A Mathematical Model for Thermomechanical Behavior of Arbitrary Fiber Reinforced Viscoelastic Composites - I

Usal, Mustafa Reşit; Usal, Melek; Esendemir, Ümran

doi:10.1515/secm.2006.13.4.291

Cited by 3 publications

(3 citation statements)

References 7 publications

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“…Relationships between material and spatial forms of values appearing in this inequality have been presented as follows [18,19]:…”

Section: Electrostatic a D Thermo-mecha Ic Bala Ce Equatio Smentioning

confidence: 99%

“…Thus, in a elastic-piezoelectric anisotropic medium, in a situation where both mechanical interactions and electrical interactions are assumed non-linear, the constitutive equations for symmetric stress and polarization on material coordinates in terms of their components can be expressed through expressions (17) and (18). First term on the right part of the the constitutive equation for the symmetric stress (17) is the classical term of the Hooke law and contributes to the stress through the strain tensor.…”

Section: Determi Atio Of Symmetric Stress a D Polarizatio Co Stitutivmentioning

confidence: 99%

“…The last term shows the stress formed by the non-linear effect of the electric field. Considering expression (18), which yields the constitutive equation of the polarization field, linear effects of the electric field and the strain tensor, non-linear effects of the electric field and the strain tensor, mutual interaction between the strain tensor and the electric field contribute to the formation of polarization field in the said medium.…”

Section: Determi Atio Of Symmetric Stress a D Polarizatio Co Stitutivmentioning

confidence: 99%

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On Constitutive Equations for Anisotropic Nonlinearly Piezoelectric Materials

Usal

Yünlü

2011

MCA

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In this paper, the elastic-piezoelectric continuum has been investigated theoretically and its non-linear constitutive equations have been defined. The theory is formulated in the context of continuum electrodynamics. The solid medium is assumed to be non-linear, homogeneous, compressible and isothermal, has elastic and piezoelectric anisotropy. Basic principles of modern continuum mechanics and balance equations of electrostatic have provided guidance and have been determining in the process of this study. From the formulation belonging to the constitutive equations, it has been observed that the symmetric stress and polarization have been derived from a scalar-valued thermodynamic potential defined in calculations. As a result of thermodynamic constraints, it has been determined that the free energy function is dependent on a symmetric tensor and a vector. The free energy function has been represented by a power series expansion and the type and number of terms taken into consideration in this series expansion has determined the non-linearity of the medium. Finally, the quasi-linear constitutive equations are substituted in the balance equations to obtain the field equations.

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“…Relationships between material and spatial forms of values appearing in this inequality have been presented as follows [18,19]:…”

Section: Electrostatic a D Thermo-mecha Ic Bala Ce Equatio Smentioning

confidence: 99%

Section: Determi Atio Of Symmetric Stress a D Polarizatio Co Stitutivmentioning

confidence: 99%

Section: Determi Atio Of Symmetric Stress a D Polarizatio Co Stitutivmentioning

confidence: 99%

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On Constitutive Equations for Anisotropic Nonlinearly Piezoelectric Materials

Usal

Yünlü

2011

MCA

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A Constitutive Formulation for the Linear Thermoelastic Behavior of Arbitrary Fiber‐Reinforced Composites

Usal

2010

Mathematical Problems in Engineering

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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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On Magneto-Viscoelastic Behavior of Fiber-Reinforced Composite Materials Part - II: Isotropic Matrix Material

Usal¹,

Usal²,

Erdem³

2009

Science and Engineering of Composite Materials

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In this study, a fiber reinforced magnetic viscoelastic material with isotropic matrix has been investigated under the effect of external magneto-mechanical loads. The response comes about as elastic stress distribution, dissipative stress and magnetization. Constitutive equations for those response functions are obtained by the use of thermodynamics, objectivity, and the theory of invariants for the isotropic materials. Our material is assumed to be isotropic, the only anisotropy being as a result of fiber distribution. Constitutive equations for elastic stress distribution, dissipative stress, and magnetization have been obtained in material and in spatial coordinates.

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A Mathematical Model for Thermomechanical Behavior of Arbitrary Fiber Reinforced Viscoelastic Composites - I

Cited by 3 publications

References 7 publications

On Constitutive Equations for Anisotropic Nonlinearly Piezoelectric Materials

On Constitutive Equations for Anisotropic Nonlinearly Piezoelectric Materials

A Constitutive Formulation for the Linear Thermoelastic Behavior of Arbitrary Fiber‐Reinforced Composites

On Magneto-Viscoelastic Behavior of Fiber-Reinforced Composite Materials Part - II: Isotropic Matrix Material

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