A Variational Model of Elasto-Plastic Behavior of Materials

2022 ◽  
Author(s):  
Pietro Pascale ◽  
Kumar Vemaganti
Keyword(s):  
Variational Model ◽  
Plastic Behavior

Delamination in the scoring and folding of paperboard

TAPPI Journal ◽  
2012 ◽  
Vol 11 (1) ◽  
pp. 61-66 ◽  
Author(s):  
DOEUNG D. CHOI ◽  
SERGIY A. LAVRYKOV ◽  
BANDARU V. RAMARAO
Keyword(s):  
Finite Element ◽  
Plane Deformation ◽  
Strain Analysis ◽  
Local Strain ◽  
Uniaxial Stress ◽  
Material Model ◽  
Element Model ◽  
Plastic Behavior ◽  
Stress Strain ◽  
Strain Fields

Delamination between layers occurs during the creasing and subsequent folding of paperboard. Delamination is necessary to provide some stiffness properties, but excessive or uncontrolled delamination can weaken the fold, and therefore needs to be controlled. An understanding of the mechanics of delamination is predicated upon the availability of reliable and properly calibrated simulation tools to predict experimental observations. This paper describes a finite element simulation of paper mechanics applied to the scoring and folding of multi-ply carton board. Our goal was to provide an understanding of the mechanics of these operations and the proper models of elastic and plastic behavior of the material that enable us to simulate the deformation and delamination behavior. Our material model accounted for plasticity and sheet anisotropy in the in-plane and z-direction (ZD) dimensions. We used different ZD stress-strain curves during loading and unloading. Material parameters for in-plane deformation were obtained by fitting uniaxial stress-strain data to Ramberg-Osgood plasticity models and the ZD deformation was modeled using a modified power law. Two-dimensional strain fields resulting from loading board typical of a scoring operation were calculated. The strain field was symmetric in the initial stages, but increasing deformation led to asymmetry and heterogeneity. These regions were precursors to delamination and failure. Delamination of the layers occurred in regions of significant shear strain and resulted primarily from the development of large plastic strains. The model predictions were confirmed by experimental observation of the local strain fields using visual microscopy and linear image strain analysis. The finite element model predicted sheet delamination matching the patterns and effects that were observed in experiments.

Elastic-plastic behavior of coldworked holes

1983 ◽  
Author(s):  
H. ARMEN ◽  
A. LEVY ◽  
H. EIDINOFF
Keyword(s):  
Plastic Behavior ◽  
Elastic Plastic

A Multiscale Variational Model for Image Decomposition

2014 ◽  
Vol 35 (5) ◽  
pp. 1190-1195
Author(s):  
Jian Bai ◽  
Xiang-chu Feng ◽  
Xu-dong Wang
Keyword(s):  
Image Decomposition ◽  
Variational Model

scholarly journals Lath Martensite Microstructure Modeling: A High-Resolution Crystal Plasticity Simulation Study

Materials ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 691
Author(s):  
Francisco-José Gallardo-Basile ◽  
Yannick Naunheim ◽  
Franz Roters ◽  
Martin Diehl
Keyword(s):  
High Resolution ◽  
Mechanical Behavior ◽  
Crystal Plasticity ◽  
Lath Martensite ◽  
Three Dimensional ◽  
Building Blocks ◽  
Quantitative Agreement ◽  
Carbon Steels ◽  
Plastic Behavior ◽  
Austenitic Phase

Lath martensite is a complex hierarchical compound structure that forms during rapid cooling of carbon steels from the austenitic phase. At the smallest, i.e., ‘single crystal’ scale, individual, elongated domains, form the elemental microstructural building blocks: the name-giving laths. Several laths of nearly identical crystallographic orientation are grouped together to blocks, in which–depending on the exact material characteristics–clearly distinguishable subblocks might be observed. Several blocks with the same habit plane together form a packet of which typically three to four together finally make up the former parent austenitic grain. Here, a fully parametrized approach is presented which converts an austenitic polycrystal representation into martensitic microstructures incorporating all these details. Two-dimensional (2D) and three-dimensional (3D) Representative Volume Elements (RVEs) are generated based on prior austenite microstructure reconstructed from a 2D experimental martensitic microstructure. The RVEs are used for high-resolution crystal plasticity simulations with a fast spectral method-based solver and a phenomenological constitutive description. The comparison of the results obtained from the 2D experimental microstructure and the 2D RVEs reveals a high quantitative agreement. The stress and strain distributions and their characteristics change significantly if 3D microstructures are used. Further simulations are conducted to systematically investigate the influence of microstructural parameters, such as lath aspect ratio, lath volume, subblock thickness, orientation scatter, and prior austenitic grain shape on the global and local mechanical behavior. These microstructural features happen to change the local mechanical behavior, whereas the average stress–strain response is not significantly altered. Correlations between the microstructure and the plastic behavior are established.

