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Corrigendum to “Orientational evolution of plastic orthotropy in sheet metals” [J. Mech. Phys. Solids 48 (2000) 2231–2255]
Journal of the Mechanics and Physics of Solids 50 (2002) 677
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Corrigendum
Corrigendum to “Orientational evolution of plastic orthotropy in sheet metals” [J. Mech. Phys. Solids 48 (2000) 2231–2255] Yannis F. Dafalias ∗ Department of Civil and Environmental Engineering, University of California at Davis, 1 Shields Avenue, Davis, CA 95616, USA
In relation to the discussion of the work by Valery Levitas (J. Mech. Phys. Solids 46 · (1998) 557–590) in Section 7, the minimization of the rate of dissipation 9 in Eq. (25) p p requires a choice of the plastic spin Wi , with a bounded norm |Wi |, which maximizes the trace of its product with a =xed antisymmetric tensor given by [ai (99=9ai ] − [(99=9ai )ai ] : Wip (no sum over i). Such requirement leads to Eq. (26) for Wip with the plastic spin coe?cient of i ¿ 0. The positive sign of i is based on the statement made after Eq. (26) that the foregoing trace equals the inner product of the axial vectors corresponding to the two antisymmetric tensors. This statement is wrong, because the trace equals two times the negative of the inner product of the axial vectors. This implies that i in Eq. (26), in Eq. (27), and ; in the text following Eq. (27) must all be negative · instead of positive. Thus, the postulate of minimum 9 by Levitas does accommodate a negative plastic spin coe?cient for the reorientation of plastic orthotropy, which was found necessary in order to =t experimental data, and all statements to the contrary in Sections 7 and 8 must be discarded. However, it also yields a negative plastic spin coe?cient a for kinematic hardening, which has not been found to yield a reasonable stress–strain response. The above =ndings about the sign of the plastic spin coe?cient were communicated with V. Levitas, for similar corrections in his paper.
PII of the original article: S00225096(00)00014-4
∗
Tel.: +1-530-752-0586; fax: +1-510-752-7872. E-mail address: [email protected] (Y.F. Dafalias).
0022-5096/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 5 0 9 6 ( 0 1 ) 0 0 0 8 4 - 9
www.elsevier.com/locate/jmps
Corrigendum
Corrigendum to “Orientational evolution of plastic orthotropy in sheet metals” [J. Mech. Phys. Solids 48 (2000) 2231–2255] Yannis F. Dafalias ∗ Department of Civil and Environmental Engineering, University of California at Davis, 1 Shields Avenue, Davis, CA 95616, USA
In relation to the discussion of the work by Valery Levitas (J. Mech. Phys. Solids 46 · (1998) 557–590) in Section 7, the minimization of the rate of dissipation 9 in Eq. (25) p p requires a choice of the plastic spin Wi , with a bounded norm |Wi |, which maximizes the trace of its product with a =xed antisymmetric tensor given by [ai (99=9ai ] − [(99=9ai )ai ] : Wip (no sum over i). Such requirement leads to Eq. (26) for Wip with the plastic spin coe?cient of i ¿ 0. The positive sign of i is based on the statement made after Eq. (26) that the foregoing trace equals the inner product of the axial vectors corresponding to the two antisymmetric tensors. This statement is wrong, because the trace equals two times the negative of the inner product of the axial vectors. This implies that i in Eq. (26), in Eq. (27), and ; in the text following Eq. (27) must all be negative · instead of positive. Thus, the postulate of minimum 9 by Levitas does accommodate a negative plastic spin coe?cient for the reorientation of plastic orthotropy, which was found necessary in order to =t experimental data, and all statements to the contrary in Sections 7 and 8 must be discarded. However, it also yields a negative plastic spin coe?cient a for kinematic hardening, which has not been found to yield a reasonable stress–strain response. The above =ndings about the sign of the plastic spin coe?cient were communicated with V. Levitas, for similar corrections in his paper.
PII of the original article: S00225096(00)00014-4
∗
Tel.: +1-530-752-0586; fax: +1-510-752-7872. E-mail address: [email protected] (Y.F. Dafalias).
0022-5096/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 5 0 9 6 ( 0 1 ) 0 0 0 8 4 - 9