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Showing papers in "Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik in 2009"


Journal ArticleDOI
TL;DR: In this paper, the authors considered the plate as a deformable surface and derived the effective stiffness tensors appearing in the two-dimensional constitutive equations of a micropolar material.
Abstract: We discuss the general linear six-parametric theory of plates based on the direct approach. We consider the plate as a deformable surface. Each material point of the surface can be regarded as an infinitesimal small rigid body with six degrees of freedom. The kinematics of the plate is described by using the vector of translation and the vector of rotation as the independent variables. The relations between the equilibrium conditions of a three-dimensional micropolar plate-like body and the two-dimensional equilibrium equations of the deformable surface are established. Using the three-dimensional constitutive equations of a micropolar material we discuss the determination of the effective stiffness tensors appearing in the two-dimensional constitutive equations.

171 citations


Journal ArticleDOI
TL;DR: In this article, a linear Cosserat model with weakest possible constitutive assumptions on the curvature energy still providing for existence, uniqueness and stability is presented, where the curvatures are assumed to be the conformally invariant expression L 2 k dev symr axlAk 2, where axlA is the axial vector of the skewsymmetric microrotation A 2 so(3), dev is the orthogonal projection on the Lie-algebra sl(3) of trace free matrices and sym is the Orthogonal Projection onto symm
Abstract: This is an essay on a linear Cosserat model with weakest possible constitutive assumptions on the curvature energy still providing for existence, uniqueness and stability. The assumed curvature energy is the conformally invariant expression L 2 k dev symr axlAk 2 , where axlA is the axial vector of the skewsymmetric microrotation A 2 so(3), dev is the orthogonal projection on the Lie-algebra sl(3) of trace free matrices and sym is the orthogonal projection onto symmetric matrices. It is observed that unphysical singular stiening for small samples is avoided in torsion and bending while size eects are still present. The number of Cosserat parameters is reduced from six to four: in addition to the (size-independent) classical linear elastic Lam e moduli and only one Cosserat coupling constant c > 0 and one length scale parameter Lc > 0 need to be determined. We investigate those deformations not leading to moment stresses for dierent curvature

122 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigate the numerical response of the linear Cosserat model with conformal curvature and compare it with a conformal model in torsion and highlight its intriguing features.
Abstract: We investigate the numerical response of the linear Cosserat model with conformal curvature. In our simulations we compare the standard Cosserat model with a novel conformal Cosserat model in torsion and highlight its intriguing features. In all cases, free boundary conditions for the microrotations overline A are applied. The size-effect response is markedly changed for the novel curvature expression. Our results suggest that the Cosserat couple modulus µc > 0 remains a true material parameter independent of the sample size which is impossible for stronger, pointwise positive curvature expressions.

84 citations


Journal ArticleDOI
TL;DR: This work presents a hierarchy of mathematical models for the numerical simulation of the production process of technical textiles that range from highly complex three‐dimensional fluid‐solid interactions to one‐dimensional fiber dynamics with stochastic aerodynamic drag.
Abstract: In this work we present a hierarchy of mathematical models for the numerical simulation of the production process of technical textiles. The models range from highly complex three-dimensional fluid-solid interactions to one-dimensional fiber dynamics with stochastic aerodynamic drag and further to efficiently manageable stochastic surrogate models for fiber lay-down. They are theoretically and numerically analyzed and coupled via asymptotic analysis, similarity estimates, and parameter identification. The model hierarchy is applicable to a wide range of industrially relevant production processes and enables the optimization, control, and design of technical textiles.

