# Finite Pure Plane Strain Bending of Inhomogeneous Anisotropic Sheets

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## Abstract

**:**

## 1. Introduction

## 2. Statement of the Problem

## 3. General Solution

#### 3.1. Purely Elastic Solution

#### 3.2. Solution in Plastic Regions Where ${\sigma}_{\eta}>{\sigma}_{\zeta}$

#### 3.3. Solution in Plastic Regions Where ${\sigma}_{\eta}<{\sigma}_{\zeta}$

## 4. Initiation of Plastic Yielding

## 5. Rigid Plastic Solution

## 6. Unloading

## 7. Practical Example

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of the pure bending process: (

**a**) initial configuration, (

**b**) intermediate and final configurations.

**Figure 3.**Variation of the locations of the elastic/plastic boundaries and the neutral line with H/r

_{CD}at the beginning of the process.

**Figure 4.**Distribution of the stress σ

_{ζ}at H/r

_{CD}= 0.04 found using the elastic/plastic and rigid/plastic solutions.

**Figure 5.**Distribution of the stress σ

_{η}at H/r

_{CD}= 0.04 found using the elastic/plastic and rigid/plastic solutions.

Surface (ζ = 0 and ζ = −1) | ζ = −1/4 and ζ = −3/4 | Center (ζ = −1/2) |
---|---|---|

0.644 | 0.659 | 0.6 |

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**MDPI and ACS Style**

Alexandrov, S.; Lyamina, E.; Hwang, Y.-M.
Finite Pure Plane Strain Bending of Inhomogeneous Anisotropic Sheets. *Symmetry* **2021**, *13*, 145.
https://doi.org/10.3390/sym13010145

**AMA Style**

Alexandrov S, Lyamina E, Hwang Y-M.
Finite Pure Plane Strain Bending of Inhomogeneous Anisotropic Sheets. *Symmetry*. 2021; 13(1):145.
https://doi.org/10.3390/sym13010145

**Chicago/Turabian Style**

Alexandrov, Sergei, Elena Lyamina, and Yeong-Maw Hwang.
2021. "Finite Pure Plane Strain Bending of Inhomogeneous Anisotropic Sheets" *Symmetry* 13, no. 1: 145.
https://doi.org/10.3390/sym13010145