Modelling the material behaviour of magnetorheological fluids under shear deformation

In recent years the interest in materials with specific adjustable properties has increased due to higher requirements on the material performance. Here a smart composite material is to be developed, whose stiffness can be varied subjected to a magnetic field. To realise this aim a magnetorheological fluid (MRF) embedded in a polymeric matrix material is considered. To model the material behaviour of the composite a homogenisation method will be applied. Amongst others this requires the knowledge of the multiaxial material behaviour of each constituent. The modelling of the material behaviour of MRF under shear deformation, which is the aim of this work, represents the first step in this process. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computation of large shear deformations of a thermoplastic material

A specialized finite difference method with grid refinement and variable time steps is created to approximate the deformation velocity and the temperature in a simple model of the shearing of a thermoplastic material. A specific problem where the solution exhibits “blowup” in the adiabatic case is considered. The numerical method retains this property and is used to study the shape of the “blowup” function. The code is then used to investigate the solution in the closely related case where thermal conduction is included with a small conductivity coefficient. The computations indicate that the solution does not “blowup” in the nonadiabatic case. © 1996 John Wiley & Sons, Inc.     

Polymer morphology and strength characteristics in the presence of large and small deformations

An investigation of the strength characteristics of polychloroprene under the action of a chemically active agent and of polypropylene under the action of a physically active agent, as well as of polychloroprene and polyurethane in both the brittle and highly elastic states in the absence of an aggressivemedium showed that the strength properties of polymers in the small-deformation region are a function of the degree of crystallinity or spherolite size and do not depend on these parameters in the high-deformation region. The influence of the degree of crystallinity on strength characteristics at small deformations and the absence of this effect at large deformations were also demonstrated with pressed specimens having the granular structure typical of real rubbers.Scientific-Research Institute of the Rubber Industry, Moscow. Translated from Mekhanika Polimerov No. 2, pp. 222–225, March–April, 1972.     

Modelling of viscoelastic material behaviour close to the glass transition temperature

In this contribution we investigate the mechanical behaviour of polyurethane over a range of different but constant temperatures from the glass to the viscoelastic state. Therefore uniaxial tension tests are performed on dogbone specimens under different isothermal conditions. In this manner an experimental data set is provided. As a theoretical basis we present the well known thermomechanically coupled one dimensional linear viscoelastic material model which is able to display the experimentally observed material behaviour. For this we adopt temperature dependent relaxation times. The introduced model parameters are identified via a standard parameter identification tool. Finally, the experimental results are compared with the ones of simulations of the identified model parameters. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Motion of an incompressible solid with large deformations

We study the motion of a visco-elastic solid with large deformations. We prove the existence of a local-in-time motion and of a non-negative pressure, which is a measure reaction to the incompressibility condition.     

Modelling thermoplastic material behaviour of dual-phase steels on a microscopic length scale

On a microscopic length scale dual-phase steels exhibit a polycrystalline microstructure consisting of ferrite and martensite. In this work a material model for the temperature dependent hardening behaviour of the ferritic phase is presented. As the dislocation structure determines the resistance to dislocation glide, dislocation densities are introduced as state variables to capture the dependence of the material behaviour on the loading history. Motivated by the elementary processes of multiplication by the Frank-Read-mechanism and annihilation by cross-slip, evolution equations for the dislocation densities are introduced. Based on the interaction of dislocations on different slip systems and the Peierls-stress, the resistance to dislocation motion with its temperature dependence is formulated to describe the hardening behaviour. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the method of finding frequencies with large amplitudes

The paper is concerned with the problem of determining unknown frequenciesw ₁,...w ₁, using the firstN observed discrete time signals {x(m, I)} _m ^=0N–1 arising from a continuous waveform that is the superposition of a finite number of sinusoidal waves with well-defined frequenciesw _j ,j=1,2,...I. We introduce a refined way of Wiener-Levinson method to determine the unknown frequencies with the rate of convergence 1/N ^p by using aboutpN samples of the signals, wherep is any given positive integer (cf. [8]). The paper studies the results on the method to determine the frequencies with large amplitudes.     

Calculation and experimental investigation of torsion of all-rubber and rubber-cord clutches under large deformations

On the basis of a mathematical model of large deformations of homogeneous and fiber-reinforced bodies of revolution, the deformation of all-rubber and rubber-cord clutches made by using the tire technology is investigated. The results of a theoretical and numerical analysis of torsion of the clutches are compared with experimental data.     

