Section 6: Material modelling in solid mechanics - GAMM 2012

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14 Section 6: Material modelling in solid mechanics [1] I. Carol and Z. Bažant, Damage and plasticity in microplane theory, Int. J. Sol. Struct. 34, 3807–3835 (1997) [2] S. Govindjee and G.J. Hall, A computational model for shape memory alloys, Int. J. Sol. Struct. 37, 735–760 (2000) [3] R. Ostwald, T. Bartel and A. Menzel, A computational micro-sphere model applied to the simulation of phase-transformations, J. Appl. Math. Mech. 90(7-8), 605–622 (2010) S6.6: Elasticity, Viscoelasticity, -plasticity I Wed, 13:30–15:30 Chair: Merab Svanadze, Daniel Balzani S1|01–A1 Thermoviscoplasticity deduced from enhanced rheological models Christoph Bröcker, Anton Matzenmiller (Universität Kassel) In the concept of rheological models, basic elements like springs (ideal elastic), dashpots (ideal viscous) or friction elements (ideal plastic) are assembed to networks for representing complex material behaviour [1]. In case of viscoelastic material models, the phenomenological constitutive equations are usually deduced directly from a rheological network. However, in the case of elastoplasticity, the rheological models are often used only to visualise the fundamental structure of the related material model. In the presentation, a new ideal body is defined for isotropic hardening besides minor modifications of some well–known basic elements from the literature [2, 3]. Hence, a rheological model of thermoviscoplasticity may be assembled with linear isotropic and kinematic hardening and nonlinear strain rate sensitivity. The related constitutive equations including the yield function and the flow rule are directly deduced from the kinematics and the stress equilibrium of the rheological network and results in a well–known model. By evaluating the dissipation inequality, the heat conduction equation is obtained with the dissipative power term, driven by plastic deformations. Moreover, nonlinear isotropic and kinematic hardening as well as an improved description of energy storage and dissipation are accomplished by introducing several additional dissipative strain elements into the viscoplastic arrangement of the rheological model [see also 4], which corresponds to a generalization of an ideal body already used in [2, 3]. Again, the constitutive equations may be deduced from the rheological network, its kinematics, and the stress equilibrium. For that purpose, however, the dissipation inequality has to be utilized. [1] M. Reiner, Rheologie in elementarer Darstellung, Carl Hanser Verlag, 1969. [2] A. Krawietz, Materialtheorie, Springer, 1986. [3] A. Lion, Constitutive modelling in finite thermoviscoplasticity: a physical approach based on nonlinear rheological models, Int. J. Plast. 16 (2000), 469–494. [4] A. Matzenmiller, C. Bröcker, Modelling and simulation of coupled thermoplastic and thermoviscous structuring and forming processes, In: Maier et al. (eds.): Functionally graded materials in industrial mass production, Verlag Wissenschaftliche Skripten, Auerbach, 2009, 235–250.
Section 6: Material modelling in solid mechanics 15 Steady vibrations problems in the theory of viscoelasticity for Kelvin-Voigt materials with voids Maia M. Svanadze (Universität Göttingen) Viscoelastic materials play an important role in many branches of engineering, technology and biomechanics. The modern theories of viscoelasticity and thermoviscoelasticity for materials with microstructure have been a subject of intensive study in recent years. Recently, the theory of thermoviscoelastic materials with voids is constructed by Iesan (2011). In this paper the linear theory of viscoelasticity for Kelvin-Voigt materials with voids is considered and the basic internal and external boundary value problems of steady vibrations are investigated. The formulae of integral representations of regular vectors are obtained. The single-layer, double-layer and volume potentials are constructed and their basic properties are established. The uniqueness and existence of regular solutions of the boundary value problems are proved by means of the potential method. Modelling of predeformation- and frequency-dependent material behavior of filled rubber under large predeformations superimposed with harmonic deformations of small amplitudes D. Wollscheid, A. Lion (Universität der Bundeswehr München) Viscoelastic materials show a frequency- and predeformation-dependent behavior under loadings that consist of large predeformations with superimposed harmonic deformations of small amplitudes. In order to consider this materialbehavior, some static and dynamic experiments are developed. Based on Haupt & Lion [1] and Lion, Retka & Rendek [2] we introduce a recently developed constitutive approach of finite viscoelasticity in the frequency domain that is able to describe the frequency- and predeformation-dependent materialbehavior with respect to storageand loss-modulus. The constitutive equations are evaluated in the frequency domain and geometrically linearized in the neighbourhood of the predeformation. Furthermore a formulation for incompressible material behavior is introduced and the corresponding dynamic modulus tensors are derived. Besides constitutive modelling and experiments, parameter identification and some numerical simulations are presented. [1] P. Haupt, A. Lion, On finite linear viscoelasticity of incompressible isotropic materials, Acta Mechanica 159 (2002), 87 – 124. [2] A. Lion, J.Retka, M.Rendek On the calculation of predeformation-dependent dynamic modulus tensors in finite nonlinear viscoelasticity, Mechanics Research Communications 36 (2009), 653 – 658. A multi-scale modelling approach for bituminous asphalt Thorsten Schüler, Ralf Jänicke, Holger Steeb (Universität Bochum) Bituminous asphalt is a standard material e.g. in road constructions. However, the term asphalt involves an extremly broad class of complex multi-scale and multi-phase materials. Typically, asphalt consists of a mineral filler (e.g. crushed rock), a bituminous binding agent (possibly including further additive compounds) and pores. The various constituents are to be adapted for the particular application. Nowadays, requirements on noise reduction of road constructions become more and more important. In our ongoing research activities, we focus on the solid-borne acoustic properties of the
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