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.

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.

COUPLED ANALYSIS OF DAMAGE IN MULTIPHASE MEDIA

2012 ◽  
Vol 04 (02) ◽  
pp. 1250008
Author(s):  
MARZIYEH FATHALIKHANI ◽  
BEHROUZ GATMIRI
Keyword(s):  
Damage Model ◽  
Coupled Analysis ◽  
Model Parameters ◽  
State Variables ◽  
Damage Development ◽  
Water Conductivity ◽  
Internal Length ◽  
Finite Element Program ◽  
Independent State ◽  
The Impact

In this paper, the theoretical framework of a coupled thermo-hydro-mechanical damage model dedicated to non-isothermal unsaturated porous media is presented. The damage variable is a second-order tensor, and the model has been formulated in independent state variables. The approach combines thermodynamic and micromechanical theories. The behavior laws have been derived from a postulated expression of Helmholtz free energy. The damaged rigidities have been computed by applying the Principle of Equivalent Elastic Energy (PEEE). Internal length parameters have been introduced in the expressions of liquid water conductivity, to account for cracking effects on fluid flows. Damage has been assumed to have an isotropic influence on air and heat flows, through the inelastic component of volumetric strains. The damage model has been implemented in θ-Stock Finite Element program. Some numerical studies are conducted to the impact of the thermal and mechanical loading on the evaluation of response of the unsaturated bentonite, and investigation of model parameters effect on damage development.

A Physically Motivated Internal State Variable Plasticity/Damage Model Embedded With a Length Scale for Hazmat Tank Cars’ Structural Integrity Applications

2011 ◽  
Author(s):  
Fazle R. Ahad ◽  
Koffi Enakoutsa ◽  
Kiran N. Solanki ◽  
Yustianto Tjipowidjojo ◽  
Douglas J. Bammann
Keyword(s):  
Evolution Equation ◽  
Internal State ◽  
Damage Model ◽  
Mesh Size ◽  
Material Behavior ◽  
Length Scale ◽  
Internal State Variable ◽  
State Variable ◽  
Fe Simulations ◽  
The Impact

In this study, we use a physically-motivated internal state variable plasticity/damage model containing a mathematical length scale to represent the material behavior in finite element (FE) simulations of a large scale boundary value problem. This problem consists of a moving striker colliding against a stationary hazmat tank car. The motivations are (1) to reproduce with high fidelity finite deformation and temperature histories, damage, and high rate phenomena which arise during the impact and (2) to address the pathological mesh size dependence of the FE solution in the post-bifurcation regime. We introduce the mathematical length scale in the model by adopting a nonlocal evolution equation for the damage, as suggested by Pijaudier-Cabot and Bazant (1987) in the context of concrete. We implement this evolution equation into existing implicit and explicit versions of the FE subroutines of the plasticity/failure model. The results of the FE simulations, carried out with the aid of Abaqus/Explicit FE code, show that the material model, accounting for temperature histories and nonlocal damage effects, satisfactorily predicts the damage progression during the tank car impact accident and significantly reduces the pathological mesh size effects.

Size effect analysis of quasi-brittle fracture with localizing gradient damage model

2021 ◽  
pp. 105678952098387
Author(s):  
Yi Zhang ◽  
Amit S. Shedbale ◽  
Yixiang Gan ◽  
Juhyuk Moon ◽  
Leong H. Poh
Keyword(s):  
Brittle Fracture ◽  
Size Effect ◽  
Fracture Process ◽  
Fracture Process Zone ◽  
Concrete Beams ◽  
Process Zone ◽  
Damage Zone ◽  
Damage Model ◽  
Lattice Models ◽  
Gradient Enhancement

The size effect of a quasi-brittle fracture is associated with the size of fracture process zone relative to the structural characteristic length. In numerical simulations using damage models, the nonlocal enhancement is commonly adopted to regularize the softening response. However, the conventional nonlocal enhancement, both integral and gradient approaches, induces a spurious spreading of damage zone. Since the evolution of fracture process zone cannot be captured well, the conventional nonlocal enhancement cannot predict the size effect phenomenon accurately. In this paper, the localizing gradient enhancement is adopted to avoid the spurious spreading of damage. Considering the three-point bend test of concrete beams, it is demonstrated that the dissipation profiles obtained with the localizing gradient enhancement compare well with those of reference meso-scale lattice models. With the correct damage evolution process, the localizing gradient enhancement is shown to capture the size effect phenomenon accurately for a series of geometrically similar concrete beams, using only a single set of material parameters.

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