scholarly journals Energetic Approach to Large Strain Gradient Crystal Plasticity

10.14311/1666 ◽  
2012 ◽  
Vol 52 (6) ◽  
Author(s):  
Jan Kratochvíl ◽  
Martin Kružík
Keyword(s):  
Computational Experiment ◽  
Large Deformations ◽  
Large Strain ◽  
Length Scale ◽  
Energetic Approach ◽  
Deformation Substructure ◽  
Plastic Materials ◽  
Substructure Formation ◽  
External Loads ◽  
Relevant Length Scale

We formulate a problem of the evolution of elasto-plastic materials subjected to external loads in the framework of large deformations and multiplicative plasticity. We focus on a spontaneous inhomogenization interpreted as a structuralization process. Our model includes gradients of the plastic strain and of hardening variables which provide a relevant length scale of the model. A simple computational experiment interpreted as a hint of a deformation substructure formation is included.

Residual Stresses of Round Steel Rod at Elastoplastic Twisting

2020 ◽  
Vol 989 ◽  
pp. 642-646
Author(s):  
Vladimir N. Shinkin
Keyword(s):  
Residual Stresses ◽  
Cross Section ◽  
Pure Shear ◽  
Rupture Surface ◽  
Elastic Zone ◽  
Plastic Materials ◽  
Hardening Modulus ◽  
Screw Surface ◽  
Residual Deformations ◽  
External Loads

In the elastoplastic twisting of a rod under the action of an external torque, the cross-section of the rod is divided into two zones: the inner elastic zone and the outer plastic zone. After removing the external loads, we observe the residual deformations and the residual stresses inside the rod that significantly affect on the subsequent mechanical processes at manufacturing the products from the round rod. Under too much twisting, the longitudinal surface fibers of the rod begin to tear, the outer surface of the rod ceases to be cylindrical, and the rod’s cross-section ceases to be flat (the Bernoulli’s hypothesis about the flat sections is violated). Next a rupture of the rod is followed. For the plastic materials, the destruction is caused by the pure shear, and the rupture surface is perpendicular to the axis of the rod. For the brittle materials, the destruction occurs, due to the rupture along the screw surface inclined to the axis of the round rod at the angle of 45. In this paper, the residual stresses of the round rod at twisting are obtained for an elastoplastic medium with linear hardening in depending on the rod’s diameter, the shear modulus, the hardening modulus in shear and the yield strength in shear of the rod’s material.

What is the relevant length scale when studying percolating clusters: a critical study

1994 ◽  
Vol 207 (1-3) ◽  
pp. 228-233 ◽  
Author(s):  
P. Gadenne ◽  
M. Gadenne ◽  
Y. Yagil ◽  
G. Deutscher
Keyword(s):  
Critical Study ◽  
Length Scale ◽  
Relevant Length Scale

Effects of Torsion on Equivalent Bending Moment for Limit Load and EPFM Circumferential Pipe Flaw Evaluations

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Phuong H. Hoang ◽  
Kunio Hasegawa ◽  
Bostjan Bezensek ◽  
Yinsheng Li
Keyword(s):  
Finite Element ◽  
Pressure Vessel ◽  
Large Strain ◽  
Bending Moment ◽  
Limit Load ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Weighted Factor ◽  
Elastic Perfectly Plastic

The circumferential flaw evaluation procedures in ASME Boiler and Pressure Vessel Code Section XI nonmandatory Appendix C are currently limited to straight pipes under pressure and bending loads without consideration of torsion loading. The Working Group on Pipe Flaw Evaluation of the ASME Boiler and Pressure Vessel Code is developing guidance for considering the effects of torsion by a mean of an equivalent bending moment, which is a square root of sum square combination of bending moment and torsion load with a weighted factor for torsion moment. A torsion weighted factor, Ce, is established in this paper using large strain finite element limit load analysis with elastic perfectly plastic materials. Planar flaws and nonplanar flaws in a 10.75 in. (273 mm) OD pipe are investigated. Additionally, a finite element J-integral calculation is performed for a planar through wall circumferential flaw with elastic plastic materials subjected to bending and torsion load combinations. The proposed Ce factor for planar flaws is intended for use with the ASME B&PV Code Section XI, Appendix C for limit load and Elastic Plastic Fracture Mechanics (EPFM) circumferential planar flaw evaluations.

