Strain Localization in Determining the Constitutive Response of Polymers

2016 ◽  
Author(s):  
Soondo Kweon ◽  
Ahmed Amine Benzerga
Keyword(s):  
Strain Localization ◽  
Large Strain ◽  
Shear Bands ◽  
Small Strain ◽  
Careful Analysis ◽  
Polymer Materials ◽  
Large Strains ◽  
Temperature Sensitive ◽  
Polymers And Plastics ◽  
Constitutive Response

The constitutive response of glassy polymers is characterized by their complex thermo-mechanical behavior such as strain rate and temperature sensitive yielding, softening at small strains and re-hardening at large strains. These complex behaviors trigger strain localization in the deformation of polymers. Since localization can be induced by both structural and material instabilities, careful analysis needs to be performed to investigate the localization behavior of polymer specimen testing. Localization such as neck formation and propagation that typically occurs in the tensile and compressive testing of polymers and plastics makes it difficult for experimentalists to extract their intrinsic constitutive response. This problem is exacerbated when localization occurs with shear bands. In this study, a macromolecular constitutive model for polymers showing small-strain softening and large-strain directional hardening is employed to investigate the effect of localization in tension onto the constitutive identification process. Considering the complex interplay between the structural and constitutive instabilities, a method based on direct, real-time measurement of area reduction at the neck section has been proposed to extract the intrinsic constitutive response of polymer materials.

Investigation of Small- to Large-Strain Moduli Correlations of Rockfill Materials – Application to Romaine-2 Dam

2021 ◽  
Author(s):  
Ibrahim Lashin ◽  
Michael Ghali ◽  
Marc Smith ◽  
Daniel Verret ◽  
Mourad Karray
Keyword(s):  
Large Strain ◽  
Deformation Behaviour ◽  
Numerical Data ◽  
Small Strain ◽  
Hyperbolic Model ◽  
Large Strains ◽  
Initial Modulus ◽  
Rockfill Materials ◽  
Materials Used

Establishment of a relationship between the shear wave velocity (Vs) and other geotechnical parameters of rockfill soils at large strains (oedometer modulus, Moedo, tangent modulus, Et) is considered a significant step towards more precise modelling of earth-structure deformation behaviour. In this study, four samples of different gradations, reconstituted from the rockfill materials used in the construction of the Romaine-2 dam, were experimented to correlate the small strain to large strain moduli. Development of Moedo and Vs with consolidation was measured in the laboratory using the piezoelectric ring-actuator technique (P-RAT) incorporated in a large oedometer. Therefore, a correlation between Moedo and small strain shear modulus Go was proposed. Moreover, numerical simulations were performed based on the Duncan-Chang hyperbolic model to correlate the Vs to Duncan-Chang initial modulus(Ei). Based on the experimental and numerical data, a relation between Ei and Vs of the tested rockfill has been established. Verification studies were also carried out on in-situ measurements during Romaine-2 dam construction, proofing the ability of the proposed relationships to predict Ei related to the minor principal stress (σ3) from in-situ Vs measurement. The proposed correlations could help the geotechnical designers to estimate accurately the deformation of rockfill materials from in-situ Vs measurement.

Stress-Strain Behavior of Randomly Crosslinked Polydimethylsiloxane Networks

1982 ◽  
Vol 55 (4) ◽  
pp. 1108-1122
Author(s):  
M. Gottlieb ◽  
C. W. Macosko ◽  
T. C. Lepsch
Keyword(s):  
Large Strain ◽  
Strain Energy Function ◽  
Small Strain ◽  
Careful Analysis ◽  
Relative Magnitude ◽  
Polymer Backbone ◽  
Strain Behavior ◽  
Strain Data ◽  
Crosslinked Networks ◽  
Good Agreement

Abstract We have demonstrated by means of our small-strain data that suppression of junction fluctuations cannot solely account for the discrepancy between experimental modulus values and the predictions of the phantom-network theory. The good agreement between the intercepts in Figures 3 and 4 and the value of GN0 leaves little doubt regarding the relation between the two and the validity of the model represented by Equation (12). Further experiments should be carried out on materials with higher GN0 values than the PDMS chains used here. This will magnify the contribution of trapped entanglements and will demonstrate more clearly the effects discussed here. Further study is also required in order to understand the role played by the polymer backbone on the amount of junction suppression. The question raised by Dossin and Graessley as to whether differences in h values for different networks are due to differences in structure between randomly crosslinked and end-linked networks or to differences in the relative magnitude of topological contributions for different polymers was answered by this work. The agreement of the h value obtained here with those obtained for endlinked PDMS networks indicates that no inherent differences in structure exist between endlinked and crosslinked networks and that differences in polymer backbone are responsible for the values of h obtained. Objections that radiation crosslinked networks are somehow not suitable for testing rubber elasticity theories should also be laid to rest by the good agreement of our results with those of Langley and Polmanteer. The large-strain data obtained here show the ability of Flory's strain energy function to correctly model tension-compression data over the range of crosslink densities covered by this work. Edwards' model did not agree well with our data for low degree of crosslinking samples. Further work is still required since our data exhibited relatively small deviations from Mooney-Rivlin behavior. Finally, the extreme importance of the careful analysis of the materials used, the reaction employed, and the resulting networks was demonstrated. The simplest available method for the verification of the network structure is by the determination of the sol fraction. The extraction of solubles in the case of highly crosslinked networks was found to be susceptible to weighing uncertainty and the presence of unreactive material. The former can be avoided by the use of larger samples, while the latter could be removed by vacuum stripping for our material.