59 citations


Journal ArticleDOI
TL;DR: In this article, a numerical solution method for linear multi-term fractional differential equations (FDEs) with variable coefficients is presented, which is based on the concept of the analog equation, which converts the multiscale FDE into a single term FDE with a fictitious source (right hand inhomogeneous term).
Abstract: A numerical solution method is presented for linear multi-term fractional differential equations (FDEs) with variable coefficients. The presented method is based on the concept of the analog equation, which converts the multi-term FDE into a single term FDE with a fictitious source (right hand inhomogeneous term). The fictitious source is established from the integral representation of the solution of the substitute single term equation. The constructed algorithms are stable. Their accuracy depends only on the truncation and round-off errors, which, however, negligibly influence the accuracy. The method is demonstrated by the one- and two-term FDEs. The developed algorithms apply also to systems of multi-term FDEs. Several examples are presented, which demonstrate the efficiency and the accuracy of the proposed method. The method is straightforward extended to nonlinear FDEs.

59 citations


Journal ArticleDOI
TL;DR: Two fractional calculus approaches in the framework of continuum mechanics are revisited and compared in this article, where analogies and differences between the two models are outlined, and a non-local approach is proposed, according to which long-range interactions between material particles are opportunely modelled in the equilibrium equations.
Abstract: Two fractional calculus approaches in the framework of continuum mechanics are revisited and compared. The former is a local approach, which has been proposed to investigate the behaviour of fractal media. The latter is a non-local approach, according to which long-range interactions between material particles are opportunely modelled in the equilibrium equations. Analogies and differences between the two models are outlined.

46 citations


Journal ArticleDOI
TL;DR: In this paper, a micromechanical model for single-crystalline materials undergoing diffusionless solid-to-solid phase transitions is developed based on the specification of laminated microstructures on the materials' microscale.
Abstract: We develop a micromechanical model for single-crystalline materials undergoing diffusionless solid-to-solid phase transitions. It is based on the specification of laminated microstructures on the materials' microscale and hence is designed to approximate the rank-1-convex hull of the underlying energy-density for the phase-mixture. In order to capture the hysteretic behavior of such materials like shape-memory-alloys we also account for dissipation by means of evolution equations for the inelastic internal variables. In this context, we derive different evolution-laws from inelastic potentials via least-action principles. Several material-point computations emphasize the characteristics of the presented model.

42 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the constitutive and configurational aspects of phenomenological model formulations for a class of materials with history-dependent gradient microstructure, including standard micromorphic materials as well as inelastic gradient materials as special cases.
Abstract: The purpose of this work is the investigation of some constitutive and configurational aspects of phenomenological model formulations for a class of materials with history-dependent gradient microstructure. The assumption that the behavior of a material point is affected by history-dependent processes in a finite neighbor of this point yields an extended continuum characterized by non-simple material behavior and by additional degrees-of-freedom. This includes both standard micromorphic materials as well as inelastic gradient materials as special cases. As in the case of simple materials, the corresponding constitutive relations are subject to restrictions imposed by material frame-indifference and material symmetry. In the latter case, both direct and differential restrictions are obtained in the case of assuming that the free energy density is an isotropic function of its arguments. In addtion, the concept of material isomorphism is shown to extend to inelastic gradient continua, resulting in a gradient generalization of the well-known elastoplastic multiplicative decomposition of the deformation gradient. Finally, we examine the consequences of gradient extension for the formulation of configurational field and balance relations, and in particular for the Eshelby stress. This is carried out with the help of an incremental stress potential formulation as based on a continuum thermodynamic approach to the coupled field problem involved.

42 citations


Journal ArticleDOI
TL;DR: In this article, a cracked orthotropic elastic strip of finite width is analyzed under antiplane shear loading, and closed-form solutions are derived for the resulting equations, and formulae for calculating stress intensity factors are obtained for an internal crack and edge cracks subjected to arbitrarily varying loading.
Abstract: A cracked orthotropic elastic strip of finite width is analyzed under antiplane shear loading. For four frequently encountered constraint edges, i.e. free-free, clamped-clamped, free-clamped, or clamped-free edges, the Fourier series method is used to reduce triple series equations, and then to a mixed boundary value problem associated with a mode-III crack for each case to a singular integral equation. Closed-form solutions are derived for the resulting equations, and formulae for calculating stress intensity factors are obtained for an internal crack and edge cracks subjected to arbitrarily varying loading. Numerical results of the stress intensity factors for an eccentric, central, and edge crack are shown graphically for the case of uniform loading at the crack faces. Obtained formulae for determining stress intensity factors can be taken as a benchmark of numerical evaluations. The derived results are also applicable to an isotropic elastic strip with an anti-plane shear crack normal to the edges.

