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each stage of the shape- memory cycle (Fig. 3a). Once 
heated to the deformation temperature Treset, an external 
force is applied, resulting in a corresponding increase 
in stress. Upon reaching a strain εm, the sample is 
equilibrated for a specific holding time at constant 
strain, leading to initial stress relaxation. This position- 
controlled process is then switched to a stress- controlled 
process, in which the stress at the total deformation 
σm is maintained during cooling to Tlow. Finally, strain 
decreases as the external force is removed, providing 
a value for the fixed strain εu of the sample. After pro-
gramming, the sample is heated from Tlow to Treset, which 
causes recovery to the recovery strain εp. Ensuring the 
resistance of shape- memory materials to degradation 
during performance is vital for their application as 
functional devices. Plotting strain against time for multi-
ple cycles enables the assessment of the robustness of 
motion and gives information about the time depend-
ency of the change in shape of shape- memory materials 
(Fig. 3b), because any cycle- to-cycle strain shift would be 
clearly recognizable in this graph52.
The recovery process can take place under stress-free 
or constant- strain conditions (Fig. 3c,d). In a stress-free 
recovery process, the strain of the material is allowed 
to change during the shape recovery. By contrast, in 
a constant- strain condition, movement of the mate-
rial is limited to specific shape changes caused by the 
geometry of the specimen. The force exerted through 
macromolecular reorientation of the chain segments 
generates a recovery stress against the apparatus. 
A stress- free recovery enables the determination of 
the temperature at the highest recovery rate, that is, the 
inflexion point on the stress–temperature curve (Fig. 3c), 
called switching temperature TSW. Characteristic values, 
such as the recovery temperature range ΔTrec and the 
recovery rate νrec, can also be obtained from stress- free 
recovery testing. A constant- strain recovery process 
enables the determination of the maximum recovery- 
stress temperature Tσ,max and the inflexion point of the 
stress–temperature curve Tσ,inf (Fig. 3d).
These two recovery regimes provide complementary 
data. When comparing different types of polymeric 
shape- memory materials, only slight differences are 
observed between a physically crosslinked thermo-
plastic material and a covalently crosslinked polymer 
network during a stress- free recovery; however, in the 
constant- strain regime, the materials display substan-
tially different behaviour. At Tσ,max, the entropic elas-
ticity of the thermoplastic sample exactly balances the 
decrease in Young’s modulus of the softening material. In 
contrast to the covalently crosslinked polymer network, 
the increasing chain mobility of the physical netpoints 
becomes dominant beyond Tσ,max, driving a substantial 
decrease in stress.
Reversible shape- memory actuator. Similar to the 
one- way shape- memory effect, the programming pro-
cedure for a reversible shape- memory actuator contains 
deformation and fixation steps before the release of 
external stress (Fig. 4a). The deformation is performed at 
a temperature Treset above the melting transitions of the 
two crystalline domains. The fixation is performed by 
cooling to a temperature Tlow below the melting transi-
tions of the two crystalline domains. Heating and cool-
ing between a temperature Tsep, which bisects the two 
melting transitions, and Tlow causes a reversible change 
in shape of the sample. Multicyclic measurements are 
a b
d
c
e
Reversible shape-memory effect
Time (min)
T 
(°
C
)
ε (
%
)
60
40
20
0
100 600500400300200
Time (min)
40
20
30
100 600500400300200
Shape A
Shape A
T
sep
T
act,cool
T
act,heat
T
low
Shape B
Shape B
Programming
T
low
T
reset
T→
12
3
ε↑
σ
↑
σ
↑
T↑
Temperature (°C)
ε (
%
)
ε →
40
ε
m
20
30
0 20 40
σ = 0
T
act,cool
T
act,heat
T
low
T
reset
T
sep
60
1 2 3
T
low
T
reset
T
low
T
sep
T
low
T
low
T
sep
T
sep
From
 program
m
ing
Fig. 4 | Quantification of a reversible shape- memory effect. a | The stress 
(σ)–temperature (T )–strain (ε) graph is shown for the programming of a reversible shape- 
memory effect. The stages are the following: (1) deformation, (2) cooling and (3) release 
of external stress. Tlow is chosen to be beneath the melt transitions of the two crystalline 
domains; by cooling to this temperature under external stress, the shape- shifting 
pathway is defined. Treset is chosen to be above the melt transitions of the two crystalline 
domains; heating to this temperature allows the material to be deformed by the 
application of external stress. b | The reliability of actuation after programming is tested 
by performing repetitive heating to Tsep (separation temperature) and cooling to Tlow with 
ε = 0 MPa. Tsep is chosen to bisect the two crystalline domains; heating to this temperature 
before cooling generates reversible actuation. c | Schematic illustration of programming 
with subsequent actuation. A sample is first deformed at Treset (1) before undergoing 
cooling to Tlow while under external stress (2); the external stress is removed (3) before 
the temperature is cycled, and the corresponding change in strain is measured under an 
external stress- free condition. d | Schematic curve showing the actuation of a sample 
under stress- free conditions. This curve can be used to determine the highest actuation 
rate during heating Tact,heat and cooling Tact,cool. e | Recovery under different applied 
stresses is illustrated. Panels b and d are adapted with permission from reF.22, 
Wiley- VCH.
www.nature.com/natrevmats
R e v i e w s
	Reprogrammable recovery and actuation behaviour of shape-​memory polymers
	Characterization
	Reversible shape-​memory actuator. 
	Fig. 4 Quantification of a reversible shape-​memory effect.

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