scholarly journals A Finite Points Method Approach for Strain Localization Using the Gradient Plasticity Formulation

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Luis Pérez Pozo ◽  
Andy Campos ◽  
Sheila Lascano ◽  
Sergio Oller ◽  
Antonio Rodríguez-Ferran
Keyword(s):  
Strain Localization ◽  
Scale Parameter ◽  
Material Model ◽  
Gradient Plasticity ◽  
Governing Equations ◽  
Internal Length ◽  
Loss Of Ellipticity ◽  
Internal Length Scale ◽  
Discretization Technique ◽  
Method Approach

The softening elastoplastic models present an unsuitable behavior after reaching the yield strength: unbounded strain localization. Because of the material instability, which is reflected in the loss of ellipticity of the governing partial differential equations, the solution depends on the discretization. The present work proposes to solve this dependency using the meshless Finite Points Method. This meshfree spatial discretization technique allows enriching the governing equations using gradient’s plasticity and introducing an internal length scale parameter at the material model in order to objectify the solution.

Stress–elastic strain relation for a two-phase isotropic strain gradient plastic composite

2009 ◽  
Vol 20 (4) ◽  
pp. 319-342
Author(s):  
VIET HA HOANG
Keyword(s):  
Strain Gradient ◽  
Elastic Strain ◽  
Constitutive Law ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Two Phase ◽  
Internal Length ◽  
Plastic Composite ◽  
Strain Relationship ◽  
Internal Length Scale

The stress–elastic strain relationship is studied for a composite under a plastic deformation. The constitutive law of each component is described by a deformation theory of strain gradient plasticity which introduces an internal length scale. The conventional deformation plastic theory is obtained when the internal length scale tends to 0. The Hashin–Shtrikman upper bound for a two-phase composite governed by a power law is derived. It is predicted, by differentiating the bounds, that in most cases, the stress and the elastic strain follow a non-linear relation immediately after the elastic range. However, for some particular values of the ratio of the internal length scale and the micro-scale of the composite, this relation is linear. The prediction is illustrated by various numerical examples.

Gradient plasticity used for modeling extrinsic and intrinsic size effects in the torsion of Au microwires

2016 ◽  
Vol 25 (1-2) ◽  
pp. 53-56
Author(s):  
Xiaokun Wei ◽  
Avraam Konstantinidis ◽  
Chengzhi Qi ◽  
Elias Aifantis
Keyword(s):  
Grain Size ◽  
Sample Size ◽  
Plasticity Theory ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Internal Length ◽  
Size Dependent ◽  
Internal Length Scale ◽  
Model Size ◽  
Phenomenological Coefficients

AbstractThe gradient plasticity theory proposed by Aifantis and coworkers has been successfully used to model size effect phenomena at the microscale and nanoscale, by introducing into the formulation an internal length scale associated with the phenomenological coefficients of the gradient plasticity model. In this paper, Aifantis’ gradient plasticity theory is applied to model the sample size-dependent torsion of thin wires, with a strain-dependent internal length scale as well as grain size dependence based on the Hall-Petch relationship. This study reveals that internal length scale is related with sample size and grain size, with such a connection determined by the ductility of the material.

A regularized continuum model for fault zones with rate and state friction

2021 ◽  
Author(s):  
Mohsen Goudarzi ◽  
René de Borst ◽  
Taras Gerya ◽  
Meng Li ◽  
van Dinther Ylona
Keyword(s):  
Numerical Model ◽  
Fault Zone ◽  
Induced Seismicity ◽  
Subduction Zones ◽  
Bulk Material ◽  
Fault Zones ◽  
Length Scale ◽  
Internal Length ◽  
Internal Length Scale ◽  
Earthquake Sequences

<p>Accurate representation of fault zones is important in many applications in Earth sciences, including natural and induced seismicity. The framework developed here can efficiently model fault zone localization, evolution, and spontaneous fully dynamic earthquake sequences in a continuum plasticity framework. The geometrical features of the faults are incorporated into a regularized continuum framework, while the response of the fault zone is governed by a rate and state-dependent friction. Although a continuum plasticity model is advantageous to discrete approaches in representing evolving, unknown, or arbitrarily positioned faults, it is known that either non-associated plasticity or strain-softening can lead to mesh sensitivity of the numerical results in absence of an internal length scale. A common way to regularize the numerical model and introduce an internal length scale is by the adoption of a Kelvin-type visco-plasticity element. The visco-plastic rheological behavior for the bulk material is implemented along with a return-mapping algorithm for accurate stress and strain evolution. High slip rates (in the order of 1 m/s) are captured through numerical examples of a predefined strike-slip fault zone, where a detailed comparison with a reference discrete fault model is presented. Additionally, the regularization effect of the Kelvin viscosity parameter is studied on the fault slip velocity for a growing fault zone due to an initial material imperfection.  The model is consistently linearized leading to quadratic convergence of the Newton solver. Although the proposed framework is a step towards the modeling of earthquake sequences for induced seismicity applications, the numerical model is general and can be applied to all tectonic settings including subduction zones.</p><div> <div> <div> </div> <div> <div> <div> </div> <div> <p> </p> <p> </p> </div> </div> </div> </div> </div>

