Elastic Theory Has Zero Radius of Convergence

Journal Article · Thu Aug 01 04:00:00 EDT 1996 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.77.1520· OSTI ID:287004

Buchel, A; Sethna, J P ^[1]

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1. Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York, 14853-2501 (United States)

In nonlinear elastic theory, the inverse bulk modulus {ital K}, for example, depends on the compression {ital P}: 1/{ital K}({ital P})={ital c}{sub 0}+{ital c}{sub 1}{ital P}+{ital c}{sub 2}{ital P}{sup 2}+{center_dot}{center_dot}{center_dot}+{ital c}{sub {ital nP}}{sup {ital n}}+{center_dot}{center_dot}{center_dot}. Elastic materials that allow cracks are unstable at finite temperature with respect to fracture under a stretching load. As a result, the above power series has zero radius of convergence: it is an asymptotic series. For a two-dimensional isotropic elastic medium allowing cracks we compute the asymptotic form {ital c}{sub {ital n}+1}/{ital c}{sub {ital n}}{r_arrow}{ital Cn}{sup 1/2} as {ital n}{r_arrow}{infinity}. We present an explicit formula for {ital C} as a function of temperature and material properties. {copyright} {ital 1996 The American Physical Society.}

• DOE Contract Number: FG02-88ER45364
• OSTI ID: 287004
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 8 Vol. 77; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ASYMPTOTIC SOLUTIONS
CONVERGENCE
CRACKS
DISLOCATIONS
ELASTICITY
NONLINEAR PROBLEMS
TEMPERATURE DEPENDENCE
THERMODYNAMIC PROPERTIES