In this study, behavior of a viscoelastic material under external loading has been systematically investigated in the frame of continuum mechanics, where the material was brought to a composite state by two independent and non-expansive fiber families. The matrix material is supposed to be made of viscoelastic material involving an artificial anisotropy due to fiber reinforcing by arbitrary distribution. In terms of behavior the object responds to the environment prompting it through elastic stress and dissipative stress, whose constitutive equations have been obtained. While elastic stress is derived from the thermodynamic potential, dissipative stress was formed as a tensorial function that depends on certain arguments. These arguments are Green deformation tensor, deformation rate tensor, fiber distribution tensor and temperature field. As a result, constitutive equations obtained were used as substitutes in balance equations, yielding field equations.
In this study two deflection functions due to both the flexure and the shear of an orthotropic simply supported beam loaded linearly are obtained by means of the anisotropic elasticity theory. In order to see the effect of shear, the deflections are calculated for different fiber directions. Two different composite materials are used during the deflection analysis. The error level and the shear deflection for the thermoplastic composite beam are the smallest for 45 orientation angle, and that for the polymer-matrix composite beam are the smallest for 90 orientation angle. When the cross-sectional height to the beam-length ratio increases, the shear effect also increases.
This study examines the behavior of a material under electro-mechanical loads arising of the external medium in a viscoelastic and dielectric material, provided that isotropy constraint is imposed on the material. The reaction of the object to external loads is expressed in elastic stress, dissipative stress and electrical polarization. Based on constitutive axioms and concepts pertaining to the symmetry group of the material, constitutive functionals have been obtained. To materially determine arguments of these functionals, findings of the theory of invariants have been used as a routine method. As a result constitutive equations pertaining to elastic stress, polarization field and dissipative stress have been found in material and spatial coordinates whereas symmetric and asymmetric stresses have been found in terms of displacement gradient and its derivative by using the expressions of elastic stress, polarization field and dissipative stress.
In this study, two deflection functions due to flexure and shear have been obtained for the global form of composite materials. Two different composite materials are selected for comparison of these deflection functions. These composites are: polymer matrix composite simply supported beam, reinforced by unidirectional fibers; and thermoplastic simply supported beam, reinforced by woven Cr-Ni steel fibers. In accordance with these different material properties, analytical and numerical solutions have been carried out. For 0, 30, 45, 60, and 90 fiber orientation angles, static and dynamic behavior of the two different composite materials are examined. Numerical solutions are given as graphical forms. In addition to modal analysis, two different composite materials have been realized. Natural frequencies and vibration modes are given as graphical forms. ANSYS and MATLAB software are used for numerical analysis of the different composite materials.
The linear thermoelastic behavior of a composite material reinforced by two independent and inextensible fiber families has been analyzed theoretically. The composite material is assumed to be anisotropic, compressible, dependent on temperature gradient, and showing linear elastic behavior. Basic principles and axioms of modern continuum mechanics and equations belonging to kinematics and deformation geometries of fibers have provided guidance and have been determining in the process of this study. The matrix material is supposed to be made of elastic material involving an artificial anisotropy due to fibers reinforcing by arbitrary distributions. As a result of thermodynamic constraints, it has been determined that the free energy function is dependent on a symmetric tensor and two vectors whereas the heat flux vector function is dependent on a symmetric tensor and three vectors. The free energy and heat flux vector functions have been represented by a power series expansion, and the type and the number of terms taken into consideration in this series expansion have determined the linearity of the medium. The linear constitutive equations of the stress and heat flux vector are substituted in the Cauchy equation of motion and in the equation of conservation of energy to obtain the field equations.
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