Two-Dimensional Numerical Simulations of a Biphasic Representation of Human Tibia in Car-Pedestrian Accidents

2008 ◽  
Author(s):  
Haibin Chen ◽  
Xuemei Cheng ◽  
King H. Yang
Keyword(s):  
Simulation Analysis ◽  
Fluid Phase ◽  
Material Model ◽  
Injury Mechanism ◽  
Two Dimensional ◽  
Governing Equations ◽  
Human Tibia ◽  
Pedestrian Accidents ◽  
Poroelastic Material ◽  
Poroelastic Model

A two-dimensional poroelastic model of the tibia was developed to improve the understanding of injury mechanism of tibia during car-to-pedestrian impacts. A “poroelastic” approach was utilized to establish the governing equations of human tibia, and the finite element method was applied to solve these governing equations. Both the cortical and cancellous components of tibia were represented using a poroelastic material model consisted of a solid and a fluid phase. The geometry of the model was reconstructed from CT scans of the left tibia of a living human volunteer. A lateral-medial impact direction was selected in the simulation analysis. Correspondingly, the tibia poroelastic model was validated against published shearing experiments with the whole PMHS tibia. The model predictions showed good agreement against the PMHS test data. The developed poroelastic model can be used as a helpful tool to investigate injury mechanism of the tibia in car-to-pedestrian accidents.

Intrinsic and Extrinsic Size Effects in Plasticity by Dislocation Glide

2000 ◽  
Vol 653 ◽  
Author(s):  
J. Gil Sevillano
Keyword(s):  
Size Effects ◽  
Mixed Effects ◽  
Length Scale ◽  
Internal Length ◽  
Strain Gradients ◽  
Dislocation Glide ◽  
Spatial Gradients ◽  
Internal Length Scale ◽  
Plastic Process

AbstractA classification of size effects (SE) in plasticity is attempted. ”Intrinsic” SE are perceived when any internal length scale directly influencing some process or property interferes with the size of the material region where the process is going on or when two internal length scales directly affecting the same process or property interfere. ”Extrinsic” SE arise from the external imposition of spatial gradients in the plastic process or by the building up of internal gradients by the (externally induced) process itself. In dislocation-mediated plasticity plastic strain gradients are resolved by the storage of geometrically necessary dislocations (GND) leading to prominent size effects. Of course, mixed effects with intrinsic and extrinsic contributions can be found as well as superposed effects involving more than two characteristic lengths (i.e., size effects on size effects).The inclusion of both types of SE in continuum or crystallographic theories is commented.

A Modified Gradient Plasticity Theory for Micro-Bending and Micro-Torsion Size Effects

2004 ◽  
Author(s):  
George Z. Voyiadjis ◽  
Rashid K. Abu Al-Rub
Keyword(s):  
Size Effects ◽  
Scale Parameter ◽  
Plasticity Theory ◽  
Material Behavior ◽  
Length Scale Parameter ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Non Local ◽  
Material Length Scale ◽  
Material Length

The definition and magnitude of the intrinsic length scale are keys to the development of the theory of plasticity that incorporates size effects. Gradient plasticity theory with a material length scale parameter is successfully in capturing the size dependence of material behavior at the micron scale. However, a fixed value of the material length-scale is not always realistic and that different problems could require different values. Moreover, a linear coupling between the local and non-local terms in the gradient plasticity theory is not always realistic and that different problems could require different couplings. A generalized gradient plasticity model with a non-fixed length scale parameter is proposed. This model assesses the sensitivity of predictions in the way in which the local and non-local parts are coupled. The proposed model gives good predictions of the size effect in micro-bending tests of thin films and micro-torsion tests of thin wires.

Use of Digital Image Correlation to Track Strain Evolution in Compressed Masonry Piers

2015 ◽  
Vol 732 ◽  
pp. 337-340
Author(s):  
Jakub Antoš ◽  
Václav Nežerka ◽  
Pavel Tesárek
Keyword(s):  
Digital Image Correlation ◽  
Digital Image ◽  
Strain Localization ◽  
Material Model ◽  
Element Model ◽  
Image Correlation ◽  
Full Field ◽  
Constitutive Material Model ◽  
The Cost ◽  
Constitutive Material

In order to develop a constitutive material model and to verify its consistency when implemented in a computational code, it is necessary to understand the material and to carry out a comprehensive experimental analysis. This can be a challenging task in the case of composite materials and structures, such as masonry, when using conventional measurements. Strain gauges and allow recording strains at a limited number of discrete points and do not provide sufficient amount of data, thus increasing the cost of the analysis. From that reason a full-field non-contact measurements, such as Digital Image Correlation (DIC), became very popular and valuable for analysis of structures subjected to mechanical loading and precise detection of the onset of strain localization. The presented study deals with tracking the strain localization using DIC in the case of masonry piers loaded by the combination of bending and compression. In such case the strain localizes into more compliant mortar joints while the complete collapse occurs when the masonry blocks fail to transfer tensile stress due to transversal expansion. The obtained data will be used for the validation of a finite element model to predict the behavior of masonry structures.

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