28 citations


Journal ArticleDOI
TL;DR: The first band of the essential spectrum can include eigenvalues in the point spectrum under a certain symmetry assumption, and it is demonstrated in this article that the first band can include the eigenvalue of self-adjoint positive operators.
Abstract: Examples of periodic elastic waveguides are constructed, the essential spectrum of which has a gap, i.e. an open interval in the positive real semiaxis intersecting with the discrete spectrum only. The gap is detected with the help of an inequality of Korn's type and the max-min principle for eigenvalues of self-adjoint positive operators. Under a certain symmetry assumption, it is demonstrated that the first band of the essential spectrum can include eigenvalues in the point spectrum.

26 citations


Journal ArticleDOI
TL;DR: In this article, the Lavrentiev regularization method is used to improve the regularity of the Lagrange multipliers in constrained optimal control problems with state constraints, namely the scalar wave equation.
Abstract: The Lavrentiev regularization method is a tool to improve the regularity of the Lagrange multipliers in pde constrained optimal control problems with state constraints. It has already been used for problems with parabolic and elliptic systems. In this paper we consider Lavrentiev regularization for problems with a hyperbolic system, namely the scalar wave equation. We show that also in this case the regularization yields multipliers in the Hilbert space L 2 . We present numerical examples, where we compare the Lavrentiev regularization, Lavrentiev Prox regularization, a fixed point iteration to improve feasibility, and a penalty method.

Journal ArticleDOI
TL;DR: In this article, a computer assisted proof of solutions of the Orr-Sommerfeld equation describing hydrodynamic stability of Poiseuille flow is presented, and a numerical verification method for computing eigenpair enclosures for this non-selfadjoint eigenvalue problem is described.
Abstract: This paper presents a computer-assisted proof of solutions of the Orr-Sommerfeld equation describing hydrodynamic stability of Poiseuille flow. A numerical verification method for computing eigenpair enclosures for this non-selfadjoint eigenvalue problem is described. Some verification results confirm the effectiveness of the method. This constitutes the first strict mathematical instability proof for the Poiseuille flow.

Journal ArticleDOI
TL;DR: In this paper, it was shown that a finite element mesh optimized with respect to discrete configurational forces also renders superior results in terms of classical error measures. But this was not the case in the case of finite element meshes.
Abstract: Over the recent years configurational mechanics has developed into a very active and successful topic both in continuum mechanics as well as in computational mechanics. On the continuum mechanics side the basic idea is to consider energy variations that go along with changes of the material configuration. Configurational forces are then energetically dual to these configurational changes. Configurational forces take the interpretation as being the driving forces in the kinetics of defects; like e.g., cracks, inclusions, phase boundaries, dislocations and the like. On the computational side it turns out that a discretisation scheme brings in artificial, discrete configurational forces that indicate in a certain sense the quality, e.g., of a finite-element mesh. This information can then be used to optimize the nodal material positions. Surprisingly, even driven by energetical arguments, it turns out that a finite element mesh optimized with respect to discrete configurational forces also renders superior results in terms of classical error measures. The manuscript will span the field from the underlying theoretical foundations over the algorithmic challenges to various computational applications.

Journal ArticleDOI
TL;DR: In this paper, the Navier slip boundary condition has been used to remove the corner singularity induced by the no-slip boundary condition, which has been shown to increase the critical Reynolds number for Hopf bifurcation.
Abstract: We study the driven cavity flow using the Navier slip boundary condition. Our results have shown that the Navier slip boundary condition removes the corner singularity induced by the no-slip boundary condition. In the low Reynolds number case, the behavior of the tangential stress is examined and the results are compared with the analytic results obtained in [14]. For the high Reynolds number, we study the effect of the slip on the critical Reynolds number for Hopf bifurcation. Our results show that the first Hopf bifurcation critical Reynolds number is increasing with slip length. c

