Existence of solutions for a finite nonlinearly hyperelastic rod

A theoretical investigation of a mathematical model for the capillary-tissue fluid exchange, including the characteristics and influence of the boundaries and media through which the fluid flows, has been studied. Filtration from the cylindrical capillary into the concentrically surrounding tissue-space and flow from a capillary into the tissue across the thin membrane are analyzed in detail. It has been observed that the filtration efficiency of the functional unit decreases as the peripherallayer viscosity increases, and that contrary to the results of Apelblat, Katziv-Kutchalsky and Silborberg (Biorheology2 (1974), 1–49), the slip velocity plays dominant role on filtration efficiency. It is also noted that he filtration efficiency decreases as the slip velocity at the porous boundary increases.     

The Signorini problem with Coulomb friction for a hyperelastic body under finite deformations

The quasi-static three-dimensional problem of elasticity theory for a hyperelastic body under finite deformations, loading by bulk and surface forces, partial fastening and unilateral contact with a rigid punch and in the presence of time-dependent anisotropic Coulomb friction is considered. The equivalent variational formulation contains a quasi-variational inequality. After time discretization and application of the iteration method, the problem arising with “specified” friction is reduced to a non-convex miniumum functional problem, which is studied by Ball's scheme. The operator in contact stress space is determined. It is shown that a threshold level of the coefficient of friction corresponds to each level of loading, below which there is at least one fixed point of the operator. If the solution at a certain instant of time is known, the iteration process converges to the solution of the problem at the next, fairly close instant of time.     

Longitudinal bulk strain solitons in a hyperelastic rod with quadratic and Cubic nonlinearities

Theoretical and Mathematical Physics - We study long nonlinear longitudinal bulk strain waves in a hyperelastic rod of circular cross section in the framework of general weakly nonlinear elasticity...     

A finite element method and variable transformations for a forward-backward heat equation

The Galerkin finite element method for the forward-backward heat equation is generalized to a wider class of equations with the use of a result on the existence and uniqueness of a weak solution to the problems. First, the theory for the Galerkin method is extended to forward-backward heat equations which contain additional convection and mass terms on an irregular domain. Second, variable transformations are constructed and applied to solve a wide class of forward-backward heat equations that leads to a substantial improvement. Third, Error estimates are presented. Finally, conducted numerical tests corroborate the obtained results. Received February 4, 1997 / Revised version received December 8, 1997     

A stable three-level finite difference scheme for solving the parabolic two-step model in a 3D micro-sphere heated by ultrashort-pulsed lasers

Ultrashort-pulsed lasers with pulse durations of the order of sub-picosecond to femtosecond domain possess exclusive capabilities in limiting the undesirable spread of the thermal process zone in the heated sample. Parabolic two-step micro heat transport equations have been widely applied for thermal analysis of thin metal films exposed to picosecond thermal pulses. In this study, we develop a three level finite difference scheme for solving the heat transport equations in a three-dimensional micro-sphere heated by ultrashort-pulsed lasers. It is shown that the scheme is unconditionally stable. The method is illustrated by numerical examples.     

The range order of a product of i transformations from a finite full transformation semigroup

Communicated by N. R. Reilly     

Scale transformations in phase space and stretched states of a harmonic oscillator

We consider scale transformations (q, p) → (λq, λp) in phase space. They induce transformations of the Husimi functions H(q, p) defined in this space. We consider the Husimi functions for states that are arbitrary superpositions of n-particle states of a harmonic oscillator. We develop a method that allows finding so-called stretched states to which these superpositions transform under such a scale transformation. We study the properties of the stretched states and calculate their density matrices in explicit form. We establish that the density matrix structure can be described using negative binomial distributions. We find expressions for the energy and entropy of stretched states and calculate the means of the number-ofstates operator. We give the form of the Heisenberg and Robertson–Schrödinger uncertainty relations for stretched states.     

A phase field model for martensitic transformations with a temperature-dependent separation potential

Metallic materials often exhibit a complex microstructure with varying material properties in the different phases. Of major importance in mechanical engineering is the evolution of the austenitic and martensitic phases in steel. The martensitic transformation can be induced by heat treatment or by plastic surface deformation at low temperatures. A two dimensional elastic phase field model for martensitic transformations considering several martensitic orientation variants to simulate the phase change at the surface is introduced in [1]. However here, only one martensitic orientation variant is considered for the sake of simplicity. The separation potential is temperature dependent. Therefore, the coefficients of the Landau polynomial are identified by results of molecular dynamics (MD) simulations for pure iron [1]. The resulting separation potential is applied to analyse the mean interface velocity with respect to temperature and load. The interface velocity is computed by use of the dissipative part to the configurational forces balance as suggested in [3]. The model is implemented in the finite element code FEAP using standard 4-node elements with bi-linear shape functions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Geometrical series and phase space in a finite oscillatory motion

This article discusses some interesting physical propertiesof oscillatory motion of a particle on two joined inclined planes.The geometrical series demonstrates that the particle will oscillateduring a finite time. Another detail is the converging pathto the origin of the phase space. Due to its simplicity, thismotion may be used as a didactic example for the non-lineardynamic study.     

