Universal relations in linear thermoelastic theories of thermally-responsive shape memory polymers
R. Kazakeviciute-Makovska, M. Heuchel, K. Kratz, H. Steeb,
Volume: 82. Pages: 140--158
DOI: 10.1016/j.ijengsci.2014.05.009
Published: 2014
Abstract
Abstract In this paper we formulate a one-dimensional linear thermo-elastic
(LTE) model in integral form for describing the behavior of thermally-responsive
shape memory polymers (SMPs), which unifies and slightly generalizes
numerous theories proposed in the literature starting with the seminal
approach proposed by Liu et al. (2006). The presented model in its
most general form requires the calibration of three response functions.
Detailed analysis of four types of shape memory cycles (SMCs) used
to quantify the shape memory effect in thermally-responsive \{SMPs\}
and the corresponding forms of constitutive relations derived within
\{LTE\} model display a number of critical properties. In particular,
two of three response functions may be determined in many different
ways from strain and stress storage/recovery profiles measured in
\{SMCs\} (the third response function may be determined from an independent
test). As implication of this fact, we show that the \{LTE\} model
predicts a number of inter-relations between the measured strain
and stress storage/recovery profiles. All these relations are universal
in the sense that for any shape memory polymer, which may be correctly
described by \{LTE\} model, the strain/stress storage/recovery profiles
measured in \{SMCs\} must satisfy (at least approximately) these
relations. Their role within the \{LTE\} model is analogous to the
role of universal relations in the theory of finite deformation elasticity.
In particular, these universal relationships provide a theoretical
basis for the validation of any model within the \{LTE\} class. The
basic theoretical results derived in this paper are illustrated using
data obtained by Liu et al. (2006).