20
2 Literature Review
2.6 Modeling of Piezo-Fiber Composite Bonded Structures
2.6.1 Types of Piezo Fiber Composite Materials
Is is known that piezoelectric ceramics are brittle and piezoelectric polymers are with
weak actuation forces. To overcome the limitations of conventional piezoelectric
materials, piezoelectric fiber based composites were invented through mixture of
piezoceramic fibrous phase and epoxy matrix phase.
The first type of piezo-fiber based composite material was proposed by Skinner et
al. [215], known as 1-3 composite. In the type of 1-3 composite, the piezoelectric
fibers with rectangular or circular cross section place along in the thickness direction.
Due to the piezoelectric fiber orientation, this type of piezo composite still has weak
actuation forces along the in-plane directions.
Placing the piezoelectric fiber with circular cross section along the in-plane direction, one obtains an active fiber composite (AFC), initially invented by MIT [216,
217]. Because of the circular cross section, a certain electric field volume is invalid
for the actuation performance. Replacing the circular cross section with rectangular
cross section, yields a macro-fiber composite (MFC), which was invented by NASA
Langley Research Center [218]. The MFC piezoelectric composites have no loss on
electric field, resulting in large actuation forces. For more details of MFC piezoelectric composites, it refers to Williams et al. [219], Sodano et al. [220], Bowen et
al. [221]. Since MFC has many beneficial properties, many applications for vibration
control [222, 223] and health monitoring [224–226] were investigated.
2.6.2 Homogenization of Piezo Fiber Composite
The structures of fiber based piezoelectric composite are complicated. For easy
implementation in simulations, piezoelectric composites are usually homogenized
to orthotropic materials, by experimental and numerical investigations. MFCs have
large application potentials due to their beneficial properties. Therefore, most of
the studies were dealing with the homogenization of MFC materials. Williams et
al. [227], Williams [228] obtained the basic elasticity constants of MFC patches for
the elastic and plastic constitutive behavior through experimental investigations. Linear piezoelectric composite material properties were predicted by using classical lamination theory [229], representative volume element (RVE) technique with mixing
rules [230–232], and asymptotic expansion homogenization (AEH) method [233].
More precisely, an electroelastic nonlinear material constitutive equations was developed by Williams et al. [234] for MFC patches. In addition, hysteresis and creep
effects were studies experimentally by Schröck et al. [235] for dynamic performance
of MFC integrated structures. For achieving complete material parameters, including
not only the elastic constants but also the transverse shear moduli and the piezoelectric
2 Literature Review
2.6 Modeling of Piezo-Fiber Composite Bonded Structures
2.6.1 Types of Piezo Fiber Composite Materials
Is is known that piezoelectric ceramics are brittle and piezoelectric polymers are with
weak actuation forces. To overcome the limitations of conventional piezoelectric
materials, piezoelectric fiber based composites were invented through mixture of
piezoceramic fibrous phase and epoxy matrix phase.
The first type of piezo-fiber based composite material was proposed by Skinner et
al. [215], known as 1-3 composite. In the type of 1-3 composite, the piezoelectric
fibers with rectangular or circular cross section place along in the thickness direction.
Due to the piezoelectric fiber orientation, this type of piezo composite still has weak
actuation forces along the in-plane directions.
Placing the piezoelectric fiber with circular cross section along the in-plane direction, one obtains an active fiber composite (AFC), initially invented by MIT [216,
217]. Because of the circular cross section, a certain electric field volume is invalid
for the actuation performance. Replacing the circular cross section with rectangular
cross section, yields a macro-fiber composite (MFC), which was invented by NASA
Langley Research Center [218]. The MFC piezoelectric composites have no loss on
electric field, resulting in large actuation forces. For more details of MFC piezoelectric composites, it refers to Williams et al. [219], Sodano et al. [220], Bowen et
al. [221]. Since MFC has many beneficial properties, many applications for vibration
control [222, 223] and health monitoring [224–226] were investigated.
2.6.2 Homogenization of Piezo Fiber Composite
The structures of fiber based piezoelectric composite are complicated. For easy
implementation in simulations, piezoelectric composites are usually homogenized
to orthotropic materials, by experimental and numerical investigations. MFCs have
large application potentials due to their beneficial properties. Therefore, most of
the studies were dealing with the homogenization of MFC materials. Williams et
al. [227], Williams [228] obtained the basic elasticity constants of MFC patches for
the elastic and plastic constitutive behavior through experimental investigations. Linear piezoelectric composite material properties were predicted by using classical lamination theory [229], representative volume element (RVE) technique with mixing
rules [230–232], and asymptotic expansion homogenization (AEH) method [233].
More precisely, an electroelastic nonlinear material constitutive equations was developed by Williams et al. [234] for MFC patches. In addition, hysteresis and creep
effects were studies experimentally by Schröck et al. [235] for dynamic performance
of MFC integrated structures. For achieving complete material parameters, including
not only the elastic constants but also the transverse shear moduli and the piezoelectric