Section 6: Material modelling in solid mechanics - GAMM 2012

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.