On a Sachs bound for stress-induced phase transformations in polycrystalline shape memory alloys

In earlier work [3], a Sachs and a Taylor bound on the transformation yield stress in shape memory polycrystals were derived in the context of a variational model. The aim of this article is to compare the Sachs with the Taylor bound for cubic-toorthorhombic phase transformations under biaxial loading, where the material parameters are chosen explicitly (CuAlNi). It turns out that the gap between the two bounds can be quite large depending on the underlying texture and the loading direction. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Assessing the of potential of e-business models: towards a framework for assisting decision-makers

Decision makers are faced with an enormous range of electronic business models from which to choose. The process of fully researching each of these models can prove daunting. Such research is a feature of what has been termed the “intelligence phase” of decision making. This phase is important as options excluded at this stage do not get considered at a later stage. This paper develops a prerequisites framework for use at the intelligence phase to exclude models that are incompatible with prevailing organisational and supply chain characteristics. The framework assesses the following characteristics: economic control, supply chain integration, functional integration, innovation and input sourcing. The paper utilises a series of five point Likert scales to operationalise these characteristics so that they can be used by decision makers to efficiently manage “intelligence phase” activities.     

Numerical treatment of a finite strain viscoplasticity model based on a double multiplicative split

A viscoplastic material model of overstress type is analyzed. The model is based on the kinematic assumption of a double multiplicative split in order to simulate a nonlinear kinematic hardening. We investigate theoretically and numerically two implicit time–stepping methods, which were used lately in engineering literature to integrate the evolution equations in the context of multiplicative plasticity/viscoplasticity. A common feature of both methods is that the plastic incompressibility constraint is exactly satisfied. Moreover, we show that both methods preserve the symmetry of internal variables, which is inherent to the problem. According to testing results, both methods are equivalent regarding robustness, accuracy, and computational efficiency. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Homogenization of a fully coupled thermoelasticity problem for a highly heterogeneous medium with a priori known phase transformations

We investigate a linear, fully coupled thermoelasticity problem for a highly heterogeneous, two‐phase medium. The medium in question consists of a connected matrix with disconnected, initially periodically distributed inclusions separated by a sharp interface undergoing an a priori known interface movement because of phase transformations. After transforming the moving geometry to an ? ‐periodic, fixed reference domain, we establish the well‐posedness of the model and derive a number of ? ‐independent a priori estimates. Via a two‐scale convergence argument, we then show that the ? ‐dependent solutions converge to solutions of a corresponding upscaled model with distributed time‐dependent microstructures. Copyright © 2017 John Wiley & Sons, Ltd.     

Finite strain inelasticity for isotropy,a simple and efficient finite element formulation

We consider a formulation of associative isotropic J₂‐elastoplasticity at finite inelastic strains and aspects of its numerical implementation. The essential ingredients include the multiplicative decomposition of the deformation gradient in elastic and inelastic parts, the definition of a convex elastic domain in stress space and a material representation of the constitutive equations for general non‐Cartesian coordinate charts. On the numerical side we propose a stress update algorithm for elasto‐plastic response, including isotropic hardening. The finite element formulation is based on assumed strain and enhanced strain variational principles, for a complete outline see [3]. Remarkably the formulation is very similar to the case of infinitesimal plasticity: (i) The scheme of linear return mapping algorithm takes the form of standard return mapping of the infinitesimal theory for the case of isotropic elastic response. (ii) The algorithmic elastoplastic moduli have a similar structure as in the linear case. Together with an exact fulfillment of plastic incompressibility by means of a simple correction one achieves an advantageously efficient finite element formulation. Its performance is documented by a numerical example.     

Networking strategies and methods for connecting theoretical approaches: first steps towards a conceptual framework

The article contributes to the ongoing discussion on ways to deal with the diversity of theories in mathematics education research. It introduces and systematizes a collection of case studies using different strategies and methods for networking theoretical approaches which all frame (qualitative) empirical research. The term ‘networking strategies’ is used to conceptualize those connecting strategies, which aim at reducing the number of unconnected theoretical approaches while respecting their specificity. The article starts with some clarifications on the character and role of theories in general, before proposing first steps towards a conceptual framework for networking strategies. Their application by different methods as well as their contribution to the development of theories in mathematics education are discussed with respect to the case studies in the ZDM-issue.     

Existence and approximation for a 3D model of thermally-induced phase transformations in shape-memory alloys

This note deals with a three–dimensional model for thermal stress–induced transformations in shape–memory materials. Microstructure, like twined martensites, is described mesoscopically by a vector of internal variables containing the volume fractions of each phase. The problem is formulated mathematically within the energetic framework of rate–independent processes. An existence result is proved and we study space–time discretizations and establish convergence of these approximations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)