Journal ArticleDOI
TL;DR: In this paper, the authors studied the onset of convection in a binary viscoelastic fluid-saturated porous layer using a linear and a weak nonlinear stability analyses.
Abstract: The onset of convection in a binary viscoelastic fluid-saturated porous layer is studied using a linear and a weak nonlinear stability analyses The modified Darcy-Oldroyd model is employed as a momentum equation The onset criterion for stationary, oscillatory, and finite amplitude convection is derived analytically There is a competition between the processes of thermal, solute diffusions, and viscoelasticity that causes the convection to set in through oscillatory rather than stationary The effect of solute Rayleigh number, Prandtl number, diffusivity ratio, relaxation, and retardation parameters on the stability of the system is investigated The nonlinear theory based on the truncated representation of Fourier series method is used to find the heat and mass transfer The effect of various parameters on heat and mass transfer is also brought out The transient behaviour of the Nusselt number and Sherwood number is investigated by solving the finite amplitude equations using Runge-Kutta method

Journal ArticleDOI
TL;DR: In this paper, a two-component model of the solid of complex structure is presented, governed by a system of equations describing dynamics of the thermoelastic body of complex structures and accounting for the force and energy exchange between the material components.
Abstract: A mechanical two-component model of the solid of complex structure is presented. The suggested structural-rheological model is governed by a system of equations describing dynamics of thermoelastic body of complex structure and accounting for the force and energy exchange between the material components of the body. Propagation of mechanical and temperature disturbances due to a pulse laser excitation is considered. The influence of the material structure on the character of transfer of the temperature disturbances is studied. The possibility of transfer of temperature disturbances with the velocity close to that of the mechanical pulse propagation is shown.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the direct and inverse electromagnetic scattering problem by a piecewise homogeneous sphere, excited by an interior or exterior dipole, and used the low-frequency assumption to derive asymptotic far-field expansions of the Green's function.
Abstract: This paper deals with the investigation of the direct and the inverse electromagnetic scattering problem by a piecewise homogeneous sphere, excited by an interior or exterior dipole. The research is motivated by important physical, biomedical, and technological applications detailed in the introduction. First, we utilize Sommerfeld's and T-matrix method to determine the exact electromagnetic Green's function, that is the solution of the direct scattering problem. Then, we use the low-frequency assumption to derive asymptotic far-field expansions of the Green's function of an electrically small piecewise homogeneous sphere. These low-frequency expansions contribute essentially to the development of far-field inverse scattering algorithms for the determination of the sphere's geometrical and physical characteristics. It is shown that for these algorithms interior dipoles offer additional information, which may be utilized effectively for the localization and reconstruction of the sphere. Several numerical results exhibit the variations of the far-field quantities with respect to the dipole's and the sphere's characteristics. Reductions to plane wave scattering by a layered sphere and exterior dipole scattering by a homogeneous sphere are pointed out.

Journal ArticleDOI
TL;DR: In this article, the torsional wave dispersion in pre-stretched bi-material compounded cylinders is investigated under the assumption that the elasticity relations of the materials of the components of the cylinders are given through the Murnaghan potential.
Abstract: Within the framework of the piecewise homogeneous body model and through the application of the three-dimensional linearized theory of elastic waves in an initially stressed body, the torsional wave dispersion in pre-stretched bi-material compounded cylinders is investigated. It is assumed that the elasticity relations of the materials of the components of the cylinders are given through the Murnaghan potential. The numerical investigations are made for steel (St) (as a material for the solid cylinder) and bronze (Br) (as a material for a hollow covering cylinder). According to the numerical results obtained, the influence of the problem parameters such as the initial stresses in the components of the bi-material compounded cylinder, the values of the mechanical and physical constants of the components, and the geometrical parameters (such as the relation of the thickness of the covering cylinder with the radius of the inner solid cylinder on the dispersion curves) are analyzed.

