounded by free space. Electro-elastic bodies are of particular interest since they can develop large elastic deformations as a response to the presence of electric fields.

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Tufts University

^{1}TL;DR: In this article, the effect of preconditioning in one direction on the mechanical response when loaded in a perpendicular direction is discussed and a simple phenomenological model is derived to account for stress softening and changes in material symmetry.

Abstract: When an unfilled or particle reinforced rubber is subjected to cyclic loading–unloading with a fixed amplitude from its natural reference configuration, the stress required on reloading is less than on the initial loading for a deformation up to the maximum value of the stretches achieved. The stress differences in successive loading cycles are largest during the first and second cycles and become negligible after about 4–6 cycles. This phenomenon is known as the Mullins effect. In this paper new experimental data are reported showing the change in material symmetry for an initially undamaged and isotropic material subjected to uniaxial and biaxial extension tests. The effect of preconditioning in one direction on the mechanical response when loaded in a perpendicular direction is discussed. A simple phenomenological model is derived to account for stress softening and changes in material symmetry. The formulation is based on the theory of pseudo-elasticity, the basis of which is the inclusion of scalar variables in the energy function. When active, these variables modify the form of the energy function during the deformation process and therefore change the material response. The general formulation is specialized to pure homogeneous deformation in order to fit the new data. The numerical results are in very good agreement with the experimental data.

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TL;DR: In this paper, a variational method was proposed to study the bifurcation of growing cylinders with circular section, accounting for a constant axial pre-stretch, providing a locally isochoric mapping.

Abstract: Morphoelastic theories have demonstrated that elastic instabilities can occur during the growth of soft materials, initiating the transition toward complex patterns. Within the framework of non-linear elasticity, the theory of incremental elastic deformations is classically employed for solving stability problems with finite strains. In this work, we define a variational method to study the bifurcation of growing cylinders with circular section. Accounting for a constant axial pre-stretch, we define a set of canonical transformations in mixed polar coordinates, providing a locally isochoric mapping. Introducing a generating function to derive an implicit gradient form of the mixed variables, the incompressibility constraint for the elastic deformation is solved exactly. The canonical representation allows to transform a generic boundary value problem, characterized by conservative body forces and surface traction loads, into a completely variational formulation. The proposed variational method gives a straightforward derivation of the linear stability analysis, which would otherwise require lengthy manipulations on the governing incremental equations. The definition of a generating function can also account for the presence of local singularities in the elastic solution. Bifurcation analysis is performed for few constrained growth problems of biomechanical interests, such as the mucosal folding of tubular tissues and surface instabilities in tumor growth. In a concluding section, the theoretical results are discussed for clarifying how anisotropy, residual strains and external constraints can affect the stability properties of soft tissues in growth and remodeling processes.

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TL;DR: Ogden-type extensions of the free energy densities currently used to model the mechanical behavior of nematic elastomers are proposed and analyzed in this article, based on a multiplicative decomposition of the deformation gradient into an elastic and a spontaneous or remanent part, they provide a suitable framework to study the stiffening response at high imposed stretches.

Abstract: Ogden-type extensions of the free-energy densities currently used to model the mechanical behavior of nematic elastomers are proposed and analyzed. Based on a multiplicative decomposition of the deformation gradient into an elastic and a spontaneous or remanent part, they provide a suitable framework to study the stiffening response at high imposed stretches. Geometrically linear versions of the models (Taylor expansions at order two) are provided and discussed. These small strain theories provide a clear illustration of the geometric structure of the underlying energy landscape (the energy grows quadratically with the distance from a non-convex set of spontaneous strains or energy wells). The comparison between small strain and finite deformation theories may also be useful in the opposite direction, inspiring finite deformation generalizations of small strain theories currently used in the mechanics of active and phase-transforming materials. The energy well structure makes the free-energy densities non-convex. Explicit quasi-convex envelopes are provided, and applied to compute the stiffening response of a specimen tested in plane strain extension experiments (pure shear).

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TL;DR: In this paper, the propagation of wave in soft dielectric elastomer layers is investigated and incremental motions superimposed on homogeneous finite deformations induced by bias electric fields and pre-stretch are determined.

Abstract: The propagation of waves in soft dielectric elastomer layers is investigated. To this end incremental motions superimposed on homogeneous finite deformations induced by bias electric fields and pre-stretch are determined. First we examine the case of mechanically traction free layer, which is an extension of the Rayleigh–Lamb problem in the purely elastic case. Two other loading configurations are accounted for too. Subsequently, numerical examples for the dispersion relations are evaluated for a dielectric solid governed by an augmented neo-Hookean strain energy. It is found that the phase speeds and frequencies strongly depend on the electric excitation and pre-stretch. These findings lend themselves at the possibility of controlling the propagation velocity as well as filtering particular frequencies with suitable choices of the electric bias field.

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TL;DR: In this article, a theoretical model is developed to predict the sound transmission loss (STL) characteristics of simply supported double-leaf partitions with corrugated core, where the boundary conditions are accounted for by writing the displacements of the face plates in a series form of modal functions.

Abstract: Due to the promising applications of lightweight double-leaf structures in noise control engineering, numerous investigations have been performed to study the vibroacoustic properties of these structures. However, no attention has been focused on the vibroacoustic properties of finite double-leaf structures with corrugated core used extensively in constructing the hulls of bullet passenger trains. In the present paper, a theoretical model is developed to predict the sound transmission loss (STL) characteristics of simply supported double-leaf partitions with corrugated core. The boundary conditions are accounted for by writing the displacements of the face plates in a series form of modal functions. The model predictions are validated by comparing with existing experimental measurements. The vibroacoustic properties of the sandwich construction are examined and the physical mechanisms for sound transmission through the structure explored, including the phenomena of ‘coincidence resonance’ and ‘standing wave resonances’. The effects of structural links, structural dimensions, inclination angle of the corrugated core, as well as the thickness of face plates and core layer on the STL are systematically investigated.

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TL;DR: In this article, the authors present a total Lagrangian quadrature element formulation for planar frames undergoing large displacements and rotations, based on the geometrically exact beam theory, first proposed by Reissner and later extended by Simo and Vu-Quoc.

Abstract: This paper presents a total Lagrangian quadrature element formulation for planar frames undergoing large displacements and rotations. The geometrically exact beam theory, first proposed by Reissner and later extended by Simo and Vu-Quoc, is used as the basis for the formulation. Quadrature element analysis starts with evaluation of the integrals involved in the weak form description of the problem. Neither the placement of nodes nor the number of nodes in a quadrature element is fixed, being adjustable according to convergence need. As a result, not only a member can be modeled with one quadrature element but the total number of degrees of freedom is minimized as well. Several examples of planar frames are given and comparison with analytical and finite element results is made to illustrate the high computational efficiency and accuracy of the weak form quadrature element method (QEM).