Effective Theories for Brittle Materials

A Derivation of Cleavage Laws and Linearized Griffith Energies from Atomistic and Continuum Nonlinear Models

By (author) Manuel Friedrich

Book cover: Effective Theories for Brittle Materials

Extent: 291 pages

Publisher: Logos Verlag Berlin

Subjects: Technical Sciences: Computer Science, Engineering, IT, & Math

Series: Augsburger Schriften zur Mathematik, Physik und Informatik

Series volume number: 28

Language: English

Paperback (Published)

(July 2015)

ISBN: 9783832540289

5.71 x 8.27 inches

Price: $60.00

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A thorough understanding of crack formation in brittle materials is of great interest in both experimental sciences and theoretical studies. Such materials show an elastic response to very small displacements and develop cracks already at moderately large strains. Typically there is no plastic regime in between the restorable elastic deformations and complete failure due to fracture. The main focus of this book lies on the derivation of effective models for brittle materials in the simultaneous passage from discrete-to-continuum and nonlinear to linearized systems. In the first part the cleavage behavior of brittle crystals is investigated including the identification of critical loads for failure and the analysis of the geometry of crack paths that occur in the fractured regime. In the second part Griffith functionals in the realm of linearized elasticity are derived from nonlinear and frame indifferent energies by means of a quantitative geometric rigidity result for special functions of bounded deformation.

  • By (author) Manuel Friedrich

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