A properly invariant theory of small deformations superposed on large deformations of an elastic rod

1995 ◽  
Vol 39 (2) ◽  
pp. 97-131 ◽  
Author(s):  
Oliver M. O'Reilly
Keyword(s):  
Invariant Theory ◽  
Large Deformations ◽  
Elastic Rod ◽  
Small Deformations

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.

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.

Large Deflections of an Inflated Cylindrical Tent

1969 ◽  
Vol 36 (4) ◽  
pp. 845-851 ◽  
Author(s):  
E. W. Ross
Keyword(s):  
Numerical Analysis ◽  
Cross Section ◽  
Large Deformations ◽  
Wind Pressure ◽  
Large Deflections ◽  
Theoretical Interest ◽  
Membrane Theory ◽  
Small Strains ◽  
Deformed State ◽  
Small Deformations

This report analyzes the large deformations of a cylindrical, inflated, single-wall tent due to wind pressure and is based on the membrane theory for large deflections but small strains. The tent cross section is a sector of a circle in the undeformed position, and the wind is blowing on it in the broadside direction. The tent motion is taken as plane, and it is assumed that the wind pressure distribution is known in the deformed state. The problem is solved by numerical analysis and results are presented for the stress, deformed shape, aerodynamic resultants, and anchor forces. The problem is of theoretical interest because the linear membrane theory does not have a unique solution for it, and also because it illustrates that the method of small deformations superposed on large is of little help when the large deformation is of inextensional type.

Averaging Models for Heterogeneous Viscoplastic and Elastic Viscoplastic Materials

2001 ◽  
Vol 124 (1) ◽  
pp. 62-70 ◽  
Author(s):  
Alain Molinari
Keyword(s):  
Large Deformations ◽  
Approximate Solutions ◽  
Local Response ◽  
Nonlinear Properties ◽  
Average Strain Rate ◽  
The Matrix ◽  
Reference Medium ◽  
Homogeneous Matrix ◽  
Small Deformations ◽  
Eshelby Problem

Averaging models are proposed for viscoplastic and elastic-viscoplastic heterogeneous materials. The case of rigid viscoplastic materials is first discussed. Large deformations are considered. A first class of models is based on different linearizations of the nonlinear local response. A second class of models is obtained from approximate solutions of the nonlinear Eshelby problem. In this problem, an ellipsoid with uniform nonlinear properties is embedded in an infinite homogeneous matrix. An approximate solution is obtained by approaching the matrix behavior with an affine response. Using this solution of the nonlinear Eshelby problem, the average strain rate is calculated in each phase of the composite material, each phase being represented by an ellipsoid embedded in an infinite reference medium. By adequate choices of the reference medium, different averaging models are obtained (self-consistent scheme, nonlinear Mori Tanaka model…). Finally, elasticity is included in the modelling, but with a restriction to small deformations.

scholarly journals Investigation of deformation behavior of PETG-FDM-printed metamaterials with pantographic substructures based on different slicing strategies

2021 ◽  
Vol 30 ◽  
pp. 263498332110164
Author(s):  
Arda Özen ◽  
Gregor Ganzosch ◽  
Emilio Barchiesi ◽  
Dietmar W Auhl ◽  
Wolfgang H Müller
Keyword(s):  
Finite Element ◽  
Deformation Behavior ◽  
Large Deformations ◽  
Material Behavior ◽  
Image Correlation ◽  
Isotropic Model ◽  
Linear Elastic ◽  
Transverse Isotropic ◽  
Elastic Transverse ◽  
Small Deformations

Based on the progress and advances of additive manufacturing technologies, design and production of complex structures became cheaper and therefore rather possible in the recent past. A promising example of such complex structure is a so-called pantographic structure, which can be described as a metamaterial consisting of repeated substructure. In this substructure, two planes, which consist of two arrays of beams being orthogonally aligned to each other, are interconnected by cylinders/pivots. Different inner geometries were taken into account and additively manufactured by means of fused deposition modeling technique using polyethylene terephthalate glycol (PETG) as filament material. To further understand the effect of different manufacturing parameters on the mechanical deformation behavior, three types of specimens have been investigated by means of displacement-controlled extension tests. Different slicing approaches were implemented to eliminate process-related problems. Small and large deformations are investigated separately. Furthermore, 2D digital image correlation was used to calculate strains on the outer surface of the metamaterial. Two finite-element simulations based on linear elastic isotropic model and linear elastic transverse isotropic model have been carried out for small deformations. Standardized extension tests have been performed on 3D-printed PETG according to ISO 527-2. Results obtained from finite-element method have been validated by experimental results of small deformations. These results are in good agreement with linear elastic transverse isotropic model (up to about [Formula: see text] of axial elongation), though the response of large deformations indicates a nonlinear inelastic material behavior. Nevertheless, all samples are able to withstand outer loading conditions after the first rupture, resulting in resilience against ultimate failure.

The Influence of Initial Stresses on Blood Vessel Mechanics

2003 ◽  
Vol 03 (02) ◽  
pp. 215-229 ◽  
Author(s):  
Paola Nardinocchi ◽  
Luciano Teresi
Keyword(s):  
Blood Flow ◽  
Stress State ◽  
Blood Vessel ◽  
Mechanical Behavior ◽  
Large Deformations ◽  
Blood System ◽  
Initial Stresses ◽  
Small Deformations ◽  
Vessel Mechanics

In order to account for the in vivo conditions of blood vessels, we investigate the mechanical behavior of a stressed tube-like membrane when small deformations are superimposed on large deformations: the latter simulate the stretches present in the in vivo arteries while the superimposed deformations account for the small — but essential for the blood propagation — deformations due to the pulsatile nature of the blood flow. Our aim is to discuss how a stress state influence the response of the vessel-blood system.

Free Rotation of an Elastic Rod With an End Mass

1986 ◽  
Vol 53 (4) ◽  
pp. 864-868 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Angular Momentum ◽  
Large Deformations ◽  
Free Rotation ◽  
Centrifugal Forces ◽  
Governing Equations ◽  
Elastic Rod ◽  
Critical Rotation ◽  
Minimum Total Energy ◽  
Equilibrium Configurations ◽  
Flexible Antenna

This paper models a rotating space satellite with a long flexible antenna. Large deformations of the elastic rod are caused by the centrifugal forces. Bifurcation analysis shows the effect of end mass on the critical rotation speeds above which sinuous equilibrium configurations occur. The nonlinear governing equations are then integrated numerically. We find a class of solutions with a looped configuration whose existence requires a certain minimum total energy and minimum angular momentum. Catastrophic changes are possible.

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