scholarly journals Plane strain pure bending of sheets with damage evolution at large strains

2011 ◽  
Vol 48 (11-12) ◽  
pp. 1637-1643 ◽  
Author(s):  
Sergei Alexandrov ◽  
Jean-Claude Gelin
Keyword(s):  
Plane Strain ◽  
Damage Evolution ◽  
Large Strains ◽  
Pure Bending

An Alternative Approach to Analysis of Plane-Strain Pure Bending at Large Strains

2006 ◽  
Vol 41 (5) ◽  
pp. 397-410 ◽  
Author(s):  
S Alexandrov ◽  
Ji Hoon Kim ◽  
Kwansoo Chung ◽  
Tae Jin Kang
Keyword(s):  
Plane Strain ◽  
Large Strains ◽  
Pure Bending ◽  
Alternative Approach

scholarly journals Finite Pure Plane Strain Bending of Inhomogeneous Anisotropic Sheets

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 145
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Yeong-Maw Hwang
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
Large Strains ◽  
Rigid Plastic ◽  
Plastic Properties ◽  
Elastic Plastic ◽  
Starting Point ◽  
The Difference ◽  
Inside Radius ◽  
Elastic Unloading

The present paper concerns the general solution for finite plane strain pure bending of incompressible, orthotropic sheets. In contrast to available solutions, the new solution is valid for inhomogeneous distributions of plastic properties. The solution is semi-analytic. A numerical treatment is only necessary for solving transcendent equations and evaluating ordinary integrals. The solution’s starting point is a transformation between Eulerian and Lagrangian coordinates that is valid for a wide class of constitutive equations. The symmetric distribution relative to the center line of the sheet is separately treated where it is advantageous. It is shown that this type of symmetry simplifies the solution. Hill’s quadratic yield criterion is adopted. Both elastic/plastic and rigid/plastic solutions are derived. Elastic unloading is also considered, and it is shown that reverse plastic yielding occurs at a relatively large inside radius. An illustrative example uses real experimental data. The distribution of plastic properties is symmetric in this example. It is shown that the difference between the elastic/plastic and rigid/plastic solutions is negligible, except at the very beginning of the process. However, the rigid/plastic solution is much simpler and, therefore, can be recommended for practical use at large strains, including calculating the residual stresses.

Influence of Bauschinger effect on springback and residual stresses in plane strain pure bending

2011 ◽  
Vol 220 (1-4) ◽  
pp. 47-59 ◽  
Author(s):  
Sergei Alexandrov ◽  
Yeong-Maw Hwang
Keyword(s):  
Residual Stresses ◽  
Plane Strain ◽  
Bauschinger Effect ◽  
Pure Bending

The Improved Johnson-Cook’s Strength Model Taking Account of the Rate-Dependent Micro-Damage Evolution for C30 Concrete

2006 ◽  
Vol 326-328 ◽  
pp. 1101-1104
Author(s):  
Shao Chiu Shih ◽  
Yong Zhong Wang ◽  
Li Li Wang
Keyword(s):  
Damage Evolution ◽  
High Pressures ◽  
Engineering Application ◽  
Experimental Results ◽  
Rate Coefficients ◽  
Large Strains ◽  
Strain Rates ◽  
Strength Model ◽  
Rate Dependent ◽  
Wide Range

The dynamic mechanical behavior of C30 concrete under a wide range of strain rates from 10-4s-1 up to 102s-1 is studied. According to Johnson-Cook’s strength model, the strain rate coefficients and related material constants of C30 concrete subjected to large strains, high strain rates and high pressures are determined experimentally: C=0.34*10-1, A=1.05, B=1.65, N=0.76, TC =3.162MPa, fc’=39.2MPa. The damage evolution for C30 concrete is a rate-dependent process, which can be formulated to a rate-dependent damage evolution law in a simple form for engineering application. When ε > ε th, ( ) 1 D th D = K ε&α − ε −ε . The corresponding dynamic coefficients of C30 concrete are also obtained from impact experimental results: KD=530.2, a=0.83. Due to a<1, the damage evolution corresponds to an impact toughening process that coincide well with the dynamic experimental results for C30 concrete.

Plane-Strain Bending With Isotropic Strain Hardening at Large Strains

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
Sergei Alexandrov ◽  
Yeong-Maw Hwang
Keyword(s):  
Strain Hardening ◽  
Plane Strain ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Form Solution ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Rigid Plastic ◽  
Elastic Plastic ◽  
Hardening Law

Finite deformation elastic-plastic analysis of plane-strain pure bending of a strain hardening sheet is presented. The general closed-form solution is proposed for an arbitrary isotropic hardening law assuming that the material is incompressible. Explicit relations are given for most popular conventional laws. The stage of unloading is included in the analysis to investigate the distribution of residual stresses and springback. The paper emphasizes the method of solution and the general qualitative features of elastic-plastic solutions rather than the study of the bending process for a specific material. In particular, it is shown that rigid-plastic solutions can be used to predict the bending moment at sufficiently large strains.

Plane strain bending of a bimetallic sheet at large strains

2016 ◽  
Vol 58 (4) ◽  
pp. 641-659
Author(s):  
Sergei E. Alexandrov ◽  
Nguyen D. Kien ◽  
Dinh V. Manh ◽  
Fedor V. Grechnikov
Keyword(s):  
Plane Strain ◽  
Large Strains ◽  
Bimetallic Sheet

scholarly journals A Theory of Elastic/Plastic Plane Strain Pure Bending of FGM Sheets at Large Strain

Materials ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 456 ◽  
Author(s):  
Sergey Alexandrov ◽  
Yun-Che Wang ◽  
Lihui Lang
Keyword(s):  
Residual Stresses ◽  
Plane Strain ◽  
Material Properties ◽  
Large Strain ◽  
Thickness Distribution ◽  
Functionally Graded ◽  
Pure Bending ◽  
Lagrangian Coordinate ◽  
Lagrangian Coordinate System ◽  
General Method

An efficient analytical/numerical method has been developed and programmed to predict the distribution of residual stresses and springback in plane strain pure bending of functionally graded sheets at large strain, followed by unloading. The solution is facilitated by using a Lagrangian coordinate system. The study is concentrated on a power law through thickness distribution of material properties. However, the general method can be used in conjunction with any other through thickness distributions assuming that plastic yielding initiates at one of the surfaces of the sheet. Effects of material properties on the distribution of residual stresses are investigated.

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