A viscoelastic thin rod model for large deformations: Numerical examples

2011 ◽  
Vol 16 (8) ◽  
pp. 887-896 ◽  
Author(s):  
Joelle Beyrouthy ◽  
Patrizio Neff
Keyword(s):  
Finite Strain ◽  
Large Deformations ◽  
Splitting Method ◽  
Evolution Problem ◽  
The Finite Element Method ◽  
Numerical Examples ◽  
Numerical Resolution ◽  
Incremental Formulation ◽  
Lagrange Elements ◽  
Strain Model

We present a Cosserat-based 3D–1D dimensional reduction for a viscoelastic finite strain model. The numerical resolution of the reduced coupled minimization/evolution problem is based on a splitting method. We start by approximating the minimization problem using the finite element method with P1 Lagrange elements. The solution of this problem is used in the time-incremental formulation of the evolution problem.

scholarly journals A LARGE DEFORMATION, VISCOELASTIC, THIN ROD MODEL: DERIVATION AND ANALYSIS

2009 ◽  
Vol 19 (10) ◽  
pp. 1907-1928 ◽  
Author(s):  
J. BEYROUTHY ◽  
H. LE DRET
Keyword(s):  
Existence And Uniqueness ◽  
Finite Strain ◽  
Three Dimensional ◽  
Evolution Problem ◽  
Well Posedness ◽  
One Dimensional ◽  
Uniqueness Of The Solution ◽  
Model Derivation ◽  
Regularity Results ◽  
Strain Model

We present a Cosserat-based three-dimensional to one-dimensional reduction in the case of a thin rod, of the viscoelastic finite strain model introduced by Neff. This model is a coupled minimization/evolution problem. We prove the existence and uniqueness of the solution of the reduced minimization problem. We also show a few regularity results for this solution which allow us to establish the well-posedness of the evolution problem. Finally, the reduced model preserves observer invariance.

Large Elasto-Plastic Deformations of Work-Hardening Metal Alloys

1984 ◽  
Vol 8 (2) ◽  
pp. 77-83
Author(s):  
G.Z. Voyiadjis ◽  
S. Navaee
Keyword(s):  
Thick Plate ◽  
Large Deformations ◽  
Metal Alloys ◽  
The Finite Element Method ◽  
Plastic Deformations ◽  
Numerical Examples ◽  
Concentration Problem ◽  
Moderately Thick Plate ◽  
Aluminum Alloy 2024 ◽  
Spatial Formulation

The work outlined in this research demonstrates the applicability and effectiveness of the elasto-plastic model presented by the First author in [1] in solving complex (i.e., any shape and any deformation) finite deformation problems. The use of the Lagrangian formulation in this work eliminates the controversy regarding the choice of the appropriate co-rotational stress rate, and provides a more convenient theory than the more common spatial formulation. The aluminum alloy 2024 is used in this work as it closely displays the properties outlined by the proposed constitutive equations [1]. The problem of analysis of displacements, stresses, and strains in elements made of this material subject to arbitrarily large deformations under the conditions of plane strain or plane stress is formulated in terms of the finite element method. Numerical examples include the bending of a moderately thick plate and the stress concentration problem of a plate with a hole subjected to an uniform uniaxial loading. Experimental verification is provided for the bending of the moderately thick plate.

scholarly journals A Thermal Model for Three-Core Armored Submarine Cables Based on Distributed Temperature Sensing

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3897
Author(s):  
Miguel Ángel González-Cagigal ◽  
Juan Carlos del-Pino-López ◽  
Alfonso Bachiller-Soler ◽  
Pedro Cruz-Romero ◽  
José Antonio Rosendo-Macías
Keyword(s):  
Temperature Sensing ◽  
The Finite Element Method ◽  
Current Profile ◽  
Distributed Temperature Sensing ◽  
Numerical Resolution ◽  
Electromagnetic Model ◽  
Proposed Model ◽  
Relative Errors ◽  
Dynamic Loading Conditions ◽  
Submarine Cables

This paper presents a procedure for the derivation of an equivalent thermal network-based model applied to three-core armored submarine cables. The heat losses of the different metallic cable parts are represented as a function of the corresponding temperatures and the conductor current, using a curve-fitting technique. The model was applied to two cables with different filler designs, supposed to be equipped with distributed temperature sensing (DTS) and the optical fiber location in the equivalent circuit was adjusted so that the conductor temperature could be accurately estimated using the sensor measurements. The accuracy of the proposed model was tested for both stationary and dynamic loading conditions, with the corresponding simulations carried out using a hybrid 2D-thermal/3D-electromagnetic model and the finite element method for the numerical resolution. Mean relative errors between 1 and 3% were obtained using an actual current profile. The presented procedure can be used by cable manufacturers or by utilities to properly evaluate the cable thermal situation.