The fundamental integral for small deformations superposed on finite triaxial extension of a neo-Hookean material

Résumé Nous considérons un matériau élastique néo-hookéen qui remplit l'espace entier et qui subit une forte déformation homogène et élastique. Nous trouvons le champ élastique additionnel induit par une petite charge concentrée agissant dans le sens d'une des extensions principales. Nous exprimons la solution en fonctions potentielles.     

Modeling of nonlinear viscoelastic contact problems with large deformations

Contact problems are one of the most important engineering problems. These problems become much more tedious when one of the contacting bodies behaves nonlinear viscoelasticity and large deformations. This paper presents an incremental-iterative finite element model for the analysis of two dimensional quasistatic frictionless contact problems. Nonlinear viscoelastic behavior and large deformations are considered. The Schapery’s single-integral creep model with stress-dependent properties is used for nonlinear viscoelasticity. The constitutive equations are transformed into an incremental form resulting in a recursive relationship. Thereby, the need to store the entire strain histories is eliminated, except that from the previous time increment. The updated Lagrangian formulation is used to model the material and geometrical nonlinearities. Also, the Lagrange multiplier method is adopted to enforce the contact constraints. The converged solution is obtained using the Newton–Raphson iterative technique. The developed model has been verified with the previously published works and found a good agreement with them. To demonstrate the efficient capability of the developed computational model, three contact problems with different nature are analyzed.     

A regularization technique for the XFEM: extension to finite deformations,inelastic material behaviour and multifield problems

Within the XFEM often near linear dependencies between the standard degrees of freedom and enriched degrees of freedom and also among enriched degrees of freedom occur. During the last years, several remedies to that problem have been presented. Here, an extension of the regularization technique described in [1] to finite deformation problems and inelastic material behaviour as well as to multifield problems is proposed. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The 3D motion of a solid with large deformations

We study in dimension 3 the motion of a solid with large deformations. The solid may be loaded on its surface by needles, rods, beams, shells, etc. Therefore, it is wise to choose a third gradient theory for the body. It is known that the stretch matrix of the polar decomposition has to be symmetric. This is an internal constraint, which introduces a reaction stress in the Piola–Kirchhoff–Boussinesq stress. We prove that there exists a motion that satisfies the complete equations of Mechanics in a convenient variational framework. This motion is local-in-time for it may be interrupted by a crushing, which entails a discontinuity of velocity with respect to time, i.e., an internal collision.     

Formation of cracks under deformations with finite energy

With a map , , that belongs to the John Ball class where n-1 < p < n and one can associate a set valued map F whose values are subsets of describing the topological character of the singularity of f at . verak conjectured that , where S is the set of points at which f is not continuous and is the Hausdorff measure. The purpose of our paper is to confirm this expectation.Received: 3 March 2003, Accepted: 15 April 2003, Published online: 1 July 2003Mathematics Subject Classification (2000): 74B20Piotr Hajasz: Hajasz was supported by KBN grant 2 PO3A 028 22 and Koskela by the Academy of Finland,SA-34082. Part of this research was done while Hajasz was at the Department of Mathematics of the University of Michigan. He wishes to thank UM for the support and hospitality.     

On the limiting behaviour of solutions to boundary integral equations associated with time harmonic wave equations for small frequencies

The treatment of boundary value problems for Helmholtz equation and for the time harmonic Maxwell's equations by boundary integral equations leads to integral equations of the second kind which are uniquely solvable for small positive frequencies λ. However, the integral equations obtained in the limiting case λ = 0 which are related to boundary value problems of potential theory in general are not uniquely solvable since the corresponding boundary value problems are not. By first considering in a general setting of a Banach space X the limiting behaviour of solutions ?_λ to the equation ?_λ – K λ ? λ = fλ as λ → 0 where {K_λ: X → X, λ ∈ (0,α)}, α > 0, denotes a family of compact linear operators such that I - K_λ (I identity) is bijective for λ∈(0,α) whilst I - K₀ is not and ‖ K_λ – K₀‖ →, 0, ‖f_λ – f0‖ → 0, λ → 0, and then applying the results to the boundary integral operators, the limiting behaviour of the integral equations is considered. Thus, the results obtained by Mac Camey for the Helmholtz equation are extended to the case of non-connected boundaries and Werner's results on the integral equations for the Maxwell's equations are extended to the case of multiply connected boundaries.