Analytical Solutions for Circular Bars Subjected to Large Strain Plastic Torsion

1990 ◽  
Vol 57 (2) ◽  
pp. 298-306 ◽  
Author(s):  
K. W. Neale ◽  
S. C. Shrivastava
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Large Strain ◽  
Kinematic Hardening ◽  
Flow Theory ◽  
Constitutive Laws ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Inelastic Behavior ◽  
Rate Dependent

The inelastic behavior of solid circular bars twisted to arbitrarily large strains is considered. Various phenomenological constitutive laws currently employed to model finite strain inelastic behavior are shown to lead to closed-form analytical solutions for torsion. These include rate-independent elastic-plastic isotropic hardening J2 flow theory of plasticity, various kinematic hardening models of flow theory, and both hypoelastic and hyperelastic formulations of J2 deformation theory. Certain rate-dependent inelastic laws, including creep and strain-rate sensitivity models, also permit the development of closed-form solutions. The derivation of these solutions is presented as well as numerous applications to a wide variety of time-independent and rate-dependent plastic constitutive laws.

The Further Exploration of Applying Small-Strain and Large-Strain Formulations to SMA

2012 ◽  
Vol 529 ◽  
pp. 228-235
Author(s):  
Jie Yao ◽  
Yong Hong Zhu
Keyword(s):  
Phase Transformation ◽  
Constitutive Model ◽  
Uniaxial Tension ◽  
Driving Force ◽  
Research Team ◽  
Large Strain ◽  
Small Deformation ◽  
Small Strain ◽  
Proportional Loading ◽  
The Difference

Recently, our research team has been considering to applying shape memory alloys (SMA) constitutive model to analyze the large and small deformation about the SMA materials because of the thermo-dynamics and phase transformation driving force. Accordingly, our team use simulations method to illustrate the characteristics of the model in large strain deformation and small strain deformation when different loading, uniaxial tension, and shear conditions involve in the situations. Furthermore, the simulation result unveils that the difference is nuance concerning the two method based on the uniaxial tension case, while the large deformation and the small deformation results have huge difference based on shear deformation case. This research gives the way to the further research about the constitutive model of SMA, especially in the multitiaxial non-proportional loading aspects.

A Zebrafish Embryo Behaves both as a “Cortical Shell – Liquid Core” Structure and a Homogeneous Solid when Experiencing Mechanical Forces

2014 ◽  
Vol 20 (6) ◽  
pp. 1841-1847 ◽  
Author(s):  
Fei Liu ◽  
Dan Wu ◽  
Ken Chen
Keyword(s):  
Mechanical Properties ◽  
Mechanical Behavior ◽  
Zebrafish Embryo ◽  
Large Strain ◽  
Liquid Core ◽  
Small Strain ◽  
Core Structure ◽  
Mechanical Forces ◽  
Cortical Shell ◽  
A Cell

AbstractMechanical properties are vital for living cells, and various models have been developed to study the mechanical behavior of cells. However, there is debate regarding whether a cell behaves more similarly to a “cortical shell – liquid core” structure (membrane-like) or a homogeneous solid (cytoskeleton-like) when experiencing stress by mechanical forces. Unlike most experimental methods, which concern the small-strain deformation of a cell, we focused on the mechanical behavior of a cell undergoing small to large strain by conducting microinjection experiments on zebrafish embryo cells. The power law with order of 1.5 between the injection force and the injection distance indicates that the cell behaves as a homogenous solid at small-strain deformation. The linear relation between the rupture force and the microinjector radius suggests that the embryo behaves as membrane-like when subjected to large-strain deformation. We also discuss the possible reasons causing the debate by analyzing the mechanical properties of F-actin filaments.

scholarly journals Micro Shear Bands: Precursor for Strain Localization in Sheared Granular Materials

2019 ◽  
Vol 145 (2) ◽  
pp. 04018104 ◽  
Author(s):  
Siavash Amirrahmat ◽  
Andrew M. Druckrey ◽  
Khalid A. Alshibli ◽  
Riyadh I. Al-Raoush
Keyword(s):  
Granular Materials ◽  
Strain Localization ◽  
Shear Bands

The Axisymmetric Deformation of Linearly and Nonlinearly Elastic Spinning Tubes Under End Thrusts and Torques

