In the setting of antiplane linearized elasticity, we show the existence of quasistatic evolutions of cracks in brittle materials by using a vanishing viscosity approach, thus taking into account local minimization. The main feature of our model is that the path followed by the crack need not be prescribed a priori: indeed, it is found as the limit (in the sense of Hausdorff convergence) of curves obtained by an incremental procedure. The result is based on a continuity property for the energy release rate in a suitable class of admissible cracks.
A model for crack propagation based on viscous approximation / Lazzaroni, Giuliano; Toader, R.. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - 21:10(2011), pp. 2019-2047. [10.1142/S0218202511005647]
|Titolo:||A model for crack propagation based on viscous approximation|
|Autori:||Lazzaroni, Giuliano; Toader, R.|
|Data di pubblicazione:||2011|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1142/S0218202511005647|
|Appare nelle tipologie:||1.1 Journal article|