## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2013, Special Issue (2013), Article ID 671321, 9 pages.

### A Generalized Version of a Low Velocity Impact between a Rigid Sphere and a Transversely Isotropic Strain-Hardening Plate Supported by a Rigid Substrate Using the Concept of Noninteger Derivatives

Abdon Atangana, O. Aden Ahmed, and Necdet Bıldık

**Full-text: Open access**

#### Abstract

A low velocity impact between a rigid sphere and transversely isotropic strain-hardening plate supported by a rigid substrate is generalized to the concept of noninteger derivatives order. A brief history of fractional derivatives order is presented. The fractional derivatives order adopted is in Caputo sense. The new equation is solved via the analytical technique, the Homotopy decomposition method (HDM). The technique is described and the numerical simulations are presented. Since it is very important to accurately predict the contact force and its time history, the three stages of the indentation process, including (1) the elastic indentation, (2) the plastic indentation, and (3) the elastic unloading stages, are investigated.

#### Article information

**Source**

Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 671321, 9 pages.

**Dates**

First available in Project Euclid: 26 February 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1393448858

**Digital Object Identifier**

doi:10.1155/2013/671321

**Mathematical Reviews number (MathSciNet)**

MR3039156

**Zentralblatt MATH identifier**

1364.74039

#### Citation

Atangana, Abdon; Ahmed, O. Aden; Bıldık, Necdet. A Generalized Version of a Low Velocity Impact between a Rigid Sphere and a Transversely Isotropic Strain-Hardening Plate Supported by a Rigid Substrate Using the Concept of Noninteger Derivatives. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 671321, 9 pages. doi:10.1155/2013/671321. https://projecteuclid.org/euclid.aaa/1393448858

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