Non-local continuum mechanics and fractional calculus

被引：150
|
作者：
Lazopoulos, K. A. [1 ]
机构：
[1] Natl Tech Univ Athens, Sch Appl Sci, Mech Div, GR-15773 Athens, Greece
来源：
MECHANICS RESEARCH COMMUNICATIONS | 2006年 / 33卷 / 06期
关键词：
elasticity; fractional calculus; non-local strain energy density; coexistence of phases;
D O I：
10.1016/j.mechrescom.2006.05.001
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
The present work introduces fractional calculus into the continuum mechanics area describing non-local constitutive relations. Considering a one-dimensional body and assuming total stored energy depending not only upon the local strain but also upon a fractional derivative of the stain, an elastic model with non-local stress-strain behavior is introduced. Fractional calculus provides a natural framework for describing non-local constitutive relations and requires no assumptions for the interval of non-local influence. Furthermore, the proposed method works in finite intervals contrary to the existing theories requiring infinite domains. (C) 2006 Elsevier Ltd. All rights reserved.
引用
收藏
页码：753 / 757
页数：5
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