Modelling the interaction between athlete and sports surfaces

Sports surfaces are often seen as one possible factor for sports injuries as the vertical ground reaction force (VGRF) depends not only on the athlete's movement but also on the mechanical properties of the ground. Therefore, the athlete-surface-interaction has to be analysed in order to minimize the loading on the athlete. The aim of this work is to understand the behaviour during landing and the associated impact forces during ground contact. Thus a simplified mechanical model is presented. Results for feasible surface material parameters are identified. A first assumption of the effect of the VGRF is presented. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three-dimensional reconstruction of M. gastrocnemius contraction

There exist many different approaches investigating the contraction mechanisms of skeletal muscles. Thereby, the mechanical behavior, such as force generation in association with kinematic and microstructure, play an important role in modeling of muscle behavior. Besides the mechanical behaviour, the validation of muscle models requires the geometrical environment, too. The geometry of a muscle can be divided into macrostructure, existing of aponeurosis-tendon-complex (ATC) and muscle tissue (MT), as well as the fascicle architecture, representing the microstructure of the MT. In this study, the macrostructure of the isolated M. gastrocnemius was observed during isometric contraction by using three-dimensional optical measurement systems in combination with mechanical measurement techniques. The surface deformation was reconstructed at specific force and length relationships and further the muscle tissue, aponeurosis, and tendon were distinguished, building up a macroscopic geometrical dataset. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental and numerical investigation of a degradable collagen foil

A collagen foil, which plays an important role for cultivating and investigating tendon cells, is investigated experimentally and numerically: The foil, which should later serve as a scaffold for tendon cells in a custom made bioreactor, is stimulated periodically in an in situ experiment. Additionally, a material model to describe the anisotropic structure and the relaxation behaviour of the collagen foil is used to simulate the material response. By comparing the measurements and simulations, the stress and strain states in the foil can be determined. Hence, the material parameters for the presented experimental set up are identified. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Representation of the linear viscoelastic behaviour of wood with a constitutive theory based on fractional time derivatives

Like many other materials used in mechanical and civil engineering, wood shows a pronounced history-dependent mechanical material behaviour. Due to its anisotropy its rheological behaviour is strongly dependent on the direction. In this research project, the material behaviour is represented with a phenomenological theory of anisotropic fractional viscoelasticity. In order to identify the material functions and parameters, the time-dependent creep compliances are measured in three orthogonal directions under tension and shear. As a result of the developed constitutive approach, the experimentally observed creep data is described by several power functions. In the second part of the presentation, some differences between classical models of viscoelasticity which are based on Kelvin-Voigt or Maxwell elements and the fractional approach are presented. The assets and drawbacks with respect to wood are discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical modelling of twin helical spring under tensile loading

This paper presents a 3D geometric modelling of a twin helical spring and its finite element analysis to study the spring mechanical behaviour under tensile axial loading. The spiralled shape graphic design is achieved through the use of Computer Aided Design (CAD) tools, of which a finite element model is generated. Thus, a 3D 18-dof pentaedric elements are employed to discretise the complex “wired-shape” of the spring, allowing the analysis of the mechanical response of the twin spiralled helical spring under an axial load. The study provides a clear match between the evolution of the theoretical and the numerical tensile and compression normal stresses, being of sinusoidal behaviour. The overall equivalent stress isovalues increases radially from 0° to 180°, being maximal on the internal radial zone at the section 180°. On the other hand, the minimum stress level is located in the centre of the filament cross section.     

Cellular rubber: Dependency between relaxation time and pretreatment

In this contribution we investigate experimentally a porous carbon-filled rubber. The main focus is on the dependency of the mechanical behaviour using different pretreatments. Therfore, cyclic tests and relaxation tests with different pretreatment are performed. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

MULTISCALE FINITE ELEMENT METHOD FOR SUBDIVIDED PERIODIC ELASTIC STRUCTURES OF COMPOSITE MATERIALS

1. IntroductionFor a kind of elastic structures of composite materials of which the geometric and physicalparameters are of some periodicity3 e.g. ) common laminated plate and shell, and fibre reinforced,particle reinforced, and woved composite materials and so forth, we can regard them as theperiodic structures with a unit cell.Generally speaking, it is extremely difficult to compute directly the above elastic structuresby using usual FEM, due to the complicated geometric configurations and …     

Effects of active muscle contraction on whiplash injury

The objective of this work is to develop a finite element model of active human skeletal muscle, which can mimic its contraction behaviour. The model is then used to analyse the effects of active muscle contraction into occupant kinematics and injuries during rear-end collision. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mechanical Synchronization in Dual-Rotor Vibroactuator

