Fractal materials, beams, and fracture mechanics

Article

Abstract.

Continuing in the vein of a recently developed generalization of continuum thermomechanics, in this paper we extend fracture mechanics and beam mechanics to materials described by fractional integrals involving D, d and R. By introducing a product measure instead of a Riesz measure, so as to ensure that the mechanical approach to continuum mechanics is consistent with the energetic approach, specific forms of continuum-type equations are derived. On this basis we study the energy aspects of fracture and, as an example, a Timoshenko beam made of a fractal material; the local form of elastodynamic equations of that beam is derived. In particular, we review the crack driving force G stemming from the Griffith fracture criterion in fractal media, considering either dead-load or fixed-grip conditions and the effects of ensemble averaging over random fractal materials.

Keywords.

Fractal materials beams fracture mechanics 

Copyright information

© Birkhäuser Verlag, Basel 2009

Authors and Affiliations

  1. 1.Department of Mechanical Science and Engineering and Institute for Condensed Matter TheoryUniversity of Illinois at Urbana-ChampaignUrbanaU.S.A.

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