Spacetime dimensional analysis and self-similar solutions of linear elastodynamics and cohesive dynamic fracture

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:48

Article

Abedi, R.¹  Haber, R. B.¹ 

[1] Univ Illinois, Dept Mech Sci & Engn, Urbana, IL 61801 USA

关键词: Dimensional analysis;    Similitude;    Elastodynamics;    Fracture mechanics;    Cohesive model;    Traction-separation relation;    Ductile-to-brittle transition;   

DOI  :  10.1016/j.ijsolstr.2011.03.013

来源: Elsevier

【 摘 要 】

We present a dimensional analysis and self-similar solutions for linear elastodynamics with extensions to dynamic fracture models based on cohesive traction-separation relations. We formulate the problem using differential forms in spacetime and show that the scaling rules expressed in terms of forms are simpler and more uniform than those obtained for tensor representations of the solution. In the extension to cohesive elastodynamic fracture, we identify and study the influence of certain intrinsic cohesive scales on dynamic fracture behavior and describe a fundamental set of nondimensional groups that uniquely identifies families of self-similar solutions. We present numerical studies of the influence of selected nondimensional parameters on dynamic fracture response to verify the dimensional analysis, including the identification of the fundamental set for cohesive fracture mechanics. We show that distinct values of a widely-used nondimensional quantity can produce self-similar solutions. Therefore, this quantity is not fundamental, and it cannot parameterize dynamic, cohesive-fracture response. Published by Elsevier Ltd.

【 授权许可】

Free