Journal ArticleDOI
TL;DR: In this paper, a viscous, electrically conducting fluid past a wedge having a permeable surface is analyzed and the equations governing the flow and the magnetic field being reduced to local non-similarity equations are solved numerically.
Abstract: Flow of a viscous, electrically conducting fluid past a wedge having permeable surface is analyzed. A constant transpiration through the wedge surface is assumed. The equations governing the flow and the magnetic field being reduced to local non-similarity equations are solved numerically. The implicit finite difference method, as well as the local non-similarity method is being used in finding the solutions of the reduced equations against the transpiration parameter, ξ. Perturbation solutions for small and large ξ values are also obtained. Effect of the physical parameters, such as, the magnetic force parameter, S, the magnetic Prandtl number, Pm and free stream velocity gradient, n, on the local skin-friction coefficient, f'' (0, ξ), and the local current density coefficient, g'' (0, ξ ), are shown graphically. It is found that the perturbation solutions agreed excellently with other solutions at the two extreme ranges of ξ values. From the present investigation we further observe that, incase of withdrawal of fluid both the momentum and magnetic boundary layers decrease with the increase of ξ. On the other hand these layers increase with ξ value when fluid is being injected trough the surface. Further we notice that there is an onset of reverse flow in the down-stream region in case of blowing of fluid and the starting point of this flow, approximately, is ξ = -0.6.

Journal ArticleDOI
TL;DR: In this article, the computation of discretized constitutive models of evolutionary-type (like models of viscoelasticity, plasticity, and viscoplasticity) with quasi-static finite elements using diagonally implicit Runge-Kutta methods (DIRK) combined with the multilevel-Newton algorithm (MLNA) is treated.
Abstract: This article treats the computation of discretized constitutive models of evolutionary-type (like models of viscoelasticity, plasticity, and viscoplasticity) with quasi-static finite elements using diagonally implicit Runge-Kutta methods (DIRK) combined with the Multilevel-Newton algorithm (MLNA). The main emphasis is on promoting iterative methods, as opposed to the more traditional direct methods, for solving the non-symmetric systems which occur within the DIRK/MLNA. It is shown that iterative solution of the arising sequences of linear systems can be substantially accelerated by various techniques that aim at sharing part of the computational effort throughout the sequence. In this way iterative solution becomes attractive at clearly lower dimensions than the dimensions where direct solvers start to fail for memory reasons. The applications are related to small strain viscoplasticity of a smooth constitutive model for plastics and a finite strain plasticity model with non-linear kinematic hardening developed for metals.

Journal ArticleDOI
TL;DR: This paper forms a coupled thermo‐mechanical problem for non linear composites having properties depending on temperature and proposes a “problem‐oriented” technique of solution using the Finite Element Method to solve the elastic‐plastic problem.
Abstract: This paper presents a development of the usual generalized self-consistent method for homogenization of composite materials. The classical self-consistent scheme is appropriate for phases that are "disordered", i.e. what is called "random texture". In the case of both linear and non linear components, the self-consistent homogenization can be used to identify expressions for bounds of effective mechanical characteristics. In this paper we formulate a coupled thermo-mechanical problem for non linear composites having properties depending on temperature. The solution is found in a non-classical way, as we use the Finite Element Method to solve the elastic-plastic problem at hand. In this sense we propose a "problem-oriented" technique of solution. The method is finally applied to the real case of superconducting strands used for the coils of the future ITER experimental reactor.

Journal ArticleDOI
TL;DR: In this article, the effect of material softening during cyclic loading is discussed, where the decrease of stress is caused by a damage evolution in the micro-scale, e.g. due to micro-void growth.
Abstract: We discuss the effect of material softening during cyclic loading. The decrease of stress is caused by a damage evolution in the microscale, e.g. due to micro-void growth. For a numerical treatment of this material behaviour, phenomenological damage approaches are used in daily engineering practice. For a better understanding of the micromechanical process, multiscale methods are becoming increasingly important. The physical quantities which are responsible for the microstructural evolution associated with the damage process are transferred into the numerical model. In this context, the method of configurational forces is used to describe the geometrical changes of damaged areas. With the help of a homogenization technique, macro- and microscale are coupled. In consequence, each Gaussian point of the macromechanical finite element discretization represents a microstructure (representative volume element - RVE), where the microscale evolves during the loading process according to observable damage phenomena. We present the general case of hyperelastic materials at finite strains.