1998 ◽  
Vol 65 (1) ◽  
pp. 99-106
Author(s):  
T. J. McDevitt ◽  
J. G. Simmonds
Keyword(s):  
Anisotropic Material ◽  
Large Strain ◽  
Axisymmetric Deformation ◽  
Large Strains ◽  
Shells Of Revolution ◽  
Large Rotation ◽  
Elastic Tubes ◽  
Axisymmetric Bending ◽  
Combined Parameters ◽  
Nonlinearly Elastic

We consider the steady-state deformations of elastic tubes spinning steadily and attached in various ways to rigid end plates to which end thrusts and torques are applied. We assume that the tubes are made of homogeneous linearly or nonlinearly anisotropic material and use Simmonds” (1996) simplified dynamic displacement-rotation equations for shells of revolution undergoing large-strain large-rotation axisymmetric bending and torsion. To exploit analytical methods, we confine attention to the nonlinear theory of membranes undergoing small or large strains and the theory of strongly anisotropic tubes suffering small strains. Of particular interest are the boundary layers that appear at each end of the tube, their membrane and bending components, and the penetration of these layers into the tube which, for certain anisotropic materials, may be considerably different from isotropic materials. Remarkably, we find that the behavior of a tube made of a linearly elastic, anisotropic material (having nine elastic parameters) can be described, to a first approximation, by just two combined parameters. The results of the present paper lay the necessary groundwork for a subsequent analysis of the whirling of spinning elastic tubes under end thrusts and torques.

scholarly journals Tilt and strain change during the explosion at Minami-dake, Sakurajima, on November 13, 2017

2021 ◽  
Author(s):  
Kohei Hotta ◽  
Masato Iguchi
Keyword(s):  
Ground Deformation ◽  
Large Strain ◽  
Phase 1 ◽  
Small Strain ◽  
Phase 2 ◽  
The North ◽  
Strombolian Eruption ◽  
Strain Change ◽  
Tilt Change

Abstract We herein propose an alternative model for deformation caused by an eruption at Sakurajima, which have been previously interpreted as being due to a Mogi-type spherical point source beneath Minami-dake. On November 13, 2017, a large explosion with a plume height of 4,200 m occurred at Minami-dake. During the three minutes following the onset of the explosion (November 13, 2017, 22:07–22:10 (Japan standard time (UTC+9); the same hereinafter), phase 1, a large strain change was detected at the Arimura observation tunnel (AVOT) located approximately 2.1 km southeast from the Minami-dake crater. After the peak of the explosion (November 13, 2017, 22:10–24:00), phase 2, a large deflation was detected at every monitoring station due to the continuous Strombolian eruption. Subsidence toward Minami-dake was detected at five out of six stations whereas subsidence toward the north of Sakurajima was detected at the newly installed Komen observation tunnel (KMT), located approximately 4.0 km northeast from the Minami-dake crater. The large strain change at AVOT as well as small tilt changes of all stations and small strain changes at HVOT and KMT during phase 1 can be explained by a very shallow deflation source beneath Minami-dake at 0.1 km below sea level (bsl). For phase 2, a deeper deflation source beneath Minami-dake at a depth of 3.3 km bsl was found in addition to the shallow source beneath Minami-dake which turned inflation after the deflation obtained during phase 1. However, this model cannot explain the tilt change of KMT. Adding a spherical deflation source beneath Kita-dake at a depth of 3.2 km bsl can explain the tilt and strain change at KMT and the other stations. The Kita-dake source was also found in a previous study of long-term ground deformation. Not only the deeper Minami-dake source MD but also the Kita-dake source deflated due to the Minami-dake explosion.

Numerical Modelling of Plastic Deformation and Subsequent Recrystallization in Polycrystalline Materials, Based on a Digital Material Framework

2007 ◽  
Vol 558-559 ◽  
pp. 1133-1138 ◽  
Author(s):  
Roland E. Logé ◽  
M. Bernacki ◽  
H. Resk ◽  
H. Digonnet ◽  
T. Coupez
Keyword(s):  
Level Set ◽  
Large Strain ◽  
Voronoi Tessellation ◽  
Constitutive Law ◽  
Polycrystalline Materials ◽  
Large Strains ◽  
Element Mesh ◽  
Digital Material ◽  
Digital Sample ◽  
Level Set Approach

The development of a digital material framework is presented, allowing to build virtual microstructures in agreement with experimental data. The construction of the virtual material consists in building a multi-level Voronoï tessellation. A polycrystalline microstructure made of grains and sub-grains can be obtained in a random or deterministic way. A corresponding finite element mesh can be generated automatically in 3D, and used for the simulation of mechanical testing under large strain. In the examples shown in this work, the initial mesh was non uniform and anisotropic, taking into account the presence of interfaces between grains and sub-grains. Automatic remeshing was performed due to the large strains, and maintained the non uniform and anisotropic character of the mesh. A level set approach was used to follow the grain boundaries during the deformation. The grain constitutive law was either a viscoplastic power law, or a crystallographic formulation based on crystal plasticity. Stored energies and precise grain boundary network geometries were obtained directly from the deformed digital sample. This information was used for subsequent modelling of grain growth with the level set approach, on the same mesh.

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