A spectral approach for nonlinear transversely isotropic elastic bodies, for a new class of constitutive equation: Applications to rock mechanics

2020 ◽  
Vol 231 (11) ◽  
pp. 4803-4818
Author(s):  
M. H. B. M. Shariff ◽  
R. Bustamante
Keyword(s):  
Constitutive Equation ◽  
Rock Mechanics ◽  
Transversely Isotropic ◽  
Spectral Approach ◽  
New Class ◽  
Elastic Bodies

Some topics on a new class of elastic bodies

2009 ◽  
Vol 465 (2105) ◽  
pp. 1377-1392 ◽  
Author(s):  
Roger Bustamante
Keyword(s):  
Constitutive Equation ◽  
Stress Tensor ◽  
Cauchy Stress ◽  
Cauchy Stress Tensor ◽  
Weak Formulation ◽  
New Class ◽  
Elastic Bodies ◽  
Small Deformations

In this paper, we study the problem of prescribing deformation as a function of stresses. For the particular case of small deformations, we find a weak formulation, from which we define the constitutive equation of a Green-like material, where an energy function that depends on the Cauchy stress tensor is proposed. Constraints on the deformation are studied for this new class of elastic bodies.

Some Universal Solutions for a Class of Incompressible Elastic Body that is Not Green Elastic: The Case of Large Elastic Deformations

2020 ◽  
Vol 73 (2) ◽  
pp. 177-199
Author(s):  
R Bustamante
Keyword(s):  
Constitutive Equation ◽  
Strain Tensor ◽  
Elastic Deformations ◽  
Hencky Strain ◽  
New Class ◽  
Elastic Bodies ◽  
Kirchhoff Stress Tensor ◽  
New Type ◽  
Incompressible Elastic Body ◽  
Universal Solutions

Summary Some universal solutions are studied for a new class of elastic bodies, wherein the Hencky strain tensor is assumed to be a function of the Kirchhoff stress tensor, considering in particular the case of assuming the bodies to be isotropic and incompressible. It is shown that the families of universal solutions found in the classical theory of nonlinear elasticity, are also universal solutions for this new type of constitutive equation.

Fiber symmetry

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Composite Materials ◽  
Constitutive Equation ◽  
Transversely Isotropic ◽  
Fiber Reinforced ◽  
Fiber Reinforced Materials ◽  
Reinforced Materials

This chapter develops the general constitutive equation for transversely isotropic, fiber-reinforced materials. Applications include composite materials and bio-elasticity.

The State of Stress and Strain Adjacent to Notches in a New Class of Nonlinear Elastic Bodies

2019 ◽  
Vol 135 (1-2) ◽  
pp. 375-397 ◽  
Author(s):  
Vojtěch Kulvait ◽  
Josef Málek ◽  
K. R. Rajagopal
Keyword(s):  
The State ◽  
Stress And Strain ◽  
New Class ◽  
Elastic Bodies ◽  
State Of Stress ◽  
Nonlinear Elastic

On the inhomogeneous shearing of a new class of elastic bodies

2012 ◽  
Vol 17 (7) ◽  
pp. 762-778 ◽  
Author(s):  
R Bustamante ◽  
KR Rajagopal
Keyword(s):  
New Class ◽  
Elastic Bodies

Universal relations for a new class of elastic bodies

2013 ◽  
Vol 19 (4) ◽  
pp. 440-448 ◽  
Author(s):  
KR Rajagopal ◽  
Alan S Wineman
Keyword(s):  
New Class ◽  
Elastic Bodies

Large deformations of a new class of incompressible elastic bodies

2016 ◽  
Vol 67 (3) ◽  
Author(s):  
R. Bustamante ◽  
O. Orellana ◽  
R. Meneses ◽  
K. R. Rajagopal
Keyword(s):  
Large Deformations ◽  
New Class ◽  
Elastic Bodies

Numerical technique for solving truss and plane problems for a new class of elastic bodies

2016 ◽  
Vol 227 (11) ◽  
pp. 3147-3176 ◽  
Author(s):  
L. S. Shankar ◽  
S. Rajthilak ◽  
U. Saravanan
Keyword(s):  
Numerical Technique ◽  
New Class ◽  
Elastic Bodies
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