Erratum to “On the continuum formulation of higher gradient plasticity for single and polycrystals”

Journal of the Mechanics and Physics of Solids 49 (2001) 1179 – 1180

Erratum

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Erratum to “On the continuum formulation of higher gradient plasticity for single and polycrystals” [Journal of the Mechanics and Physics of Solids 48 (2000) 1777–1796]
A. Menzel, P. Steinmann ∗ Chair for Applied Mechanics, University of Kaiserslautern, Postfach 3049, 67653, Kaiserslautern, Germany

The Publisher regrets that the following errors occurred in the printed version of the above article. We apologise for any inconvenience or embarrassment caused. p. 1784, Eq. (14) should read:
t ’I = ]I : dis = mI · dis · sI = I − I ;

(14)

p. 1788, Remark 3.2. should read: Remark 3.2. De:ne the functional ;:Rndim ×ndim × Rndim ×ndim × R → R as  (
;
p ; ) dv ;(
;
p ; ) = B

with

=

mac

(
−
p ) +

inc

(inc
p ) +

mic

().

p. 1789, Eq. (36) should read: yinc = Gl4 Wp = Gl4 inc
p




and

Rinc = Gl4 inc Wp = Gl4 inc(inc
p ):

PII of the original article: S0022-5096(99)00024-1

∗

Corresponding author. Tel.: +49-0631-205-2421; fax: +49-0631-205-2128. E-mail addresses: [email protected] (A. Menzel), [email protected] (P. Steinmann).

c 2001 Elsevier Science Ltd. All rights reserved. 0022-5096/01/$ - see front matter  PII: S 0 0 2 2 - 5 0 9 6 ( 0 0 ) 0 0 0 4 5 - 4

(36)

1180

A. Menzel, P. Steinmann / J. Mech. Phys. Solids 49 (2001) 1179 – 1180

p. 1793, the layout of Eq. (48) should be:  +L=2  +w=2 u = L F = e d x + p d x −L=2

=

−w=2

 √ √ √  L  − Y0  + w − 2l[tan(w=2 2l) + tanh(w=2 2l)] : G H inc

(48)

p. 1795, the layout of Appendix A. Boundary Conditions should be
t p (3) Ddis = − ydis : ˙p = −yjidis ˙pij = −yjidis h˙jk; l elki   p (3) dis ˙p (3) = − yjidis h˙jk elki + yji; l hjk elki ;l

 @B

: dis ˙p (3) dis ˙p dis hjk = yji;l hjk elki = −kj DB    p (3) dis D@B da = − yjidis h˙jk elki dv B

;l

 p
dis = − yjidis nˆik h˙jk D@B (3)

(3)

p Dinc = −yinc : W˙p = −yijinc ˙pij = −yijinc eikm j˙kl; mn ejln   (3) (3) (3) p inc (3) ˙p = − yijinc eikm j˙kl; m ejln + yij; n eikm jkl; m ejln ;n

    (3) (3) (3) p inc (3) ˙p (3) inc (3) ˙p e e = − yijinc eikm j˙kl; m ejln + yij; −yij; j n ikm kl jln nm eikm jkl ejln ;n

(3)

 @B

;m

(3)

inc inc inc ˙p ˙p jkl DB = −yij; ˙ − kl nm eikm jkl ejln =      (3) (3) p p (3) inc inc (3) ˙ e e j D@B da = − yijinc eikm j˙kl; m ejln + yij; dv ikm jln n kl B

;n

 
inc  p (3) (3) p inc inc D@B = − yij nˆjl j˙lk; m emki − yij; n enjl nˆik j˙lk

;m