Relevant Length Scale of Barchan Dunes

2002 ◽  
Vol 89 (26) ◽  
Author(s):  
Pascal Hersen ◽  
Stéphane Douady ◽  
Bruno Andreotti
Keyword(s):  
Length Scale ◽  
Barchan Dunes ◽  
Relevant Length Scale

Solid Formulation, Comparison of Two Formulations, and Concluding Remarks

1989 ◽  
Author(s):  
Shiro Kobayashi ◽  
Soo-Ik Oh ◽  
Taylan Altan
Keyword(s):  
Finite Element ◽  
Field Equation ◽  
Boundary Value Problem ◽  
Metal Forming ◽  
Large Strain ◽  
Boundary Value ◽  
Elastic Plastic ◽  
Plastic Materials ◽  
Elastic Plastic Materials ◽  
Selection Of

In the previous chapters we have discussed only the applications of flow formulation to the analysis of metal-forming processes. Lately, elastic-plastic (solid) formulations have evolved to produce techniques suitable for metal-forming analysis. This evolution is the result of developments achieved in large-strain formulation, beginning from the infinitesimal approach based on the Prandtl–Reuss equation. A question always arises as to the selection of the approach—“flow” approach or “solid” approach. A significant contribution to the solution of this question was made through a project in 1978, coordinated by Kudo, in which an attempt was made to examine the comparative merits of various numerical methods. The results were compiled for upsetting of circular solid cylinders under specific conditions, and revealed the importance of certain parameters used in computation, such as mesh systems and the size of an increment in displacement. This project also showed that the solid formulation needed improvement, particularly in terms of predicting the phenomenon of folding. For elastic-plastic materials, the constitutive equations relate strain–rate to stress–rates, instead of to stresses. Consequently, it is convenient to write the field equation in the boundary-value problem for elastic-plastic materials in terms of the equilibrium of stress rates. In this chapter, the basic equations for the finite-element discretization involved in solid formulations are outlined both for the infinitesimal approach and for large-strain theory. Further, the solutions obtained by the solid formulation are compared with those obtained by the flow formulation for the problems of plate bending and ring compression. A discussion is also given concerning the selection of the approach for the analysis. In conclusion, significant recent developments in the role of the finite-element method in metal-forming technology are summarized. The field equation for the boundary-value problem associated with the deformation of elastic-plastic materials is the equilibrium equation of stress rates. As stated in Chap. 1 (Section 1.3), the internal distribution of stress, in addition to the current states of the body, is supposed to be known, and the boundary conditions are prescribed in terms of velocity and traction-rate.

Catalogue of maximum crack opening stress for CC(T) specimen assuming large strain condition

2013 ◽  
Vol 3 (2) ◽  
Author(s):  
Marcin Graba
Keyword(s):  
Large Strain ◽  
Crack Opening ◽  
Strain Condition ◽  
Plastic Materials ◽  
Strain Formulation ◽  
Maximum Crack ◽  
Crack Opening Stress ◽  
Elastic Plastic Materials ◽  
Work Hardening Exponent ◽  
Maximum Opening

AbstractIn this paper, values for the maximum opening crack stress and its distance from crack tip are determined for various elastic-plastic materials for centre cracked plate in tension (CC(T) specimen) are presented. Influences of yield strength, the work-hardening exponent and the crack length on the maximum opening stress were tested. The author has provided some comments and suggestions about modelling FEM assuming large strain formulation.

scholarly journals The Exponentiated Hencky Strain Energy in Modeling Tire Derived Material for Moderately Large Deformations

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Giuseppe Montella ◽  
Sanjay Govindjee ◽  
Patrizio Neff
Keyword(s):  
Constitutive Model ◽  
Strain Energy ◽  
Large Deformations ◽  
Large Strain ◽  
Strain Tensor ◽  
Strain Energy Function ◽  
Cold Forging ◽  
Central Feature ◽  
Hencky Strain ◽  
Highly Nonlinear

