Carbon Fibre Prepregs: Simulation of a Thermo-Mechanical-Chemical Coupled Problem

In automotive industry research is done to replace high strength steel by combinations of steel and carbon-fibre prepregs (pre-impregnated fibres). It is planned to form both steel and uncured prepregs in one step followed by the curing process under pressure in the forming die. The ability to simulate the mechanical behaviour during forming and curing would allow more economical processes. The simulation of prepregs must regard highly anisotropic, viscoelastic and thermal- chemical properties. For this the model is split into an anisotropic elastic part, which represents the fibre fraction and an isotropic, viscoelastic part, representing the matrix. This part also contains curing, causing a dependency on time and temperature. During deep-drawing large deformations are occurring, so a large strain model regarding anisotropy, viscoelasticity and curing has been developed. Also experiments were made to validate this model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

Simulation of Deep Drawing of Carbon Fibre Prepregs

The simulation of prepregs must regard highly anisotropic, viscoelastic and thermal-chemical properties. To this end a constitutive model is split into an anisotropic elastic part, which represents the fibre fraction and an isotropic, viscoelastic part, representing the matrix. The second part also contains curing, causing a dependency on time and temperature. During real deep-drawing processes large deformations up to 50 % occur, which is considered in a formulation at large strains. This model contains an anisotropic elastic part based on a Neo-Hooke law enhanced by an anisotropic part. A viscoelastic part is added using Hencky-strains and the work-conjugate Hill-stress to transfer a model for small strains into large strains. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multifibre polymer composites: Prediction of deformation and thermophysical properties

Conclusions A theoretical and experimental investigation was carried out to examine the possibilities of a structural approach for prediction of elastic constants, creep functions and thermophysical characteristics of hybrid polymer composites reinforced with anisotropic fibres of several types. The theoretical solutions were obtained by generalizing the self-consistent method for the case of a three phase model. The effects of brittle fibre breakdown under tension in the direction of reinforcement of a unidirectional hybrid composite were studied under conditions of a short-term loading and a long-term creep. It has been shown that a creep of viscoelastic fibres plays a principal role in creep of the hybrid composite. It is just this creep that significantly increases the fibre damage during creep of the composite.A variant of the solution has been proposed for predicting the thermorheologically complex behavior of hybrid composites containing not only elastic but also viscoelastic thermorheologically simple components with different temperature-time shift factors. The peculiarities of thermal expansion of hybrid composites and the possibilities for a purposeful control of thermal expansion coefficients by hybridization were studied. The considered thermal interval included a region of transition of the polymer matrix from a glass state into a viscoelastic one.The control tests were performed for specimens of organic/glass, organic/carbon, glass/carbon and organic/boron polymer composites with different ratios of fibre volume contents. On the whole, the obtained accuracy of predicting the characteristics of the examined hybrid composites may be considered as acceptable for engineering applications.Published in Mekhanika Kompozitnykh Materialov, Vol. 30, No. 3, pp. 299–313, May–June, 1994.     

Interface cracks in anisotropic composites

The linear model equations of elasticity often give rise to oscillatory solutions in some vicinity of interface crack fronts. In this paper we apply the Wiener–Hopf method which yields the asymptotic behaviour of the elastic fields and, in addition, criteria to prevent oscillatory solutions. The exponents of the asymptotic expansions are found as eigenvalues of the symbol of corresponding boundary pseudodifferential equations. The method works for three‐dimensional anisotropic bodies and we demonstrate it for the example of two anisotropic bodies, one of which is bounded and the other one is its exterior complement. The common boundary is a smooth surface. On one part of this surface, called the interface, the bodies are bonded, while on the complementary part there is a crack. By applying the potential method, the problem is reduced to an equivalent system of Boundary Pseudodifferential Equations (BPE) on the interface with the stress vector as the unknown. The BPEs are defined via Poincaré–Steklov operators. We prove the unique solvability of these BPEs and obtain the full asymptotic expansion of the solution near the crack front. As a special case we consider the interface crack between two different isotropic materials and derive an explicit criterion which prevents oscillatory solutions. Copyright © 1999 John Wiley & Sons, Ltd.     

