Stress constraints in simple bodies undergoing large strains: a variational approach

2015 ◽  
Vol 145 (6) ◽  
pp. 1183-1214 ◽  
Author(s):  
Mariano Giaquinta ◽  
Paolo Maria Mariano ◽  
Giuseppe Modica
Keyword(s):  
Large Strain ◽  
Stress Constraints ◽  
Large Strains ◽  
Kirchhoff Stress ◽  
Rank Tensor ◽  
Equilibrium Configurations ◽  
Kirchhoff Stress Tensor ◽  
Simple Body ◽  
Related Stress ◽  
Dislocation Walls

We consider a simple body that is hyperelastic in the large-strain regime until the 3-covector defining the first Piola–Kirchhoff stress, once it has been projected on the appropriate second-rank tensor space, reaches a threshold indicating critical states. No information is given on the post-critical behaviour. We determine the existence of equilibrium configurations according to the constraint. Such configurations can have a concentration of strain in regions with vanishing volume. The related stress appears naturally as a measure over the deformation graph. Once it is restricted to the regular part of the deformation, such a measure determines the first Piola–Kirchhoff stress tensor and may also be concentrated over sets with vanishing volume projections on the reference and current placements. These configurations in space can be interpreted as dislocations or dislocation walls. We analyse explicitly specific cases.

scholarly journals Correction to: An efficient and stabilised SPH method for large strain metal plastic deformations

2019 ◽  
Vol 7 (3) ◽  
pp. 541-541
Author(s):  
Giorgio Greto ◽  
Sivakumar Kulasegaram
Keyword(s):  
Stress Tensor ◽  
Large Strain ◽  
Sph Method ◽  
Plastic Deformations ◽  
Kirchhoff Stress ◽  
Time Stepping ◽  
Kirchhoff Stress Tensor

The symbol was introduced incorrectly inside the “Time-stepping the solution” box, directly under the “Compute first Piola–Kirchhoff stress tensor Pi” as in “Appendix A” listing.

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 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.

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.

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.

Large-Strain Axisymmetric Deformation of Cylindrical Shells

1987 ◽  
Vol 54 (2) ◽  
pp. 287-291 ◽  
Author(s):  
G. W. Brodland ◽  
H. Cohen
Keyword(s):  
Nonlinear Equations ◽  
Energy Minimization ◽  
Parametric Analysis ◽  
Large Strain ◽  
Cylindrical Shells ◽  
Radial Force ◽  
Axisymmetric Deformation ◽  
The Other ◽  
Large Strains ◽  
Minimization Technique

Nonlinear equations are derived for the axisymmetric deformation of thin, cylindrical shells made of Mooney-Rivlin materials and subject to arbitrarily large strains and rotations. These equations are then implemented numerically using an energy minimization technique. Finally, an extensive parametric analysis is done of cylindrical shells which are clamped at one end and loaded with either a radial force or an edge moment uniformly distributed along the circumference of the other end.

Comparison of Three Material Models to Predict the Time-Dependent Deformation of a Single Cell Under Micropipette Aspiration

2008 ◽  
Author(s):  
Ruogang Zhao ◽  
Kristine Wyss ◽  
Craig A. Simmons
Keyword(s):  
Experimental Data ◽  
Large Strain ◽  
Single Cells ◽  
Material Model ◽  
Micropipette Aspiration ◽  
Time Dependent ◽  
Large Strains ◽  
Fe Model ◽  
Whole Cells ◽  
Model Combining

Micropipette aspiration is an experimental technique that is used widely to measure the mechanical properties of single cells [1]. The viscoelastic properties of the probed cell are often estimated by fitting experimental data to a three-parameter standard linear solid (SLS) half-space model (e.g., [1]). However, this analytical model does not account for the large strains that can occur with micropipette aspiration. This limitation has motivated the development of numerical methods to interpret the experimental data. For example, Zhou [2] implemented a material model combining a hyperelastic neo-Hookean material and a viscoelastic SLS material in an axisymmetric finite element (FE) model to simulate large strain micropipette aspiration of a suspended cell. The time-dependent creep deformation of cells has also been described by power-law rheology [3]; this material model has been applied to micropipette aspiration of nuclei [4], but not whole cells.

