Inverse Identification of the Internal Length Scale of Quasi-Brittle Materials Using Nonlocal Damage Models

1997 ◽  
pp. 203-212
Author(s):  
J. Carmeliet
Keyword(s):  
Brittle Materials ◽  
Length Scale ◽  
Inverse Identification ◽  
Internal Length ◽  
Nonlocal Damage ◽  
Damage Models ◽  
Internal Length Scale

Internal length scale and grain boundary yield strength in gradient models of polycrystal plasticity: How do they relate to the dislocation microstructure?

2014 ◽  
Vol 29 (18) ◽  
pp. 2116-2128 ◽  
Author(s):  
Xu Zhang ◽  
Katerina E. Aifantis ◽  
Jochen Senger ◽  
Daniel Weygand ◽  
Michael Zaiser
Keyword(s):  
Yield Strength ◽  
Grain Boundary ◽  
Length Scale ◽  
Internal Length ◽  
Polycrystal Plasticity ◽  
Internal Length Scale ◽  
Image Position ◽  
Gradient Models

Abstract

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>

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.

scholarly journals Comparison of evolving gradient damage formulations with different activity functions

2021 ◽  
Vol 91 (2) ◽  
pp. 597-627
Author(s):  
Adam Wosatko
Keyword(s):  
Strain Softening ◽  
Damage Zone ◽  
Damage Model ◽  
Length Scale ◽  
Internal Length ◽  
Internal Length Scale ◽  
Damage Theory ◽  
Simulation Results ◽  
The Impact ◽  
Gradient Enhancement

AbstractIn the paper, two existing upgrades of the gradient damage model for the simulations of cracking in concrete are compared. The damage theory is made nonlocal via a gradient enhancement to overcome the mesh dependence of simulation results. The implicit gradient model with an averaging equation, where the internal length parameter is assumed as constant during the strain softening analysis, gives unrealistically broadened damage zones. The gradient enhancement of the scalar damage model can be improved via a function of an internal length scale, so an evolution of the gradient activity is postulated during the localization process. Two different modifications of the averaging equation and respective evolving gradient damage formulations are presented. Different activity functions are tested to see whether the formation of a too wide damage zone still occurs. Activating or localizing character of the gradient influence can be introduced and the impact of both approaches on the numerical results is shown in the paper. The aforementioned variants are implemented and examined using the benchmarks of tension in a bar and bending of a cantilever beam.

Vascularized Svelte (Compact) Flow Architectures

2007 ◽  
Author(s):  
Sylvie Lorente ◽  
Adrian Bejan
Keyword(s):  
Length Scale ◽  
Smart Composite ◽  
Total Flow ◽  
Local Pressure ◽  
Internal Length ◽  
Tree Structures ◽  
Pressure Losses ◽  
Single Scale ◽  
Internal Length Scale ◽  
Parallel Microchannels

In this paper we describe a new concept for vascularizing the flow architectures of compact devices. Vascularization is achieved by using tree-shaped (dendritic) flow passages on both sides of the heat transfer surface. For each side, we propose to use an architecture that consists of trees that alternate with upside down trees. By evaluating the fluid flow performance we show that dendritic vascularization is superior to the use of parallel microchannels when the tree structures have four or more levels of bifurcation. The local pressure losses that occur at the multiple junctions of each tree structure become negligible when the svelteness of the architecture (Sv) exceeds the order of 10. The svelteness is a global geometric property defined as the external length scale of the architecture divided by the internal length scale (the total flow volume raised to the power 1/3). The combination of fluid architectures and solid constitute a “smart” composite material: the fluids that bathe the volume can be used to provide multiple functions, such as serf-healing, serf-cooling, and variable transport properties. For example, when placed in counterflow, the vascularized hot and cold sides of the surface are a compact heat exchanger. The article shows under what conditions the tree vascularization offers greater flow access than parallel single-scale channels oriented perpendicularly to the parallel lines.

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.

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