scholarly journals Mixed/Hybrid finite elements for finite deformations of quasi‐incompressible materials with non‐constant bulk moduli

PAMM ◽  
2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Patrick Schneider ◽  
Josef Arthur Schönherr ◽  
Christian Mittelstedt
Keyword(s):  
Finite Elements ◽  
Finite Deformations ◽  
Incompressible Materials

Stress Analysis for a Nonlinear Viscoelastic Compressible Cylinder

1970 ◽  
Vol 37 (4) ◽  
pp. 1127-1133 ◽  
Author(s):  
E. C. Ting
Keyword(s):  
Large Deformations ◽  
Finite Deformations ◽  
Kernel Functions ◽  
Nonlinear Viscoelastic ◽  
Stress Strain Relation ◽  
Incompressible Materials ◽  
Small Deformations ◽  
Compressible Cylinder ◽  
Elastic Casing ◽  
Finite Difference Techniques

Real solids are not incompressible, although many viscoelastic materials which undergo large deformations show only small changes in volume under ordinary loading conditions. This paper is concerned with a pressurized isotropic viscoelastic hollow cylinder bonded to an elastic casing in which, during a finite deformation, the dilatational change in any element of the cylinder is a small quantity. The analysis is based in part upon the theory of small deformations superposed on finite deformations. Numerical calculations are evaluated by using finite-difference techniques and assuming particular forms of kernel functions in the stress-strain relation. The results for compressible and incompressible materials are compared.

Notes on finite elements for nearly incompressible materials

AIAA Journal ◽  
1976 ◽  
Vol 14 (6) ◽  
pp. 824-826 ◽  
Author(s):  
T. H. H. Pian ◽  
S. W. Lee
Keyword(s):  
Finite Elements ◽  
Incompressible Materials

On volumetric locking-free behaviour of p-version finite elements under finite deformations

2007 ◽  
Vol 24 (11) ◽  
pp. 1019-1032 ◽  
Author(s):  
Ulrich Heisserer ◽  
Stefan Hartmann ◽  
Alexander Düster ◽  
Zohar Yosibash
Keyword(s):  
Finite Elements ◽  
Finite Deformations ◽  
Volumetric Locking
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