Connecting Atomistic and Continuum Models of Nonlinear Elasticity Theory : Rigorous Existence and Convergence Results for the Boundary Value Problems.

Intro -- 1 A Gamma-Convergence Result -- 1.1 Introduction and Results -- 1.2 The Model and Preliminaries -- 1.3 A General Representation Result -- 1.4 The Boundary Value Problem -- 1.5 Proof of the Main Results -- 2 The Models -- 2.1 The Continuum Model -- 2.2 The Atomistic Model -- 2.3 The Cauchy-Born Rule -- 3 Stability -- 3.1 Stability Constants -- 3.2 Representation Formulae -- 3.3 Examples -- 4 The Static Case -- 4.1 The Continuum Problem -- 4.2 Solutions to the Atomistic Equations -- 4.3 Residual Estimates -- 4.4 Proof of the Main Result -- 5 The Dynamic Case -- 5.1 Continuum Elastodynamics -- 5.2 Atomistic Elastodynamics -- 6 A Complimentary Result -- A Hyperbolic Regularity -- B Sobolev Functions -- C Elliptic Regularity.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.