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A strain‐softening bar revisited
Author(s) -
Gavrilov Serge N.,
Shishkina Ekaterina V.
Publication year - 2015
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201400155
Subject(s) - bar (unit) , stiffness , limiting , zero (linguistics) , phase (matter) , softening , mathematical analysis , mathematics , moduli , stress (linguistics) , phase transition , geometry , physics , thermodynamics , engineering , mechanical engineering , linguistics , philosophy , statistics , quantum mechanics , meteorology
We revisit, from the standpoint of the modern theory of phase transitions, the classical problem on stretching of a strain‐softening bar, considered earlier by Bažant, Belytschko et al. The known solution is singular and predicts localization of deformations at a single point (an interval with zero length) of the bar. We use the model of a phase transforming bar with trilinear stress‐strain relation and analytically consider the particular limiting case where the stiffness of a new phase inclusion in the phase‐transforming bar is much less than the stiffness of the initial phase. This allows us to construct a regular solution, which converges to the known singular solution in the limiting case of zero new phase stiffness.