On the Choice of Integrity Base of Strain Invariants for Constitutive Equations of Isotropic Materials

1991 ◽  
pp. 26-33
Author(s):  
H. Bednarczyk ◽  
C. Sansour
Keyword(s):  
Constitutive Equations ◽  
Isotropic Materials ◽  
Strain Invariants

Non-Linear Constitutive Equations for Transversely Isotropic Materials Belonging to the С∞ and С∞h Symmetry Groups

2019 ◽  
pp. 46-59
Author(s):  
S.V. Tsvetkov
Keyword(s):  
Constitutive Equations ◽  
Infinite Order ◽  
Transversely Isotropic ◽  
Material Structure ◽  
Symmetry Groups ◽  
Tensor Function ◽  
Symmetry Principle ◽  
Isotropic Materials ◽  
Irreducible Form ◽  
Transversely Isotropic Materials

Transversely isotropic materials feature infinite-order symmetry axes. Depending on which other symmetry elements are found in the material structure, five symmetry groups may be distinguished among transversely isotropic materials. We consider constitutive equations for these materials. These equations connect two symmetric second-order tensors. Two types of constitutive equations describe the properties of these five material groups. We derived constitutive equations for materials belonging to the C∞ and C∞h symmetry groups in the tensor function form. To do this, we used corollaries of Curie's Symmetry Principle. This makes it possible to obtain a fully irreducible form of the tensor function.

On the use of symmetry to simplify the constitutive equations of isotropic materials with memory

1968 ◽  
Vol 306 (1487) ◽  
pp. 449-476 ◽  
Keyword(s):  
Constitutive Equations ◽  
Material Symmetry ◽  
Materials With Memory ◽  
Material Response ◽  
Isotropic Materials ◽  
Frame Indifference ◽  
History Of ◽  
With Memory

This paper is concerned with general, compressible, isotropic materials, solid or fluid, characterized by functionals which give the stress when the history of the strain is specified. It is shown that for certain broad classes of motions the requirements of material symmetry and frame-indifference greatly simplify the form of constitutive equations. These simplifica­tions are derived without invoking integral expansions or other special hypotheses of smoothness for material response. Among the motions considered in detail are those which are locally equivalent to pure extensions and sheared extensions.

Constitutive equations of elastoplastic isotropic materials that allow for the stress mode

2009 ◽  
Vol 45 (11) ◽  
pp. 1189-1195 ◽  
Author(s):  
M. E. Babeshko ◽  
Yu. N. Shevchenko ◽  
N. N. Tormakhov
Keyword(s):  
Constitutive Equations ◽  
Isotropic Materials ◽  
Stress Mode

Study on Mechanics Behaviors of Composite and Isotropic Shells

2011 ◽  
Vol 368-373 ◽  
pp. 215-218 ◽  
Author(s):  
Yao Peng Wu
Keyword(s):  
Shell Structure ◽  
Constitutive Equations ◽  
Thin Shell ◽  
Civil Engineering ◽  
Initial Configuration ◽  
Isotropic Shell ◽  
Broad Application ◽  
Isotropic Materials ◽  
Deployable Structure ◽  
Laminate Theory

Thin shell structure can show interesting bi-stable behavior. As a novel deployable structure, it shows a broad application prospect in the field of aeronautics and civil engineering, etc. The thesis deduces the general constitutive equations of thin shell structure on the basis of classical laminate theory. If the layup of the composite is anti-symmetric, the results show that there exist tension-bend coupling in the deformation of the shell structure; if the layup is symmetric, there exist bend-twist coupling. For isotropic shell, it has no tension-bend and bend-twist coupling, but if made unstressed from isotropic materials it is only stable in the initial configuration, which coincides with the known conclusion.

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