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.

Nonlinear Viscoelasticity for Short Time Ranges

1966 ◽  
Vol 33 (2) ◽  
pp. 313-321 ◽  
Author(s):  
N. C. Huang ◽  
E. H. Lee
Keyword(s):  
Constitutive Equation ◽  
Numerical Solutions ◽  
Kernel Functions ◽  
Nonlinear Creep ◽  
Experimental Procedure ◽  
Nonlinear Viscoelastic ◽  
Tension Tests ◽  
Incompressible Materials ◽  
Inverse Interpolation ◽  
Short Time

Approximate constitutive equations for nonlinear viscoelastic incompressible materials under small finite deformation and for short time ranges are derived. The error bound of such a constitutive equation is investigated. Nonlinear creep is analyzed on the basis of the proposed equation, and also the problem of a pressurized viscoelastic hollow cylinder bonded to an elastic casing. Numerical solutions, evaluated by assuming particular forms of kernel functions in the constitutive equation, are obtained by means of an inverse interpolation technique, and the effects of nonlinearity of material properties are discussed. An experimental procedure is also proposed for measuring kernel functions from uniaxial tension tests for real materials.

scholarly journals Large deformations of a cylindrical tube with prestressed coatings

2019 ◽  
Vol 484 (5) ◽  
pp. 547-549
Author(s):  
Yu. N. Kulchin ◽  
V. E. Ragozina ◽  
O. V. Dudko
Keyword(s):  
Shock Waves ◽  
Large Deformations ◽  
Cylindrical Tube ◽  
Plastic Strains ◽  
Rotation Tensor ◽  
Plastic Deformations ◽  
Incompressible Materials ◽  
Isotropic Media ◽  
Elastic Loading ◽  
Elastic Shock

General theoretical relations for calculating the redistribution of the preliminary irreversible strain field during unloading or elastic loading of a medium are obtained for the nonlinear multiplicative gradient model of large elastic-plastic deformations. It is shown that the dynamics of elastic shock waves does not depend directly on the previously accumulated plastic strains. A formula for the plastic-strain rotation tensor is obtained. It is shown that rigid rotation of plastic strains under elastic shock waves can be jump-like. All results are obtained for the general case of model relations of isotropic media and are valid for both compressible and incompressible materials.

scholarly journals Run-Out Simulation of a Landslide Triggered by an Increase in the Groundwater Level Using the Material Point Method

Water ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 2817
Author(s):  
Antonello Troncone ◽  
Luigi Pugliese ◽  
Enrico Conte
Keyword(s):  
Groundwater Level ◽  
Large Deformations ◽  
Material Point Method ◽  
Material Point ◽  
Point Method ◽  
Deformation Mechanisms ◽  
The Finite Element Method ◽  
Numerical Techniques ◽  
Rainy Period ◽  
Small Deformations

Deformation mechanisms of the slopes are commonly schematized in four different stages: pre-failure, failure, post-failure and eventual reactivation. Traditional numerical methods, such as the finite element method and the finite difference method, are commonly employed to analyse the slope response in the pre-failure and failure stages under the assumption of small deformations. On the other hand, these methods are generally unsuitable for simulating the post-failure behaviour due to the occurrence of large deformations that often characterize this stage. The material point method (MPM) is one of the available numerical techniques capable of overcoming this limitation. In this paper, MPM is employed to analyse the post-failure stage of a landslide that occurred at Cook Lake (WY, USA) in 1997, after a long rainy period. Accuracy of the method is assessed by comparing the final geometry of the displaced material detected just after the event, to that provided by the numerical simulation. A satisfactory agreement is obtained between prediction and observation when an increase in the groundwater level due to rainfall is accounted for in the analysis.

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