Journal ArticleDOI
TL;DR: In this paper, the authors show H 1 loc -regularity of the Cauchy stress tensor and the plastic strain tensor in infinitesimal Cosserat plasticity with monotone flow rule.
Abstract: We show H 1 loc -regularity of the Cauchy stress tensor and H 1 loc -regularity of the infinitesimal strain tensor and the plastic strain tensor in infinitesimal Cosserat plasticity with monotone flow rule. We use energy estimates for difference quotients.

Journal ArticleDOI
Ulrich Werner1
TL;DR: The aim of this paper is to show the mathematical coherence concerning typical rotor eccentricities in asynchronous machines and to demonstrate the necessity to focus not only on the amplitudes relative to two fixed sensor positions, but to also consider the semi-major axis of the calculated orbit and its angular position.
Abstract: This paper presents a mathematical analysis of rotor shaft displacements in asynchronous machines caused by different types of rotor eccentricity. Based on a simplified rotor model, the theoretical coherence between electromagnetic, rotor dynamic, and the specific characteristics of sleeve bearings is shown. The orbits of the rotor mass and the shaft journal are mathematically described for each kind of eccentricity and the shaft displacement with respect to two virtual fixed sensors is derived. Based on this theoretical description and on a numerical example, the paper shows that focusing in a theoretical rotor dynamic analysis only on the calculated amplitudes in direction of two fixed sensor positions, may lead to wrong conclusions concerning the evaluation of resonances. The aim of this paper is, based on a simplified rotor model, to show the mathematical coherence concerning typical rotor eccentricities in asynchronous machines and to demonstrate the necessity to focus not only on the amplitudes relative to two fixed sensor positions, but to also consider the semi-major axis of the calculated orbit and its angular position. The aim of the paper is not to replace a detailed finite element rotor dynamic analysis by a simplified analytical rotor model for predicting the real shaft vibrations. The intension is to prepare the basis for adopting the conclusions, derived from a simplified analytical model, into a more detailed rotor dynamic model – e.g. a finite element rotor dynamic model – and therefore to derive a more precise theoretical analysis of the real shaft displacements.

Journal ArticleDOI
TL;DR: In this article, the existence and stability of a steady solution for the unsteady problem in a horizontal annulus with Prandtl number and inverse relative gap width is proved.
Abstract: The objective of our paper is to start the theoretical investigation of the most commonly used mathematical model for natural convection in a horizontal annulus. First, one shows existence of solutions for the unsteady problem. Then, for any Prandtl number and inverse relative gap width, existence, and stability of a steady solution is proved, provided that the Rayleigh number is sufficiently small. The same is also proved for any Rayleigh number provided the inverse relative gap width is sufficiently small. Furthermore, exponential decay to the steady symmetric solution and uniqueness hold true under stronger restrictions to the Rayleigh number.

Journal ArticleDOI
TL;DR: In this paper, the stabilization problem and Riesz basis property of two serially connected Timoshenko beams whose left end is simply supported and the right end is free were studied.
Abstract: In this paper we study the stabilization problem and Riesz basis property of two serially connected Timoshenko beams whose left end is simply supported and the right end is free. Suppose that the displacement and bending moments of the beams at the interior node are continuous, but the shearing force and rotational angle are discontinuous. We design the compensator and feedback controllers at the left end and the interior node of the beams so as to derive the beams back to their equilibrium position. We prove that this closed loop system is well-posed and asymptotically stable. By the spectral analysis, we also show that its root vectors form a Riesz basis with parentheses for the state space. Hence the spectrum determined growth condition holds. Further, we show that this system is not exponentially stable. Finally, we give a numerical simulation of this kind of closed loop system to support our results.

