Section 6: Material modelling in solid mechanics - GAMM 2012

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20 Section 6: Material modelling in solid mechanics equation (two-point boundary-value problem) is obtained. Experimental characterization of the viscoelastic behaviour of discontinuous glass fibre reinforced thermoplastics B. Brylka, T. Böhlke (KIT) In automotive applications short and long glass fibre reinforced thermoplastics are commonly used for non-structural parts. Due the versatile possibilities of manufacturing, forming, joining and recycling, thermoplastic matrix based composites are increasingly used also for semi-structural parts. Thermoplastics like e.g. polypropylene show a high temperature and strain-rate dependency, especially in the temperature and strain-rate ranges which are relevant for automotive applications. Additionally, the non-linear influence of the viscoelastic behaviour of the matrix material on the effective material behaviour of the composite is of high interest. The dynamic mechanical analysis (DMA) technique is an effective method to investigate the elastic and viscoelastic stiffness response of materials under cyclic loading. After a short introduction into the DMA technique, experimental results for a polypropylene and polypropylene based composite material will be presented. The composite under consideration is an discontinuous glass fibre reinforced polypropylene. In the manufacturing process, which is commonly compression or injection moulding, the flow of the mould induces an heterogeneous and anisotropic distribution of fibre orientations. Therefore, the effective properties as well as the temperature and strain-rate dependency has been investigated taking into account an anisotropic material behaviour. The comparison of the elastic and viscoelastic material response of the matrix and the composite will be discussed in detail. Additionally, a parameter identification for common viscoelastic material models will be presented. [1] Middendorf, P.: Viskoelastisches Verhalten von Polymersystemen, Fortschritt-Berichte VDI, Reihe 5, VDI Verlag (2002). [2] Deng, S., Hou, M., Ye, L.: Temperature-dependent elastic moduli of epoxies measured by DMA and their correlations to mechanical testing data, Polym. Test., 26, 803-813 (2007). [3] Schledjewski, R., Karger-Kocsis, J.: Dynamic mechanical analysis of glass mat-reinforced polypropylene (GMT-PP), J. Thermoplast. Compos., 7, 270-277 (1994). A solid-shell finite element for fibre reinforced composites J.-W. Simon, B. Stier, S. Reese (RWTH Aachen) Fibre reinforced composites are typically characterized by high Young’s modulus at low density, which makes them very attractive for lightweight constructions. The fibre composites considered here consist of several layers, each of which is composed of a woven fabric embedded in a matrix material. This structure makes the constitutive behavior of fibre composites anisotropic. Moreover, it is generally highly nonlinear, and the materials’ response in tension and compression can differ significantly. In order to describe this rather complex behavior, we use a modification of a micromechanically motivated model proposed by Reese [1]. Therein, an anisotropic model has been presented for the hyperelastic material behavior of membranes reinforced with roven-woven fibres, which is particularly suitable for the present fibre reinforced composites. The use of a fully three-dimensional material model strongly suggests using solid elements. On the other hand, fibre composites are mostly applied in thin shell-like structures, where shell
Section 6: Material modelling in solid mechanics 21 elements should usually be preferred. Therefore, we use a solid-shell element presented by Schwarze and Reese [2] which combines the advantages of both solid elements and shell elements at the same time. This element allows for displaying realistically the three-dimensional geometry while still providing the suitable shape for thin structures. In addition, the present solid-shell formulation utilizes a reduced integration scheme within the shell plane using one integration point, whereas a full integration is used in thickness direction. Thus, an arbitrary number of integration points can be chosen over the shell thickness. Thereby, different fibre orientations of the layers can be taken into account easily, since the material parameters can be defined for each integration point separately. Moreover, the proposed solid-shell formulation removes all potential locking phenomena. In particular, volumetric locking in case of (nearly) incompressible materials as well as Poisson thickness locking in bending problems of shell-like structures are eliminated by use of the enhanced assumed strain (EAS) concept. In addition, to cure the transverse shear locking which is present in standard eight-node hexahedral elements, the assumed natural strain (ANS) method is applied. [1] S. Reese. A micromechanically motivated material model for the thermo-viscoelastic material behaviour of rubber-like polymers, Int J Plast, 19, 909–940, 2003. [2] M. Schwarze, S. Reese. A reduced integration solid-shell finite element based on the EAS and the ANS concept - large deformation problems, Int J Numer Methods Engng, 85, 289–329, 2011. On consistent tangent operator derivation and comparative study of rubber-like material models at finite strains Mokarram Hossain, Paul Steinmann (Universität Erlangen-Nürnberg) The overall micro-structure of rubber-like materials can be idealized by chain-like macromolecules which are connected to each other at certain points via entanglements or cross-links. Such special structure leads to a completely random three-dimensional network [2,3]. To model the mechanical behaviour of such randomly-oriented micro-structure, several phenomenological and micro-mechanically motivated network models for nearly incompressible hyperelastic polymeric materials have been proposed in the literature. To implement these models for polymeric material (undoubtedly with widespread engineering applications) in finite element method, one would require two important ingredients, e.g. the stress tensor and the consistent fourth-order tangent operator where the latter is the result of linearization of the former. In this contribution, an extensive overview on several hyperelastic rubber-like material models has been presented. Special focus is given particularly to derive the accurate stress tensors and tangent operators which yield quadratic convergence when the governing nonlinear equations for a boundary value problem are solved by the Newton-like iterative schemes. A simple but efficient algorithm will be demonstrated to testify the correctness of the tangent operator locally of a particular model without going into details of the finite element implementation [1]. [1] Steinmann P, Hossain M, Possart G (2011), Hyperelastic models for rubber-like materials: Consistent tangent operators and suitability for Treloar’s data. Archive of Applied Mechanics, In review (2011) [2] Boyce MC, Arruda EM (2000), Constitutive models of rubber elasticity: a review. Rubber Chemistry and Technology, 73: 504-523, 2000
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