Corrigendum to “Structures undergoing discrete phase transformation”

Journal of the Mechanics and Physics of Solids 82 (2015) 61

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Journal of the Mechanics and Physics of Solids journal homepage: www.elsevier.com/locate/jmps

Corrigendum to “Structures undergoing discrete phase transformation” Itamar Benichou, Sefi Givli n Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Israel

Unfortunately a couple of typos appeared in the above paper: In Eq. (4), for ε↓S < ε , the correct expression is

⎡ ⎛1 1⎞ ⎤ ⎛1 1⎞ ⎟Δσ ⎥−⎜ − II ⎟σmin , k II ⎢ε − ⎜ I − ⎝k k* ⎠ ⎦ ⎝ k I ⎣ k ⎠

ε↓S < ε.

In Eq. (8), the correct expression for u* is:

⎛ 1 ⎡ (σ *(ε))2 1 ⎞⎤ 2 ⎢− + σmax u* = ⎜1 + ⎟⎥ μ μ ⎠⎦ ⎝ 2k ⎣ Finally, the expression for ε¯nT , Eq. (45), takes a single form (no matter what the value of λ is). That is:

ε¯nT =

σ ⎞ λ ⎛ ⎛⎜ ⎜⎜ 1 + (1 − α ) min ⎟ − λ − 1 ⎝⎝ Δσ ⎠

⎛λ − 1n ⎞⎛ λ − 1 n + 1 ⎞⎞ α⎜ − 1⎟ ⎜ − 1⎟ ⎟⎟ A, ⎝ λ N ⎠⎝ λ ⎠⎠ N

Consequently, Eq. (46) also reduces to a single expression (for all values of λ ):

Bn =

⎛ α⎜ ⎝

(

λ − 1 2n + 1 2N λ

)

(1 − ) + α ( − 1)( ( ) (1 + N ( − )(1 − α))

−1 +

1−α 2

λ−1n λ N

λ−1 2 λ

n N

λ−1n λ N

λ−1n+1 λ N

⎞ −1 ⎟ ⎠

λ λ−1

These expressions take the following simple form in the case of λ = 1:

ε¯ T =

⎛ σmax + σmin 1⎞ + ⎜n + ⎟ A¯ ⎝ 2k 2⎠

B=

¯ ⎞ 1⎛ Ak ⎜1 − ⎟ A¯ Δσ 8⎝ Δσ ⎠

and

The authors would like to, apologize for any inconvenience caused.

DOI of original article: http://dx.doi.org/10.1016/j.jmps.2012.08.009 n Corresponding author. Tel.: þ 97248293014; fax: þ 97248295711. E-mail address: [email protected] (S. Givli). http://dx.doi.org/10.1016/j.jmps.2015.05.014 0022-5096/& 2015 Elsevier Ltd. All rights reserved.

)

kA2 .