Premium
Dimensional analysis of a model problem in thermoelasto‐plasticity for cylindrical bodies under heating and cooling
Author(s) -
Wolff M.,
Böhm M.,
Frerichs F.
Publication year - 2008
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.200800021
Subject(s) - biot number , dimensionless quantity , dimension (graph theory) , quenching (fluorescence) , plasticity , distortion (music) , mechanics , cooling curve , set (abstract data type) , materials science , thermodynamics , mathematics , mathematical analysis , physics , computer science , pure mathematics , amplifier , optoelectronics , cmos , quantum mechanics , fluorescence , programming language
We perform a dimension analysis for a model problem in thermoelasto‐plasticity for (hollow) cylindrical bodies, focusing on heating and cooling processes and employing a weak or variational formulation of the arising mathematical model. After finding the dimensionless numbers by a standard procedure, we obtain another set of dimensionless numbers associated with the weak formulation. Besides this, we apply dimension analysis to investigate distortion due to quenching. In particular, we prove that for quenching processes to cause plastification, (and, thus, distortion), a suitably generalized Biot number needs to be sufficiently large.