Journal ArticleDOI
TL;DR: In this article, a detailed analysis of the inertialess ellipsoidal particle behavior in the shear flow of a Newtonian fluid has been presented, where the initial conditions and the "inertia" parameter are considered.
Abstract: The rotation of an inertialess ellipsoidal particle in a shear flow of a Newtonian fluid has been firstly analyzed by Jeffery [17]. He found that the particle rotates such that the end of its axis of symmetry describes a closed periodic orbit. In the special case of a slender particle the Jeffery solution predicts the particle alignment parallel to the streamlines. In a recent publication [3] it was shown that the orbits are no longer observable if the rotary inertia is taken into account. Furthermore, in the case of a slender particle the inertia may cause the jump over the equilibrium alignment. In this paper we address a detailed analysis of the slender particle behavior in the shear flow. We recall the constitutive equation for the hydrodynamic moment and formulate equations of rotary motion. For a special initial condition we reduce the problem to a single second-order ordinary differential equation with respect to the angle of rotation about a fixed axis. The phase portrait of this equation illustrates different cases of the particle behavior depending on the initial conditions and the "inertia" parameter. They include the particle alignment to a semi-stable equilibrium position, the non-uniform rotation about a fixed axis as well as the quantization effect (the particle locates in the neighborhood of the first equilibrium point over a relatively long time and then rotates towards the next equilibrium point).

Journal ArticleDOI
TL;DR: In this paper, the authors considered the large bending of a thin-walled cylinder made of a rubber-like material and established that there exists the limit value of the bending moment, which depends essentially upon the internal pressure.
Abstract: We consider the large bending of a thin-walled cylinder made of a rubberlike material. It is loaded by internal pressure and bending moments at the ends. The exact formulation of the problem is given within the framework of the nonlinear membrane theory taking into account large strains of the cylinder. Using the special substitution describing the pure bending of the cylinder, the problem is reduced to the system of nonlinear ordinary differential equations. The latter is solved numerically. We establish that there exists the limit value of the bending moment, which depends essentially upon the internal pressure. As an example, the Mooney-Rivlin material is considered. On the base of the calculations we propose the approximate formulae describing the bending moment dependence on the axis curvature of the cylinder and the ultimate bending moment dependence on the internal pressure.

Journal ArticleDOI
TL;DR: In this article, a study of the global thermoelastic instability of brake disk made of either the isotropic homogeneous metal matrix composite (MMC) or the inhomogeneous functionally graded material composite (FGM) is presented.
Abstract: This paper deals with study of the global thermoelastic instability of brake disk made of either the isotropic homogeneous metal matrix composite (MMC) or the isotropic inhomogeneous functionally graded material composite (FGM). The main idea of the FGM composite is a smooth variation of material properties due to continuous change in microstructure. The estimates in diffusion equation are characterized both by non-stationary heat flux and non-stationary heat convection terms enhanced by the characteristic frictional heat sources. Global instability is characterized by the Schaefer-Papkovich condition. Application of functionally graded A356R-based composite to brake disk structure prevents loss of global stability in contrast with homogeneous A356R composite and stainless steel ASTM321 brake disk which guaranties safety and durability of the braking system.

Journal ArticleDOI
TL;DR: The material force approach is an efficient, elegant, and accepted means to compute the J-integral as a fracture mechanical parameter for elastic and inelastic materials as discussed by the authors, which can be used to investigate the dwell effect of elastomeric materials.
Abstract: The material force approach is an efficient, elegant, and accepted means to compute the J-integral as a fracture mechanical parameter for elastic and inelastic materials. With the formulation of a multiplicative split of the deformation gradient at hand, rate-dependent (visco-elastic) materials described for example by the physically based Bergstrom-Boyce model can be investigated. For these investigations, the so-called material volume forces have to be computed in order to separate the driving forces acting on the visco-elastic zone around the crack tip from the driving forces acting on the crack tip itself, representing the crack driving force. To illustrate the effectiveness of this approach, the so-called dwell-effect of elastomeric materials is investigated.