scholarly journals Mathematical modeling of materially nonlinear problems in structural analyses, Part I: Theoretical fundamentals

2010 ◽  
Vol 8 (1) ◽  
pp. 67-78 ◽  
Author(s):  
Zoran Bonic ◽  
Verka Prolovic ◽  
Biljana Mladenovic
Keyword(s):  
Nonlinear Problems ◽  
Failure Surface ◽  
Plasticity Theory ◽  
Rigid Plastic ◽  
Material Models ◽  
Linear Elastic ◽  
Hardening Law ◽  
Plastic Yield ◽  
Normality Condition ◽  
Von Mises

Material models describe the way they behave when loaded. The paper presents the development of the model beginning with the simplest linear-elastic and rigid-plastic ones. The basic data in the plasticity theory have been defined, such as criterion and yield (failure) surface, hardening law, plastic yield law and normality condition. Yield criteria of Tresca, Von Mises, Mohr-Coulomb and Drucker-Prager were given separately.

scholarly journals The self-similarity theory of high pressure torsion

2016 ◽  
Vol 7 ◽  
pp. 1267-1277 ◽  
Author(s):  
Yan Beygelzimer ◽  
Roman Kulagin ◽  
Laszlo S Toth ◽  
Yulia Ivanisenko
Keyword(s):  
High Pressure ◽  
Mathematical Description ◽  
High Pressure Torsion ◽  
Similarity Theory ◽  
Lateral Wall ◽  
Self Similarity ◽  
Rigid Plastic ◽  
Hardening Law ◽  
Proper Design ◽  
Von Mises

By analyzing the problem of high pressure torsion (HPT) in the rigid plastic formulation, we show that the power hardening law of plastically deformed materials leads to self-similarity of HPT, admitting a simple mathematical description of the process. The analysis shows that the main parameters of HPT are proportional to β q , with β being the angle of the anvil rotation. The meaning of the parameter q is: q = 0 for velocity and strain rate, q = 1 for shear strain and von Mises strain, q = n for stress, pressure and torque (n is the exponent of a power hardening law). We conclude that if the hardening law is a power law in a rotation interval β, self-similar regimes can emerge in HPT if the friction with the lateral wall of the die is not too high. In these intervals a simple mathematical description can be applied based on self-similarity. Outside these ranges, the plasticity problem still has to be solved for each value of β. The results obtained have important practical implications for the proper design and analysis of HPT experiments.

Analytical Solutions of Crack Tip Plasticity Zone Shape for a Semi-Infinite Crack

2003 ◽  
Author(s):  
Peihua Jing ◽  
Tariq Khraishi ◽  
Larissa Gorbatikh
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Analytical Solutions ◽  
Yield Criterion ◽  
Plasticity Zone ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Classical Plasticity ◽  
Elastic Perfectly Plastic ◽  
Von Mises

In this work, closed-form analytical solutions for the plasticity zone shape at the lip of a semi-infinite crack are developed. The material is assumed isotropic with a linear elastic-perfectly plastic constitution. The solutions have been developed for the cases of plane stress and plane strain. The three crack modes, mode I, II and III have been considered. Finally, prediction of the plasticity zone extent has been performed for both the Von Mises and Tresca yield criterion. Significant differences have been found between the plane stress and plane strain conditions, as well as between the three crack modes’ solutions. Also, significant differences have been found when compared to classical plasticity zone calculations using the Irwin approach.

scholarly journals Representative Stress Correlation of Global Scratch Quantities at Scratch Testing: Experimental Verification

Crystals ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 154
Author(s):  
Per-Lennart Larsson
Keyword(s):  
Polymeric Materials ◽  
Experimental Results ◽  
Scratch Testing ◽  
Rigid Plastic ◽  
Viscoelastic Effects ◽  
Elasto Plasticity ◽  
The Difference ◽  
Von Mises ◽  
Experimental Findings ◽  
Static Conditions

Evaluation and correlation of global quantities, i.e., normal and tangential hardness, at scratch testing in the context of a representative stress description was investigated. In particular, verification based on experimental results is at issue. It has been shown previously that within the framework of classical von Mises elasto-plasticity and quasi-static conditions, correlation can be achieved by using a combination of stresses at different levels of plastic strains to define representative quantities at scratching, accounting for the difference in mechanical behavior at elasto-plastic and rigid plastic scratching. However, verification from experimental results is required, which has been attempted in this study. Predictions based on previous theoretical results were compared with experimental findings for polymeric materials, as well as for different metals. Good agreement was found between the two sets of results, particularly so for the case of polymers modelled by von Mises elasto-plasticity. Accordingly, these results are of direct practical, accurate, and novel relevance for semi-crystalline polymers where viscoelastic effects are negligible.

scholarly journals Bearing capacity calculation of reinforced concrete corbels under the shear action

2018 ◽  
Vol 230 ◽  
pp. 02005 ◽  
Author(s):  
Oksana Dovzhenko ◽  
Volodymyr Pohribnyi ◽  
Volodymyr Pents ◽  
Dmytro Mariukha
Keyword(s):  
Plastic Deformation ◽  
Reinforced Concrete ◽  
Plasticity Theory ◽  
Inclined Crack ◽  
Ultimate State ◽  
Rigid Plastic ◽  
Characteristic Lines ◽  
Capacity Calculation ◽  
Theory Use ◽  
Concrete Elements

The necessity of creating a general methodology for concrete and reinforced concrete elements strength calculation under the shear is established. Three failure cases of reinforced concrete corbels under the shear are considered. The solutions of problems of corbels strength with failure along the whole section, close to the normal, in the compressed zone under an inclined crack and within the compressed inclined strip are given. A variational method in the plasticity theory, the virtual velocities principle and the characteristic lines method are used for concrete and reinforced concrete elements calculations. In the ultimate state, concrete is considered as a rigid-plastic body. The shear is realized in case when the plastic deformation is localized in the compressed zone. The calculating ultimate load results for different failure cases are given. Such a design scheme is implemented, in which the console strength is minimal. This corresponds to the minimum of power of plastic deformation in concrete compressed zone. Reinforced concrete corbels calculation engineering methods are offered. The elements obtaining effective constructive decisions direction based on the plasticity theory use is determined.

