Relaxation of the Non-Convex, Incremental Energy-Minimization Problem in Single-Slip Strain-Gradient Plasticity

2015 ◽  
Vol 651-653 ◽  
pp. 963-968
Author(s):  
Keith Anguige ◽  
Patrick W. Dondl
Keyword(s):  
Existence Of Solutions ◽  
Spatial Scales ◽  
Plastic Behavior ◽  
Gradient Plasticity ◽  
Plastic Deformations ◽  
Single Slip ◽  
Side Condition ◽  
Elasto Plasticity ◽  
Slip Planes ◽  
Incremental Formulation

We consider a variational formulation of gradient elasto-plasticity, as they arise in the incremental formulation of the plastic evolution problem, subject to a class of single-slip side conditions. Such side conditions typically render the associated boundary-value problems non-convex. We first show that, for a large class of plastic deformations, a given single-slip condition (specification of Burgers' vectors and slip planes) can be relaxed by introducing a lamination microstructure. This yields a relaxed side condition which allows for arbitrary slip in a prescribed family of slip planes. This relaxed model can be thought of as an aid to simulating macroscopic plastic behavior without the need to resolve arbitrarily fine spatial scales. We also discuss issues of existence of solutions for the relaxed model.

scholarly journals Relaxation of the single-slip condition in strain-gradient plasticity

2014 ◽  
Vol 470 (2169) ◽  
pp. 20140098 ◽  
Author(s):  
Keith Anguige ◽  
Patrick W. Dondl
Keyword(s):  
Large Class ◽  
Strain Gradient ◽  
Variational Formulation ◽  
Spatial Scales ◽  
Slip Condition ◽  
Geometrically Nonlinear ◽  
Gradient Plasticity ◽  
Single Slip ◽  
Elasto Plasticity ◽  
Stage Process

We consider the variational formulation of both geometrically linear and geometrically nonlinear elasto-plasticity subject to a class of hard single-slip conditions. Such side conditions typically render the associated boundary-value problems non-convex. We show that, for a large class of non-smooth plastic distortions, a given single-slip condition (specification of Burgers vectors) can be relaxed by introducing a microstructure through a two-stage process of mollification and lamination. The relaxed model can be thought of as an aid to simulating macroscopic plastic behaviour without the need to resolve arbitrarily fine spatial scales.

New Analog Experiment for Convergent Regime an example of planet Mercury

2021 ◽  
Author(s):  
Sinan Özeren ◽  
A. M. Celal Şengör ◽  
Dursun Acar ◽  
M. Nazmi Postacıoğlu ◽  
Christian Klimczak ◽  
...  
Keyword(s):  
Coherent Structures ◽  
Spatial Scales ◽  
Regional Scale ◽  
Homogeneous Case ◽  
Thrust Faulting ◽  
Slip Planes ◽  
Series Of Experiments ◽  
Analog Experiment ◽  
Stress Patterns ◽  
Cohesive Material

<div> <div> <div> <div> <div> <div> <div> <div> <p>We conduct a series of experiments to understand the nature of thrust faulting as a result of global thermal contraction in planetary bodies such as Mercury. The spatial scales and patterns of faulting due to contraction are still not very well understood. However, the problem is complicated even for the homogeneous case where the crustal thickness and material properties do not vary spatially. Previous research showed that the thrust faulting patterns are non-random and are arranged in long systems. This is probably due to the regional-scale stress patterns interacting with each other, leading to the creation of coherent structures. We first conduct 1-Axis experiments where we simulate the contraction of the substratum using an elastic ribbon. On top of this we place the material for which the friction, cohesion and thickness can be controlled for each experiment. The shared interface between the frictional-cohesive material and the shortening elastic substratum dictates undulations and finally the generation of slip planes in the upper layer. We discuss the spatial distribution of these patterns spatially. We then speculate the interaction of such patterns on a 2D plane.</p> </div> </div> </div> </div> </div> </div> </div> <div> </div> </div><div> <div> </div> </div>

Influence of Rock Plastic Behavior on the Wellbore Stability

2021 ◽  
Author(s):  
Elena Grishko ◽  
Aboozar Garavand ◽  
Alexey Cheremisin
Keyword(s):  
Failure Criteria ◽  
Wellbore Stability ◽  
Standard Approach ◽  
Plastic Behavior ◽  
Element Formulation ◽  
Geomechanical Model ◽  
Plastic Properties ◽  
Plastic Deformations ◽  
3D Geomechanical Model

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.

HOMOGENIZATION IN GRADIENT PLASTICITY

2011 ◽  
Vol 21 (08) ◽  
pp. 1651-1684 ◽  
Author(s):  
HAUKE HANKE
Keyword(s):  
Elastic Energy ◽  
Classical Model ◽  
Scale Model ◽  
Gradient Term ◽  
Gradient Plasticity ◽  
Elastic Energy Density ◽  
Limit Model ◽  
Elasto Plasticity ◽  
Oscillating Coefficients ◽  
Stored Elastic Energy

This paper yields a two-scale homogenization result for a rate-independent elasto-plastic system. The presented model is a generalization of the classical model of linearized elasto-plasticity with hardening, which is extended by a gradient term of the plastic variables. The associated stored elastic energy density has periodically oscillating coefficients, where the period is scaled by ε > 0. The additional gradient term of the plastic variables z is contained in the elastic energy with a prefactor εγ(γ ≥ 0). We derive different limiting models for ε → 0 in dependence of γ. For γ > 1, the limiting model is the two-scale model derived in Ref. 17, where no gradient term was present. For γ = 1, the gradient term of the plastic variable survives on the microscopic cell problem, while for γ ∈ [0,1) the limit model is defined in terms of a plastic variable without microscopic fluctuation. The latter model can be simplified to a purely macroscopic elasto-plasticity model by homogenization of the elastic part.

