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Interpretation of parameters in phase field models for fracture
Author(s) -
Kuhn Charlotte,
Müller Ralf
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210071
Subject(s) - interpretation (philosophy) , fracture (geology) , nucleation , length scale , homogeneous , limit (mathematics) , stability (learning theory) , field (mathematics) , stress field , mechanics , phase (matter) , phase field models , mathematics , statistical physics , finite element method , materials science , physics , mathematical analysis , thermodynamics , computer science , composite material , machine learning , pure mathematics , programming language , quantum mechanics
Phase field fracture models typically feature a length parameter, which controls the width of the diffuse transition zone between broken and undamaged material. In the limit case of a vanishing length parameter, these models converge to a sharp crack formulation. From this point of view, the length scale parameter is a purely auxiliary numerical quantity. However, the study of the stability of homogeneous solutions in a one dimensional setting permits a different interpretation. Since the length parameter is directly related to the critical stress at which the homogeneous solution becomes unstable and crack nucleation occurs, it can be related to the strength of the material. In this regard, the length parameter itself may be seen as a material parameter. These analytical findings are approved by finite element simulations. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)