Rigid-Plastic Collapse of Cylindrical Shells

1973 ◽  
Vol 95 (1) ◽  
pp. 215-218 ◽  
Author(s):  
H. M. Haydl ◽  
A. N. Sherbourne
Keyword(s):  
Limit Analysis ◽  
Cylindrical Shells ◽  
Numerical Approach ◽  
External Pressure ◽  
Plastic Collapse ◽  
Rigid Plastic ◽  
Limit Loads ◽  
Complex Problems ◽  
Safe Side ◽  
Von Mises

This paper suggests a simple numerical approach to the limit analysis of cantilever cylindrical shells. The loads considered are external pressure and external pressure combined with a moment at the free shell end. It is shown that the collapse loads are within 4.5 percent on the safe side of the exact von Mises limit loads. The extension of the method of analysis to more complex problems is suggested.

Pressbrake Bending in the Punch-Sheet Contact Region—Part 1: Modeling Nonuniformities

1988 ◽  
Vol 110 (2) ◽  
pp. 124-130 ◽  
Author(s):  
F. Pourboghrat ◽  
K. A. Stelson
Keyword(s):  
Shear Stress ◽  
Simple Model ◽  
Stress Distribution ◽  
Plastic Material ◽  
Contact Region ◽  
Rigid Plastic ◽  
Material Models ◽  
Rigid Plastic Material

A simple model of pressbrake bending in the punch-sheet contact region is presented. The pressure and shear stress at the punch-sheet interface cause the stress distribution in the sheet to change as a function of angle. In Part 1 of this paper, a model to predict nonuniformities as a function of the geometry and the frictional conditions is presented. In Part 2, the model will be used to predict the formation of a gap between the sheet and the punch. Elastic and rigid-plastic material models of the sheet are considered, and are shown to produce remarkably similar results.

Shakedown Loads for Pressure Vessels of Strain Hardening Materials

1969 ◽  
Vol 11 (3) ◽  
pp. 340-342 ◽  
Author(s):  
T. E. Taylor
Keyword(s):  
Strain Hardening ◽  
Power Law ◽  
Pressure Vessels ◽  
Strain Hardening Exponent ◽  
Rigid Plastic ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Creep Analysis ◽  
Family Of Curves ◽  
The Relationship

A power law, well known in creep analysis, embodies a family of curves which express the stress-strain relations for a family of materials ranging from linear elastic to rigid perfectly plastic. A linearization of the relationship between stress concentration factor and the reciprocal of strain hardening exponent for geometrically similar pressure vessels made of materials within the family has enabled a view of shakedown in vessels of strain hardening materials to be formulated. The absence of discontinuities in the power law, except at the rigid plastic end point, results in shakedown loads dependent on strain hardening exponent and previous loading history.

A Unified Characteristic Theory for Plastic Plane Stress and Strain Problems

2003 ◽  
Vol 70 (5) ◽  
pp. 649-654 ◽  
Author(s):  
Y.-Q. Zhang ◽  
H. Hao ◽  
M.-H. Yu
Keyword(s):  
Plane Stress ◽  
Yield Criterion ◽  
Strength Criterion ◽  
Rigid Plastic ◽  
Strength Criteria ◽  
Special Cases ◽  
Characteristic Theory ◽  
Characteristic Methods ◽  
Von Mises ◽  
Suitable Characteristic

Based on the unified strength criterion, a characteristic theory for solving the plastic plane stress and plane strain problems of an ideal rigid-plastic body is established in this paper, which can be adapted for a wide variety of materials. Through this new theory, a suitable characteristic method for material of interest can be obtained and the relations among different sorts of characteristic methods can be revealed. Those characteristic methods on the basis of different strength criteria, such as Tresca, von Mises, Mohr-Coulomb, twin shear (TS) and generalized twin shear (GTS), are the special cases (Tresca, Mohr-Coulomb, TS, and GTS) or linear approximation (von Mises) of the proposed theory. Moreover, a series of new characteristic methods can be easily derived from it. Using the proposed theory, the influence of yield criterion on the limit analysis is analyzed. Two examples are given to illustrate the application of this theory.

Modeling of Low Energy, Low Velocity Impact Failure of a Honeycomb Sandwich Material

2014 ◽  
Vol 566 ◽  
pp. 256-261
Author(s):  
M.C. Miron ◽  
Zoltan Major ◽  
Tadaharu Adachi
Keyword(s):  
Brittle Failure ◽  
Plastic Material ◽  
Transverse Isotropy ◽  
Low Velocity Impact ◽  
Honeycomb Core ◽  
Low Velocity ◽  
Material Models ◽  
Linear Elastic ◽  
Honeycomb Sandwich ◽  
Core Components

The current work is aimed at development of a numerical model able to describe complex damage phenomena that occur during an impact event in a sandwich structure having a honeycomb core. The complex material models employed within the research include linear-elastic and elasto-plastic material models having transverse isotropy as well as damage evolution models for both brittle failure and plastic failure. Within this paper remarks concerning the failure of the skins and core components as well as dissipated impact energy and affected regions are done.

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