Dynamic Recrystallization of Zircaloy-4 during Working within the Upper α-Range

2004 ◽  
Vol 467-470 ◽  
pp. 1151-1156 ◽  
Author(s):  
Cédric Chauvy ◽  
Pierre Barbéris ◽  
Frank Montheillet
Keyword(s):  
Dynamic Recrystallization ◽  
Large Strain ◽  
Large Angle ◽  
Rate Sensitivity ◽  
Large Strains ◽  
Strain Rates ◽  
Compression Tests ◽  
Continuous Dynamic Recrystallization ◽  
Ebsd Technique ◽  
Continuous Dynamic

Compression tests were used to simulate simple deformation paths within the upper a-range of Zircaloy-4 (i.e. 500°C-750°C). The mechanical behaviour reveals two different domains : at low temperatures and large strain rates, strain hardening takes place before flow softening, whereas this first stage disappears at lower flow stress levels. Strain rate sensitivity and activation energy were determined for both domains. Dynamic recrystallization was investigated using the Electron BackScattering Diffraction (EBSD) technique. It appears that the mechanism involved here is continuous dynamic recrystallization (CDRX), based on the increasing misorientation of subgrain boundaries and their progressive transformation into large angle boundaries. At low strains (e £ 0.3), CDRX kinetics are similar whatever the deformation conditions, while higher temperatures and lower strain rates promote recrystallization at large strains.

Determination of the Anisotropic Hardening of Sheet Metals at Large Strain from Stretch Bending Test

2016 ◽  
Vol 725 ◽  
pp. 677-682
Author(s):  
Gustavo Capilla ◽  
Hiroshi Hamasaki ◽  
Fusahito Yoshida ◽  
Toshiya Suzuki ◽  
Kazuo Okamura
Keyword(s):  
Large Strain ◽  
Rolling Direction ◽  
High Strength ◽  
Uniaxial Stress ◽  
Bending Test ◽  
Weighting Coefficient ◽  
Large Strains ◽  
Sheet Metals ◽  
Stress Strain ◽  
Stretch Bending

The present study aims to determine stress-strain curves at large strains of sheet metals under the uniaxial stress state by using the in-plane stretch-bending test. The combined Swift-Voce model, which describes the large-strain work-hardening of materials by means of a weighting coefficient μ, was used for FE simulation of the stretch-bending. The coefficient μ was determined by minimizing the difference in punch stroke vs. bending strain responses between the experimental data and the corresponding experimental results. By using this inverse approach, stress-strain curves of two levels of high-strength steel sheets of a precipitation hardening type, 590R and 780R, in three sheet directions (0, 45 and 90o from rolling direction), were determined.

scholarly journals Characterization of Flow Induced Anisotropy in Sheet Metal at Large Strain

2021 ◽  
Author(s):  
F. Gutknecht ◽  
H. Traphöner ◽  
T. Clausmeyer ◽  
A. E. Tekkaya
Keyword(s):  
Strain Rate ◽  
Sheet Metal ◽  
Strain Path ◽  
Large Strain ◽  
High Strength ◽  
Bulge Test ◽  
Large Strains ◽  
Steel Grades ◽  
Strain Path Change ◽  
Cross Hardening

Abstract Background Many metals exhibit a stress overshoot, the so-called cross-hardening when subjected to a specific strain-path change. Existing tests for sheet metals are limited to an equivalent prestrain of 0.2 and show varying levels of cross-hardening for identical grades. Objective The aim is to determine cross-hardening at large strains, relevant for forming processes. Mild steel grades (DC04, DC06, DX56) and high strength steel grades (BS600, DP600, ZE800) are investigated to quantify the level of cross-hardening between different grades and reveal which grades exhibit cross-hardening at all. Method A novel test setup for large prestrain using hydraulic bulge test and torsion of curved sheets is developed to achieve an orthogonal strain-path change, i.e. the strain rate tensors for two subsequent loadings are orthogonal. The influence of strain rate differences between the tests and clamping of curved sheets on the determined cross-hardening are evaluated. The results are compared to experiments in literature. Results Cross-hardening for sheet metal at prestrains up to 0.6 true plastic strain are obtained for the first time. For DX56 grade the maximum cross-hardening for all prestrains have a constant level of approximately 6%, while the maximum cross-hardening for DC04 and DC06 grades increases, with levels between 7 and 11%. The high strength grades BS600 and ZE800 do not show cross-hardening behavior, while, differencing from previous publications, cross-hardening is observed for dual phase steel DP600. Conclusion Depending on the microstructure of the steel grade the cross-hardening increases with large prestrain or remains constant.

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