Simulating of a pressing process of a viscoelastic polymer melt

A well known and often used method to obtain anisotropic polymer films is the so-called pressing process. Here, films are squeezed under high temperatures, pressure and deformation rates. To simulate such a process, the polymeric matrix is treated as a non-Newtonian, viscoelastic melt. The modeling of such melts is done with the anisotropic molecule movement tensor generalization of the Maxwell Model for high deformation rates. The viscoelastic flow simulations are done with DEVSS stabilization techniques and an ALE based dynamic mesh Method. In this work we present simulations in order to show the difference between classical approaches using a generalized Newtonian viscosity to model the melt and the used viscoelastic models. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Crank–Nicolson collocation spectral method for the two‐dimensional viscoelastic wave equation

In this paper, we first establish the Crank–Nicolson collocation spectral (CNCS) method for two‐dimensional (2D) viscoelastic wave equation by means of the Chebyshev polynomials. And then, we analyze the existence, uniqueness, stability, and convergence of the CNCS solutions. Finally, we use some numerical experiments to verify the correctness of theoretical analysis. This implies that the CNCS model is very effective for solving the 2D viscoelastic wave equations.     

Asymptotic behaviour for a two‐dimensional thermoelastic model

In this paper we study a thermoelastic material with an internal structure which binds the materials fibres to a quadratic behaviour. Moreover, a hereditary constitutive law for heat flux is supposed. We prove results of asymptotic stability and exponential decay for the evolution problem in two‐dimensional space domain. Copyright © 2006 John Wiley & Sons, Ltd.     

Anisotropic moisture depending viscoelastic material model for wood

A moisture depending anisotropic viscoelastic material model is presented in this paper. The necessity of consideration cylindrical anisotropy is caused by the growing process. Wood exhibits different creep characteristics depending on the state of stress. Therefore, the consideration of anisotropic viscoelasticity is required. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analytical modelling of the in-plane compressive behaviour of pile fibres in Spacer Fabric Composites

The mechanical behaviour of Spacer Fabric Composites (SFC) is highly influenced by their pile fibres. Within this work, the in-plane compressive behaviour of pile fibres in SFC is investigated. An analytical model is developed based on rigid hinged struts. Therefore, a representative part of the continuous fibre is chosen. The bending behaviour and the interaction of the pile fibre with facesheet fibres is modelled using rotational and extension springs respectively. The system proposed is fully defined by three generalized coordinates. The total potential energy of the system is determined and used to obtain information about the deformation behaviour. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Linear elliptic equations in composite media with anisotropic fibres

Linear elliptic equations in composite media with anisotropic fibres are concerned. The media consist of a periodic set of anisotropic fibres with low conductivity, included in a connected matrix with high conductivity. Inside the anisotropic fibres, the conductivity in the longitudinal direction is relatively high compared with that in the transverse directions. The coefficients of the elliptic equations depend on the conductivity. This work is to derive the Hölder and the gradient $L^p$ estimates (uniformly in the period size of the set of anisotropic fibres as well as in the conductivity ratio of the fibres in the transverse directions to the connected matrix) for the solutions of the elliptic equations. Furthermore, it is shown that, inside the fibres, the solutions have higher regularity along the fibres than in the transverse directions.     

基于Kelvin-Voigt模型的粘弹性波动力学的本征化理论

利用固体力学本征化理论,研究了具有Kelvin-Voigt粘弹性质的各向异性固体的本征特性,并由此得到了各向异性粘弹性波动力学的广义Stokes方程,展现了波动过程的立体图像．讨论了几类常见各向异性固体的粘弹性波动规律,给出了一些新的结论．     

Electro–Reaction–Diffusion Systems Including Cluster Reactions of Higher Order

In this paper we consider electro–reaction–diffusion systems modelling the transport of charged species in two–dimensional heterostructures. Our aim is to investigate the case that besides of reactions with source terms of at most second order so called cluster reactions of higher order are involved. We prove the unique solvability of the model equations and show the global boundedness and asymptotic properties of the solution. In order to get necessary a priori estimates we apply an anisotropic iteration scheme followed by usual Moser iterations. Then existence is obtained by cutting off the reaction terms.     