Large Elastic-Plastic Deformation Analysis of Rectangular Plates

2002 ◽  
Author(s):  
Reza Naghdabadi ◽  
Mohsen Shahi
Keyword(s):  
Lateral Displacement ◽  
Deformation Analysis ◽  
Plastic Behavior ◽  
Rectangular Plates ◽  
Computationally Efficient ◽  
Plastic Deformations ◽  
Elastic Plastic ◽  
Various Boundary Conditions ◽  
Method Of Solution ◽  
Suitable Combination

The purpose of this paper is to find a fast and simple solution for the large deformation of rectangular plates considering elastic-plastic behavior. This analysis contains material and geometric nonlinearities. For geometric nonlinearity the concept of load analogy is used. In this method the effect of nonlinear terms of lateral displacement is considered as suitable combination of additional fictitious lateral load, edge moment and in-plane forces acting on the plate. Variable Material Property (V.M.P.) method has been used for analysis of material nonlinearity. In this method, the basic relations maintain the form of stress-strain elastic formula, while material properties are modified to take into account the path-dependency involved in elastic-plastic deformations. Therefore, the solution of a von-Karman plate enduring large elastic-plastic deformations is reduced to that of an equivalent elastic plate undergoing small deformations. The method of solution employed in this study is computationally efficient and can easily be used for various boundary conditions and loadings.

A Generalized Load-Penetration Relation for Sharp Indenters and the Indentation Size Effect

2002 ◽  
Vol 69 (3) ◽  
pp. 394-396 ◽  
Author(s):  
Z. Y. Li ◽  
S. Chandrasekar ◽  
H. T. Yang
Keyword(s):  
Size Effect ◽  
Indentation Size Effect ◽  
Material Model ◽  
Plastic Behavior ◽  
Gradient Plasticity ◽  
Indentation Size ◽  
Pressure Sensitive ◽  
Self Similar ◽  
Isotropic Solids

A dimensional analysis has been made of elastic-plastic indentation of an anisotropic solid, and of a solid showing pressure-sensitive yield behavior. It is found that, P∝δ2, for indentation with sharp, self-similar indenters, where P is the load applied by the indenter and δ is the corresponding distance of penetration of the indenter into the solid. This extends and generalizes a similar result obtained for isotropic solids showing conventional plastic behavior. When a strain-gradient plasticity is incorporated into the material model, then it is found that P is no longer proportional to δ2. Implications of the results for the indentation size-effect and for the determination of stress-strain curves from indentation are discussed.

Elasto-Plastic Modeling of Low-Velocity Impact on Functionally Graded Circular Plates

2018 ◽  
Vol 10 (04) ◽  
pp. 1850038 ◽  
Author(s):  
Jamel Mars ◽  
Lotfi Ben Said ◽  
Mondher Wali ◽  
Fakhreddine Dammak
Keyword(s):  
Numerical Algorithms ◽  
Functionally Graded ◽  
Low Velocity Impact ◽  
Plastic Behavior ◽  
Low Velocity ◽  
Velocity Impact ◽  
Hardening Law ◽  
Incremental Formulation ◽  
Graded Material ◽  
Power Law Index

Low-velocity impact of elasto-plastic functionally graded material (FGM) plates is first investigated in this paper based on Mori–Tanaka model to underline micromechanics and locally determine the effective FGM properties and self-consistent method of Suquet for the homogenization of the stress-field. The elasto-plastic behavior of the particle reinforced metal matrix FGM plate is assumed to follow Ludwik hardening law. An incremental formulation of the elasto-plastic constitutive relation is developed to predict the tangent operator. The homogenization formulation and numerical algorithms are implemented into ABAQUS/Standard via a user material subroutine (UMAT) and USDFLD subroutine. The effect of the power-law index on low-velocity impact parameters like contact force, deflection, permanent indentation, velocity distribution and the kinetic energy are examined using the proposed method. With the aim of demonstrating the accuracy and efficiency of the present method, current numerical results are compared to experimental and theoretical results from the literature and show very good agreement.

Dynamic Viscoplastic Response of a Circular Plate Subjected to Underwater Shock

2012 ◽  
Vol 56 (02) ◽  
pp. 71-79
Author(s):  
Z. Zong ◽  
Y. F. Zhang ◽  
L. Zhou
Keyword(s):  
Circular Plate ◽  
Underwater Explosion ◽  
Experimental Tests ◽  
Correct Prediction ◽  
Plastic Behavior ◽  
Marine Structures ◽  
Plastic Deformations ◽  
Structure Interaction ◽  
Double Phase ◽  
Underwater Shock

A structure subjected to underwater shock exhibits surprising dynamic behavior, different from the permanent plastic deformation of a structure subjected to air blast, due to the presence of complicated fluid-structure interaction (FSI) effect. Previous studies of a circular plate subjected to underwater shock indicate that there exist large discrepancies between theoretical and experimental results of plastic deformations. Herein we thus propose a new double-scale and double-phase (DSDP) FSI model for correct prediction of the dynamic plastic behavior of a circular plate subjected to underwater shock. Results obtained from this DSDP model are compared with several experimental tests, with excellent agreement observed. This model is believed useful for further implementation in those software programs that handle underwater explosion and its effects on marine structures.

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