A low order virtual element formulation for finite elasto-plastic deformations

Abstract Currently, the standard approach to building a geomechanical model for analyzing wellbore stability involves taking into account only elastic deformations. This approach has shown its inconsistency in the design and drilling of wells passing through rocks with pronounced plastic properties. Such rocks are characterized by the fact that when the loads acting on them change, they demonstrate not only elastic, but also plastic (irreversible) deformations. Plastic deformations have an additional impact on the distribution of stresses in the rock of the near-wellbore zone on a qualitative and quantitative level. Since plastic deformations are not taken into account in the standard approach, in this case the results of the wellbore stability analysis are based on incorrectly calculated stresses acting in the rock. As a result, it can lead to misinterpretation of the model for analysis, suboptimal choice of trajectory, incorrect calculation of safe mud window and an incorrectly selected set of measures to reduce the risks of instability. The aim of this work is to demonstrate the advantages of the developed 3D elasto-plastic program for calculating the wellbore stability in comparison with the standard elastic method used in petroleum geomechanics. The central core of the work is the process of initialization of the elasto-plastic model according to the data of core tests and the subsequent validation of experimental and numerical loading curves. The developed 3D program is based on a modified Drucker-Prager model and implemented in a finite element formulation. 3D geomechanical model of wellbore stability allows describing deformation processes in the near-wellbore zone and includes the developed failure criteria. The paper shows a special approach to the determination of the mud window based on well logging data and core tests by taking into account the plastic behavior of rocks. An important result of this study is the determination of the possibility of expanding the mud window when taking into account the plastic criterion of rock failure.

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Static Atomistic Simulations of Nanoindentation and Determination of Nanohardness

Journal of Applied Mechanics ◽

10.1115/1.1988349 ◽

2005 ◽

Vol 72 (5) ◽

pp. 738-743 ◽

Cited By ~ 2

Author(s):

Yeau-Ren Jeng ◽

Chung-Ming Tan

Keyword(s):

Finite Element ◽

Nonlinear Finite Element ◽

Deformation Mechanisms ◽

Finite Element Formulation ◽

Atomistic Simulations ◽

Element Formulation ◽

Indentation Size ◽

Plastic Deformations ◽

Nanoindentation Testing

This paper develops a nonlinear finite element formulation to analyze nanoindentation using an atomistic approach, which is conducive to observing the deformation mechanisms associated with the nanoindentation cycle. The simulation results of the current modified finite element formulation indicate that the microscopic plastic deformations of the thin film are caused by instabilities of the crystalline structure, and that the commonly used procedure for estimating the contact area in nanoindentation testing is invalid when the indentation size falls in the nanometer regime.

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Virtual element formulation for isotropic damage

Finite Elements in Analysis and Design ◽

10.1016/j.finel.2018.01.002 ◽

2018 ◽

Vol 144 ◽

pp. 38-48 ◽

Cited By ~ 12

Author(s):

Maria Laura De Bellis ◽

Peter Wriggers ◽

Blaž Hudobivnik ◽

Giorgio Zavarise

Keyword(s):

Element Formulation ◽

Isotropic Damage ◽

Virtual Element

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A low-order locking-free hybrid discontinuous Galerkin element formulation for large deformations

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2017.05.018 ◽

2017 ◽

Vol 323 ◽

pp. 353-372 ◽

Cited By ~ 14

Author(s):

Stephan Wulfinghoff ◽

Hamid Reza Bayat ◽

Atefeh Alipour ◽

Stefanie Reese

Keyword(s):

Discontinuous Galerkin ◽

Large Deformations ◽

Element Formulation ◽

Low Order

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The Double Absorbing Boundary Method Incorporated in a High-Order Spectral Element Formulation

Journal of Theoretical and Computational Acoustics ◽

10.1142/s2591728520500073 ◽

2020 ◽

Vol 28 (04) ◽

pp. 2050007

Author(s):

Symeon Papadimitropoulos ◽

Daniel Rabinovich ◽

Dan Givoli

Keyword(s):

Numerical Solution ◽

Spectral Element ◽

High Order ◽

Element Formulation ◽

Finite Element Scheme ◽

Absorbing Boundary ◽

Long Time ◽

Artificial Boundaries ◽

Wave Problems ◽

Low Order

In this paper, we consider the numerical solution of the time-dependent wave equation in a semi-infinite waveguide. We employ the Double Absorbing Boundary (DAB) method, by introducing two parallel artificial boundaries on the side where waves are outgoing. In contrast to the original implementation of the DAB, where the numerical solution involved either a low-order finite difference scheme or a low-order finite element scheme, here we incorporate the DAB into a high-order spectral element formulation, which provides us with very accurate solutions of wave problems in unbounded domains. This is demonstrated by numerical experiments. While the method is highly accurate, it suffers from long-time instability. We show how to postpone the onset of the instability by a prudent choice of the computational parameters.

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Virtual Element Formulation for Finite Strain Elastodynamics

Computer Modeling in Engineering & Sciences ◽

10.32604/cmes.2021.016851 ◽

2021 ◽

Vol 129 (3) ◽

pp. 1151-1180

Author(s):

Mertcan Cihan ◽

BlaŽ Hudobivnik ◽

Fadi Aldakheel ◽

Peter Wriggers

Keyword(s):

Finite Strain ◽

Element Formulation ◽

Virtual Element

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First-order VEM for Reissner–Mindlin plates

Computational Mechanics ◽

10.1007/s00466-021-02095-1 ◽

2021 ◽

Author(s):

A. M. D’Altri ◽

L. Patruno ◽

S. de Miranda ◽

E. Sacco

Keyword(s):

Stiffness Matrix ◽

Piecewise Linear ◽

Piecewise Linear Approximation ◽

Element Formulation ◽

Transverse Displacement ◽

Virtual Element Method ◽

First Order ◽

Independent Variables ◽

Virtual Element ◽

Displacement Based

AbstractIn this paper, a first-order virtual element method for Reissner–Mindlin plates is presented. A standard displacement-based variational formulation is employed, assuming transverse displacement and rotations as independent variables. In the framework of the first-order virtual element, a piecewise linear approximation is assumed for both displacement and rotations on the boundary of the element. The consistent term of the stiffness matrix is determined assuming uncoupled polynomial approximations for the generalized strains, with different polynomial degrees for bending and shear parts. In order to mitigate shear locking in the thin-plate limit while keeping the element formulation as simple as possible, a selective scheme for the stabilization term of the stiffness matrix is introduced, to indirectly enrich the approximation of the transverse displacement with respect to that of the rotations. Element performance is tested on various numerical examples involving both thin and thick plates and different polygonal meshes.

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