Viscoelastic Models for Ligaments and Tendons

1994 ◽  
Vol 47 (6S) ◽  
pp. S282-S286 ◽  
Author(s):  
S. L.-Y. Woo ◽  
G. A. Johnson ◽  
R. E. Levine ◽  
K. R. Rajagopal
Keyword(s):  
Constitutive Modeling ◽  
Finite Strain ◽  
Experimental Studies ◽  
Viscoelastic Behavior ◽  
Microstructural Change ◽  
Viscoelastic Models ◽  
Dependent Behavior ◽  
Recent Approach ◽  
Single Integral ◽  
Strain Model

Ligaments and tendons serve a variety of important functions in the human body. Many experimental studies have focused on understanding their mechanical behavior, mathematical modeling has also contributed important information. This paper presents a brief review of viscoelastic models that have been proposed to describe the nonlinear and time-dependent behavior of ligaments and tendons. Specific attention is devoted to quasi-linear viscoelasticity (QLV) and to our most recent approach, the single integral finite strain model (SIFS) which incorporates constitutive modeling of microstructural change. An example is given in which the SIFS model is used to describe the viscoelastic behavior of a human patellar tendon.

scholarly journals The Sum and Difference of Two Lognormal Random Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
C. F. Lo
Keyword(s):  
Stochastic Process ◽  
Probability Distributions ◽  
Operator Splitting ◽  
Splitting Method ◽  
Unified Approach ◽  
New Approach ◽  
Numerical Examples ◽  
Operator Splitting Method ◽  
Approximate Probability ◽  
Analytical Series

We have presented a new unified approach to model the dynamics of both the sum and difference of two correlated lognormal stochastic variables. By the Lie-Trotter operator splitting method, both the sum and difference are shown to follow a shifted lognormal stochastic process, and approximate probability distributions are determined in closed form. Illustrative numerical examples are presented to demonstrate the validity and accuracy of these approximate distributions. In terms of the approximate probability distributions, we have also obtained an analytical series expansion of the exact solutions, which can allow us to improve the approximation in a systematic manner. Moreover, we believe that this new approach can be extended to study both (1) the algebraic sum ofNlognormals, and (2) the sum and difference of other correlated stochastic processes, for example, two correlated CEV processes, two correlated CIR processes, and two correlated lognormal processes with mean-reversion.

A thermo-mechanically coupled finite strain model considering inelastic heat generation

2015 ◽  
Vol 28 (4) ◽  
pp. 993-1007 ◽  
Author(s):  
Vladimir Dunić ◽  
Nenad Busarac ◽  
Vukašin Slavković ◽  
Bojana Rosić ◽  
Rainer Niekamp ◽  
...  
Keyword(s):  
Heat Generation ◽  
Finite Strain ◽  
Strain Model

A finite strain model of combined viscoplasticity and rate-independent plasticity without a yield surface

2013 ◽  
Vol 224 (9) ◽  
pp. 2107-2125 ◽  
Author(s):  
V. P. Panoskaltsis ◽  
L. C. Polymenakos ◽  
D. Soldatos
Keyword(s):  
Yield Surface ◽  
Finite Strain ◽  
Strain Model

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.

Simulation of the Impact Behaviour of Diffusion-Bonded and Adhered Perforated Hollow Sphere Structures (PHSS)

2009 ◽  
Vol 294 ◽  
pp. 27-38 ◽  
Author(s):  
Fabian Ferrano ◽  
Marco Speich ◽  
Wolfgang Rimkus ◽  
Markus Merkel ◽  
Andreas Öchsner
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Mechanical Behaviour ◽  
Hollow Sphere ◽  
Large Deformations ◽  
The Finite Element Method ◽  
Impact Behaviour ◽  
New Type ◽  
The Impact

This paper investigates the mechanical properties of a new type of hollow sphere structure. For this new type, the sphere shell is perforated by several holes in order to open up the inner sphere volume and surface. The mechanical behaviour of perforated sphere structures under large deformations and strains in a primitive cubic arrangement is numerically evaluated by using the finite element method for different hole diameters and different joining techniques.

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