Correspondence Principle in Viscoelastic Functionally Graded Materials

2000 ◽  
Vol 68 (1) ◽  
pp. 129-132 ◽  
Author(s):  
G. H. Paulino ◽  
Z.-H. Jin
Keyword(s):  
Functionally Graded Materials ◽  
Correspondence Principle ◽  
Functionally Graded ◽  
Viscoelastic Materials ◽  
Viscoelastic Solids ◽  
Graded Materials ◽  
Space And Time ◽  
Separable Functions

This paper presents an extension of the correspondence principle (as applied to homogeneous viscoelastic solids) to nonhomogeneous viscoelastic solids under the assumption that the relaxation (or creep) moduli be separable functions in space and time. A few models for graded viscoelastic materials are presented and discussed. The revisited correspondence principle extends to specific instances of thermoviscoelasticity and fracture of functionally graded materials.

The Elastic-Viscoelastic Correspondence Principle for Functionally Graded Materials, Revisited

2003 ◽  
Vol 70 (3) ◽  
pp. 359-363 ◽  
Author(s):  
S. Mukherjee ◽  
Glaucio H. Paulino
Keyword(s):  
Functionally Graded Materials ◽  
Functionally Graded Material ◽  
Correspondence Principle ◽  
Functionally Graded ◽  
Graded Materials ◽  
One Dimensional ◽  
Space And Time ◽  
Graded Material ◽  
Nonhomogeneous Materials ◽  
Exponentially Graded

Paulino and Jin [Paulino, G. H., and Jin, Z.-H., 2001, “Correspondence Principle in Viscoelastic Functionally Graded Materials,” ASME J. Appl. Mech., 68, pp. 129–132], have recently shown that the viscoelastic correspondence principle remains valid for a linearly isotropic viscoelastic functionally graded material with separable relaxation (or creep) functions in space and time. This paper revisits this issue by addressing some subtle points regarding this result and examines the reasons behind the success or failure of the correspondence principle for viscoelastic functionally graded materials. For the inseparable class of nonhomogeneous materials, the correspondence principle fails because of an inconsistency between the replacements of the moduli and of their derivatives. A simple but informative one-dimensional example, involving an exponentially graded material, is used to further clarify these reasons.

Applications of the symplectic method in quasi-static analysis for viscoelastic functionally graded materials

2017 ◽  
Vol 34 (4) ◽  
pp. 1314-1331 ◽  
Author(s):  
W.X. Zhang ◽  
R.G. Liu ◽  
Y. Bai
Keyword(s):  
Functionally Graded Materials ◽  
Correspondence Principle ◽  
Separation Of Variables ◽  
Closed Form Solution ◽  
Form Solution ◽  
Functionally Graded ◽  
Symplectic Method ◽  
Graded Materials ◽  
Content Type ◽  
Displacement Constraints

Purpose For general quasi-static problems of viscoelastic functionally graded materials (VFGMs), the correspondence principle can be applied only for simple structures with a closed form solution of the corresponding elastic problem exists. In this paper, a new symplectic approach, according to the correspondence principle between linearly elastic and viscoelastic solids, is proposed for quasi-static VFGMs. Design/methodology/approach Firstly, by employing the method of separation of variables, all the fundamental eigenvectors of the governing equations are obtained analytically. Then, the satisfactions of boundary conditions prescribed on the ends and laterals are discussed based on the variable substitution and the eigenvector expansion methods. Findings In the numerical examples, some boundary condition problems are given. The results show the local effects due to the displacement constraints. Originality/value The paper provides an innovative technique for quasi-static problems of VFG Ms. Its correctness and the efficiency are well suported by numerical results.

Dynamic Analysis with Stress Recovery for Functionally Graded Materials: Numerical Simulation and Experimental Benchmarking

2014 ◽  
Vol 2 (1) ◽  
pp. 21
Author(s):  
Carlos Alberto Dutra Fraga Filho ◽  
Fernando César Meira Menandro ◽  
Rivânia Hermógenes Paulino de Romero ◽  
Juan Sérgio Romero Saenz
Keyword(s):  
Numerical Simulation ◽  
Dynamic Analysis ◽  
Functionally Graded Materials ◽  
Functionally Graded ◽  
Stress Recovery ◽  
Graded Materials
Sign in / Sign up

Export Citation Format

Share Document