Section 6: Material modelling in solid mechanics - GAMM 2012

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.