In the present work the mechanical behaviour of a dual-rotor vibrotactor has been investigated with special attention to its stationary motions and their linear stability. After the introduction of the used mechanical model, the formulae for the stationary motions are given, and characteristic stablity charts are presented. The linear stability is investigated for uncontrolled and controlled system as well. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structural hierarchies and interactions in the tendon composite

Tendon functions by transmitting tensile loads from muscle to bone. Morphologically, it can be described as a macromolecular multicomposite material, basically consisting of collagen fibrils held together by a soft, hydrated matrix material. Recently, tendon has been deformed beyond the "in vivo" elastic limit and by cyclical loading systematically damaged. Using high-resolution electron microscopy, decomposition of the collagen fibril into subfibrils (15 nm diameter) and microfibrils (3.5 nm diameter) has been noted. The interfacial adhesion between such units is strongly dependent on age, and is probably related with crosslinking phenomena observed by biochemical methods. In addition, tendon collagen contains a considerable amount of water throughout the entire structure which strongly affects its overall mechanical behavior. The various bound states of water have been identified using primarily dynamic mechanical spectroscopy coupled with more conventional methods of structural characterization.Published in Mekhanika Polimerov, No. 4, pp. 693–701, July–August, 1976.     

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)     

Numerical simulation of flow of viscoelastic fluids

The paper deals with the numerical calculation of highly viscous, non-newtonian fluid flows in apparatus of mechanical engineering. We use a differential constitutive equation to approximate the real behaviour of technical fluids like polymer melts. By means of calculated flow examples in two and three dimensional geometries we demonstrate the influence of the non-newtonian behaviour. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Asymptotic study of the macroscopic behaviour of a solid-fluid mixture

In the framework of homogenization theory we study a mixture of an elastic solid and a viscous compressible fluid with periodic structure and its limit behaviour as the period tends to zero Existence, uniqueness and convergence theorems are given. The limit behaviour is viscoelastic.     

Stability and Asymptotic Behaviour for the Numerical Solution of a Reaction--Diffusion Model for a Deterministic Diffusive Epidemic

The aim of this paper is to outline the numerical solution ofa reaction—diffusion system describing the evolution ofan epidemic in an isolated habitat. The model we consider isdescribed by two weakly coupled semi-linear parabolic equationsand we introduce a finite difference scheme for its numericalsolution. We study the behaviour of the exact solution by meansof the numerical scheme. We show the positivity, the decreaseand the decay to extinction of the numerical solution. Finallywe report the results of the numerical tests; in these simulationswe observe that the asymptotic behaviour of the reaction-diffusionsystem is the same as that of the associated ODE system (Kermack—McKendrickmodel).     

Modeling of deformation and failure in rubber-toughened polymers – effect of distributed crazing

A continuum mechanical model for rubber-toughened polymers undergoing inelastic deformation solely by distributed crazing is introduced. Scaling relations with regard to microstructural parameters are derived analytically from a simple unit cell model. The constitutive model is calibrated from experimental data for a commercial ABS material and well captures various aspects of its deformation and failure behaviour. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Revisiting the heat kernel on isotropic and nonisotropic Heisenberg groups*

The aim of this paper is threefold. First, we obtain the precise bounds for the heat kernel on isotropic Heisenberg groups by using well-known results in the three-dimensional case. Second, we study the asymptotic estimates at infinity for the heat kernel on nonisotropic Heisenberg groups. As a consequence, we give uniform upper and lower estimates of the heat kernel, and complete its short-time behavior obtained by Beals–Gaveau–Greiner. Third, we prove that the uniform asymptotic behaviour at infinity (so the small-time asymptotic behaviour) of the heat kernel for Grushin operators, obtained by the first author, are still valid in two and three dimensions.     

Asymptotic analysis in flow curves for a model of soft glassy fluids

In this article, we rigourously prove several asymptotical results for the flow curves of the Hébraud–Lequeux model, a rheological model which describes the behaviour of soft glassy fluids. This model has a control parameter α which governs the behaviour of the fluid at low shear rate. More precisely, we consider t([(g)\dot]){\tau({\dot{\rm \gamma}})} the stress in a block that is sheared at a constant rate [(g)\dot]{{\dot{\rm \gamma}}} and we prove that the system exhibits a transition in its behaviour at low shear rate when α goes through a critical value. The study is complicated by the fact that one of the parameter is only given implicitly and also we have to study two variable function in the neighbourhood of singularities.     

Dirichlet forms on fractals: Poincaré constant and resistance

Summary We study Dirichlet forms associated with random walks on fractal-like finite grahs. We consider related Poincaré constants and resistance, and study their asymptotic behaviour. We construct a Markov semi-group on fractals as a subsequence of random walks, and study its properties. Finally we construct self-similar diffusion processes on fractals which have a certain recurrence property and plenty of symmetries.Partly supported by the JSPS Program