This work presents a hyperviscoelastic model, based on the Hencky-logarithmic strain tensor, to model the response of a tire derived material (TDM) undergoing moderately large deformations. The TDM is a composite made by cold forging a mix of rubber fibers and grains, obtained by grinding scrap tires, and polyurethane binder. The mechanical properties are highly influenced by the presence of voids associated with the granular composition and low tensile strength due to the weak connection at the grain–matrix interface. For these reasons, TDM use is restricted to applications involving a limited range of deformations. Experimental tests show that a central feature of the response is connected to highly nonlinear behavior of the material under volumetric deformation which conventional hyperelastic models fail in predicting. The strain energy function presented here is a variant of the exponentiated Hencky strain energy, which for moderate strains is as good as the quadratic Hencky model and in the large strain region improves several important features from a mathematical point of view. The proposed form of the exponentiated Hencky energy possesses a set of parameters uniquely determined in the infinitesimal strain regime and an orthogonal set of parameters to determine the nonlinear response. The hyperelastic model is additionally incorporated in a finite deformation viscoelasticity framework that accounts for the two main dissipation mechanisms in TDMs, one at the microscale level and one at the macroscale level. The new model is capable of predicting different deformation modes in a certain range of frequency and amplitude with a unique set of parameters with most of them having a clear physical meaning. This translates into an important advantage with respect to overcoming the difficulties related to finding a unique set of optimal material parameters as are usually encountered fitting the polynomial forms of strain energies. Moreover, by comparing the predictions from the proposed constitutive model with experimental data we conclude that the new constitutive model gives accurate prediction.

scholarly journals The Characterization of the Stress Fields Near a Crack Tip for a Compact Specimen for Elastic-Plastic Materials Dominated by the Plane Strain State

2019 ◽  
Vol 24 (3) ◽  
pp. 549-576 ◽  
Author(s):  
M. Graba
Keyword(s):  
Stress Field ◽  
Plane Strain ◽  
Strain State ◽  
Large Strain ◽  
Crack Tip ◽  
Compact Specimen ◽  
Plane Strain State ◽  
Plastic Materials ◽  
Approximation Formulas ◽  
Elastic Plastic Materials

Abstract The paper presents a comprehensive analysis of the stress field near a crack tip for a compact specimen dominated by the plane strain state using the finite element method. The analysis also includes the calculation of some parameters of in-plane constraints, both for small and large strain assumptions. It discusses the influence of the material characteristic, relative crack length and external load for the stress field, and the in-plane constraint parameter. The approximation formulas for some in-plane constraint parameters are presented.

Finite Element Based Plastic Loads for Elbows With Local Wall Thinning

2007 ◽  
Author(s):  
Jong-Hyun Kim ◽  
Chang-Sik Oh ◽  
Joon-Hyuk Ahn ◽  
Yun-Jae Kim ◽  
Chi-Yong Park ◽  
...  
Keyword(s):  
Finite Element ◽  
Large Strain ◽  
Three Dimensional ◽  
Geometry Effect ◽  
Perfectly Plastic ◽  
Wall Thinning ◽  
Plastic Materials ◽  
Wide Range ◽  
Elastic Perfectly Plastic ◽  
Local Wall Thinning

Based on systematic three-dimensional (3-D), large strain FE limit analyses using elastic-perfectly plastic materials, this paper quantifies the effect of local wall thinning on plastic behaviors and TES (twice-elastic-slope) plastic loads for 90° elbows under in-plane bending. The thinning geometry is assumed to be rectangular rather than circular, but the nonlinear geometry effect is fully considered. Results from systematic analyses lead to simple approximations for TES plastic loads, covering a wide range of elbow and thinning geometries.

scholarly journals A Finite Element Study of Micropipette Aspiration of Single Cells: Effect of Compressibility

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Amirhossein Jafari Bidhendi ◽  
Rami K. Korhonen
Keyword(s):  
Fluid Flow ◽  
Large Deformations ◽  
Large Strain ◽  
Single Cells ◽  
Material Model ◽  
Cell Types ◽  
Micropipette Aspiration ◽  
Bulk Relaxation ◽  
Optimal Material ◽  
Different Cell Types

Micropipette aspiration (MA) technique has been widely used to measure the viscoelastic properties of different cell types. Cells experience nonlinear large deformations during the aspiration procedure. Neo-Hookean viscohyperelastic (NHVH) incompressible and compressible models were used to simulate the creep behavior of cells in MA, particularly accounting for the effect of compressibility, bulk relaxation, and hardening phenomena under large strain. In order to find optimal material parameters, the models were fitted to the experimental data available for mesenchymal stem cells. Finally, through Neo-Hookean porohyperelastic (NHPH) material model for the cell, the influence of fluid flow on the aspiration length of the cell was studied. Based on the results, we suggest that the compressibility and bulk relaxation/fluid flow play a significant role in the deformation behavior of single cells and should be taken into account in the analysis of the mechanics of cells.

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