scholarly journals Advanced Constitutive Modeling of the Thixotropic Elasto-Visco-Plastic Behavior of Blood: Steady-State Blood Flow in Microtubes

Materials ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 367
Author(s):  
Konstantinos Giannokostas ◽  
Yannis Dimakopoulos ◽  
Andreas Anayiotos ◽  
John Tsamopoulos
Keyword(s):  
Blood Flow ◽  
Steady State ◽  
Constitutive Model ◽  
Blood Plasma ◽  
Constitutive Modeling ◽  
Flow Direction ◽  
Momentum Balance ◽  
Plastic Behavior ◽  
Flow Investigation ◽  
The Impact

The present work focuses on the in-silico investigation of the steady-state blood flow in straight microtubes, incorporating advanced constitutive modeling for human blood and blood plasma. The blood constitutive model accounts for the interplay between thixotropy and elasto-visco-plasticity via a scalar variable that describes the level of the local blood structure at any instance. The constitutive model is enhanced by the non-Newtonian modeling of the plasma phase, which features bulk viscoelasticity. Incorporating microcirculation phenomena such as the cell-free layer (CFL) formation or the Fåhraeus and the Fåhraeus-Lindqvist effects is an indispensable part of the blood flow investigation. The coupling between them and the momentum balance is achieved through correlations based on experimental observations. Notably, we propose a new simplified form for the dependence of the apparent viscosity on the hematocrit that predicts the CFL thickness correctly. Our investigation focuses on the impact of the microtube diameter and the pressure-gradient on velocity profiles, normal and shear viscoelastic stresses, and thixotropic properties. We demonstrate the microstructural configuration of blood in steady-state conditions, revealing that blood is highly aggregated in narrow tubes, promoting a flat velocity profile. Additionally, the proper accounting of the CFL thickness shows that for narrow microtubes, the reduction of discharged hematocrit is significant, which in some cases is up to 70%. At high pressure-gradients, the plasmatic proteins in both regions are extended in the flow direction, developing large axial normal stresses, which are more significant in the core region. We also provide normal stress predictions at both the blood/plasma interface (INS) and the tube wall (WNS), which are difficult to measure experimentally. Both decrease with the tube radius; however, they exhibit significant differences in magnitude and type of variation. INS varies linearly from 4.5 to 2 Pa, while WNS exhibits an exponential decrease taking values from 50 mPa to zero.

scholarly journals On the Kirchhoff-Love Hypothesis (Revised and Vindicated)

2021 ◽  
Author(s):  
Olivier Ozenda ◽  
Epifanio G. Virga
Keyword(s):  
Free Energy ◽  
Dimension Reduction ◽  
Three Dimensional ◽  
Energy Functional ◽  
The Other ◽  
Variational Model ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Kinematic Constraint ◽  
Free Energy Functional

AbstractThe Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard $\varGamma $ Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with standard $\varGamma $ Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.

scholarly journals Reconstruction of Multi-Temporal Satellite Imagery by Coupling Variational Segmentation and Radiometric Analysis

2021 ◽  
Vol 10 (1) ◽  
pp. 17
Author(s):  
Nicola Case ◽  
Alfonso Vitti
Keyword(s):  
Image Segmentation ◽  
Variational Model ◽  
Great Level ◽  
Radiometric Analysis ◽  
Variational Segmentation ◽  
Landsat 7 ◽  
Multi Temporal ◽  
Original Procedure ◽  
Variational Image ◽  
Homogeneous Regions

Digital images, and in particular satellite images acquired by different sensors, may present defects due to many causes. Since 2013, the Landsat 7 mission has been affected by a well-known issue related to the malfunctioning of the Scan Line Corrector producing very characteristic strips of missing data in the imagery bands. Within the vast and interdisciplinary image reconstruction application field, many works have been presented in the last few decades to tackle the specific Landsat 7 gap-filling problem. This work proposes another contribution in this field presenting an original procedure based on a variational image segmentation model coupled with radiometric analysis to reconstruct damaged images acquired in a multi-temporal scenario, typical in satellite remote sensing. The key idea is to exploit some specific features of the Mumford–Shah variational model for image segmentation in order to ease the detection of homogeneous regions which will then be used to form a set of coherent data necessary for the radiometric reconstruction of damaged regions. Two reconstruction approaches are presented and applied to SLC-off Landsat 7 data. One approach is based on the well-known histogram matching transformation, the other approach is based on eigendecomposition of the bands covariance matrix and on the sampling from Gaussian distributions. The performance of the procedure is assessed by application to artificially damaged images for self-validation testing. Both of the proposed reconstruction approaches had led to remarkable results. An application to very high resolution WorldView-3 data shows how the procedure based on variational segmentation allows an effective reconstruction of images presenting a great level of geometric complexity.

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