TY - JOUR
T1 - Corrigendum to “Directional distortional hardening in metal plasticity within thermodynamics” [Int. J. Solids Struct. 44 (2007) 7526–7542, (S0020768307002077), (10.1016/j.ijsolstr.2007.04.025)]
AU - Feigenbaum, Heidi P.
AU - Dafalias, Yannis F.
N1 - Publisher Copyright:
© 2023 Elsevier Ltd
PY - 2023/5/1
Y1 - 2023/5/1
N2 - This corrigendum sets out to fix an error in Eq. (31) and the ensuing changes in Eqs. (32) and (34) (Eq. (33) remains as is). The changed equations in the corrigendum are indicated by a superscript [Formula presented] while they maintain the same enumeration as in the paper. At the outset, it must be stated that after the corrections the implied conclusion remains as is in the paper. Eq. (31) of the paper should read: [Formula presented] Eq. (32) then becomes: [Formula presented] Substituting Eq. (32*) into Eq. (31*), one can solve for [Formula presented] and the result is Eq. (33), which implies that either [Formula presented] or [Formula presented], so that [Formula presented]. To decide which case to choose, two requirements are considered. The first is the thermodynamic requirement in Eq. (24) applied at the limit, which leads to Eq. (35), namely, [Formula presented]. The second requirement is that [Formula presented], necessary given the definition of a norm and is found using Eq. (32*) instead of Eq. (32), yielding: [Formula presented] Substituting [Formula presented] into Eq. (34*) leads to [Formula presented], which contradicts the thermodynamic requirement of Eq. (35). Substituting [Formula presented] into Eq. (34*) leads to the same requirement as Eq. (35). Therefore, one must choose [Formula presented]. The choice of [Formula presented] is the same as the original paper. This corrigendum only clarifies the reason for this choice and corrects the errors in equations leading to this conclusion.
AB - This corrigendum sets out to fix an error in Eq. (31) and the ensuing changes in Eqs. (32) and (34) (Eq. (33) remains as is). The changed equations in the corrigendum are indicated by a superscript [Formula presented] while they maintain the same enumeration as in the paper. At the outset, it must be stated that after the corrections the implied conclusion remains as is in the paper. Eq. (31) of the paper should read: [Formula presented] Eq. (32) then becomes: [Formula presented] Substituting Eq. (32*) into Eq. (31*), one can solve for [Formula presented] and the result is Eq. (33), which implies that either [Formula presented] or [Formula presented], so that [Formula presented]. To decide which case to choose, two requirements are considered. The first is the thermodynamic requirement in Eq. (24) applied at the limit, which leads to Eq. (35), namely, [Formula presented]. The second requirement is that [Formula presented], necessary given the definition of a norm and is found using Eq. (32*) instead of Eq. (32), yielding: [Formula presented] Substituting [Formula presented] into Eq. (34*) leads to [Formula presented], which contradicts the thermodynamic requirement of Eq. (35). Substituting [Formula presented] into Eq. (34*) leads to the same requirement as Eq. (35). Therefore, one must choose [Formula presented]. The choice of [Formula presented] is the same as the original paper. This corrigendum only clarifies the reason for this choice and corrects the errors in equations leading to this conclusion.
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U2 - 10.1016/j.ijsolstr.2023.112174
DO - 10.1016/j.ijsolstr.2023.112174
M3 - Comment/debate
AN - SCOPUS:85150793908
SN - 0020-7683
VL - 269
JO - International Journal of Solids and Structures
JF - International Journal of Solids and Structures
M1 - 112174
ER -