|Kapania, Rakesh K.
|Batra, Romesh C.
|Dillard, David A.
|Inman, Daniel J.
|Johnson, Eric R.
|Plaut, Raymond H.
Over the past several decades, the use of composite materials has
grown considerably. Typically, fiber-reinforced polymer-matrix composites are modeled
as being linear elastic. However, it is well-known that polymers
are viscoelastic in nature. Furthermore, the analysis
of complex structures requires a numerical approach such as the
finite element method. In the present work, a triangular flat
shell element for linear elastic composites is extended to model linear
viscoelastic composites. Although polymers are usually modeled as being incompressible,
here they are modeled as compressible. Furthermore, the
macroscopic constitutive properties for fiber-reinforced composites are
assumed to be known and are not determined using the matrix and fiber properties along with the
fiber volume fraction. Hygrothermo-rheologically simple materials are considered for which a change in the
hygrothermal environment results in a horizontal shifting of the relaxation moduli
curves on a log time scale, in addition to the usual hygrothermal loads.
Both the temperature and moisture are taken to be prescribed.
Hence, the heat energy generated by the viscoelastic deformations is not considered.
When the deformations and rotations are small under an
applied load history, the usual engineering stress and
strain measures can be used and the time history of a viscoelastic
deformation process is determined using the original geometry of the structure.
If, however, sufficiently large loads are applied, the deflections and rotations
will be large leading to changes in the structural stiffness
characteristics and possibly the internal loads carried throughout the structure.
Hence, in such a case, nonlinear effects must be taken
into account and the appropriate stress and strain measures must
be used. Although a geometrically-nonlinear finite element code could
always be used to compute geometrically-linear deformation processes, it is inefficient to use such a
code for small deformations, due to the continual generation of the assembled internal load vector, tangent stiffness
matrix, and deformation-dependent external load vectors. Rather, for small deformations,
the appropriate deformation-independent stiffness matrices and load vectors to be used
for all times can be determined once at the start of the analysis. Of course, the
time-dependent viscoelastic effects need to be correctly taken into account in
both types of analyses. The present work details both geometrically-linear and nonlinear triangular flat shell formulations for
linear viscoelastic composites. The accuracy and capability
of the formulations are shown through a range of numerical examples involving beams,
rings, plates, and shells.