Section 6: Material modelling in solid mechanics - GAMM 2012

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4 Section 6: Material modelling in solid mechanics when the deformation is constant in time. The constitutive relations for the stress tensor and the internal variables are deduced using the Clausius-Duhem inequality. In order to sketch the main properties of the model, expressions in closed form are derived with respect to continuous and intermittent relaxation tests as well as for the compression set test. Under the assumption of near incompressible material behaviour, the theory can also represent ageing-induced changes in volume and their effect on the stress relaxation. The simulations are in accordance with experimental data from literature. [1] A. Lion, M. Johlitz, On the representation of chemical ageing of rubber in continuum mechanics, International Journal of Solids and Structures, under review. Multi-phase modeling of shape memory polymers Nico Hempel, Markus Böl (TU Braunschweig) Shape memory polymers are a highly versatile class of so-called smart materials. They are able to store a certain state of deformation and remember another one by means of an external stimulus such as light or temperature. Usually, the physical mechanism responsible for this behavior is a temperature-dependent phase transition between an “active”, entropy-elastic phase and a “frozen”, energy-elastic phase. As polymers are usually capable of experiencing large deformations, models are required which are able to represent both the phase transitions and states of large deformation. In the present work, we propose a model based on the idea of the multiplicative decomposition of the deformation gradient. Evolution equations for the several deformation components are presented that provide for the storage of the entropy-elastic strain and its recovery during the transition between the frozen phase and the active phase. First characteristic shape memory cycles will be presented as a last point. On response functions in linear thermoelastic models of shape memory polymers Aycan Özlem Aydin, Rasa Kazakevičiute-Makovska , Holger Steeb (Universität Bochum) There are two basic classes of constitutive models for thermoresponsive Shape Memory Polymers (SMPs), rheological and thermoelastic models. In this work, we present a detailed analysis of linear thermoelastic models. The first model within this class has been proposed by Liu et al. [1] and in the following years numerous modifications of that model have been presented (cf. e.g. [2]). All these models have a common mathematical structure with three basic response functions. Different models developed within this concept follow from the general theory by specifications of the relevant response functions. The general mathematical form of the response functions is discussed and an experimental methodology determining of response functions directly from experimental data is presented. Representative examples illustrate the quality and the efficiency of the proposed methodology. It is shown that a reliable evaluation of thermoelastic models for SMPs requires a comparison with data for all four steps of the termomechanical cycle, both under strain- and stress controlled conditions. [1] Y. Liu, K. Gall, M. L. Dunn, A. R. Greenberg, J. Diani, Thermomechanics of shape memory polymers: Uniaxial experiments and constitutive modeling, Int. J. Plasticity, vol. 22, pp. 279-313, 2006. [2] R. Kazakevičiute-Makovska, H. Steeb, A. Özlem Aydın, On the evolution law for the frozen fraction in the linear theories of shape memory polymers, Arch. App. Mech., in press, 2011.
Section 6: Material modelling in solid mechanics 5 Modeling the finite strain deformation and initial anisotropy of amorphous thermoplastic polymers Philipp Hempel, Thomas Seelig (KIT) The present work deals with modeling the temperature dependent finite strain deformation behavior of amorphous thermoplastic polymers incorporating the effect of an initial anisotropy. The anisotropy prevails in form of a frozen-in pre-orientation of molecular chains and results from preceding manufacturing processes (e.g. injection molding) at elevated temperatures and subsequent rapid cooling. The initial molecular orientation affects the mechanical response in terms of flow strength and hardening. The standard finite strain kinematics with a multiplicative split of the deformation gradient into an elastic and plastic part is modified by introducing a network deformation gradient which comprises the actual plastic deformation and the initial (processing induced) pre-deformation [1],[2]. As a computational example, an injection molded plate is investigated which displays nonuniform shrinkage and buckling during heating due to the action of the frozen-in network stress. The spatial distribution of molecular pre-orientation, and hence initial anisotropy, in the FE model is estimated from optical birefringence. [1] E.M. Arruda, M.C. Boyce, Evolution of plastic anisotropy in amorphous polymers during finite straining, International Journal of Plasticity (1993), 6 –697. [2] M.C. Boyce, D.M. Parks, A.S. Argon, Plastic flow in oriented glassy polymers, International Journal of Plasticity (1998), 6 – 593. Modeling of induced anisotropy at large deformations for polymers Ismail Caylak, Rolf Mahnken (Universität Paderborn) In this presentation we develop a model to describe the induced plasticity of polymers at large deformations. Polymers such as stretch films exhibit a pronounced strength in the loading direction. The undeformed state of the films is isotropic, whereas after the uni-axial loading the material becomes anisotropic. In order to consider this induced ansiotropy during the stretch process, a spectral decomposition of the inelastic Cauchy-Green tensor is done. Therefore, the yield function can be formulated as a function of the anisotropic tensor, where again the anisotropic tensor is a function of the maximum eigenvalue. A backward Euler scheme is used for updating the evolution equations, and the algorithmic tangent operator is derived. The numerical implementation of the resulting set of constitutive equations is used in a finite element program and for parameter identification. S6.3: Microstructures in Elasto-Plasticity II Tue, 16:00–18:00 Chair: Dennis Kochmann, Sebastian Heinz S1|01–A03 Microstructure development in a Cosserat continuum as a consequence of energy relaxation Muhammad Sabeel Khan, Klaus Hackl (Universität Bochum) A rate-independent inelastic material model for a Cosserat continuum is presented. The free energy of the material is enriched with an interaction potential taking into account the intergranular
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