Eigen‐frequencies in thin elastic 3‐D domains and Reissner–Mindlin plate models

The eigen‐frequencies of elastic three‐dimensional thin plates are addressed and compared to the eigen‐frequencies of two‐dimensional Reissner–Mindlin plate models obtained by dimension reduction. The qualitative mathematical analysis is supported by quantitative numerical data obtained by the p‐version finite element method. The mathematical analysis establishes an asymptotic expansion for the eigen‐frequencies in power series of the thickness parameter. Such results are new for orthotropic materials and for the Reissner–Mindlin model. The 3‐D and R–M asymptotics have a common first term but differ in their second terms. Numerical experiments for clamped plates show that for isotropic materials and relatively thin plates the Reissner–Mindlin eigen‐frequencies provide a good approximation to the three‐dimensional eigen‐frequencies. However, for some anisotropic materials this is no longer the case, and relative errors of the order of 30 per cent are obtained even for relatively thin plates. Moreover, we showed that no shear correction factor is known to be optimal in the sense that it provides the best approximation of the R–M eigen‐frequencies to their 3‐D counterparts uniformly (for all relevant thicknesses range). Copyright © 2002 John Wiley & Sons, Ltd.     

Mathematical analysis of a viscoelastic problem with temperature‐dependent coefficients—Part I: Existence and uniqueness

The aim of this article is to study the quasistatic evolution of a thermoviscoelastic problem whose behaviour law is of the Maxwell–Norton type with coefficients depending on temperature. In this law, the deformation rate tensor is a superposition of viscoelastic and thermal contributions. The existence and uniqueness of the solution is proved. Copyright © 2007 John Wiley & Sons, Ltd.     

An anisotropic viscoelastic model for collagenous soft tissues at large strains – Computational aspects

This paper focusses on computational aspects related to a recently proposed anisotropic viscoelastic model for soft biological tissues at large strains [1]. A key aspect of this model is the generalisation of micromechanically motivated one-dimensional constitutive equations to three dimensions by numerical integration over the unit sphere. A strong effect of this procedure on the accuracy and in particular on the material symmetry of the model is observed. Finally a finite element example of an artery subject to normotensive blood pressure is presented. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the deformability of anisotropic viscoelastic bodies in the presence of thermodiffusion

We give the results of theoretical studies directed toward the development of model pictures of the strain process of anisotropic viscoelastic multicomponent solid solutions taking account of the processes of heat conduction and diffusion of matter. We write a complete system of equations of the model and boundary conditions. We analyze the stressed state in a viscoelastic cylinder in diffusion saturation. Translated fromMatematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 1, 1998, pp. 78–89.     

Study of the biomechanical behaviour of structurally stable/unstable motion segments of the sheep spine

The effects of damage of intervertebral discs on their biomechanical behaviour and the factors favouring the progression of instability are studied. Healthy and damaged movement segments are analyzed experimentally and numerically. The aim is to represent and predict the effects of tissue damage and changes in the spine by comparison with healthy segments. Since the intervertebral disc acts as a mechanical damper, relaxation tests are performed in addition to pressure experiments. The experiments are carried out in a bioreactor with tempered nutrient solution. A cultivation period in the bioreactor allows detecting cell viability, solute diffusion rates and gene expression of the discs. Numerically, the nonlinear, viscoelastic, anisotropic and diffusion-dependent behaviour of the intervertebral disc is modelled with the FE-program Abaqus, using a modular material law as a UMAT subroutine. With the measurement results, the relevant parameters can be determined so that the mechanical behaviour of intervertebral discs can be simulated. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)