- Email: [email protected]
“Modeling nonlinear dissipative response of biological tissues” by M.B. Rubin and S.R. Bodner [Int. J. Solids Struct. 39 (2002) 5081–5099]
International Journal of Solids and Structures 41 (2004) 1739–1740 www.elsevier.com/locate/ijsolstr
Corrigendum
‘‘Modeling nonlinear dissipative response of biological tissues’’ by M.B. Rubin and S.R. Bodner [Int. J. Solids Struct. 39 (2002) 5081–5099] q M.B. Rubin *, S.R. Bodner Technion, Faculty of Mechanical Engineering, Technion City, 32000 Haifa, Israel Received 4 November 2003; received in revised form 4 November 2003
Typographical errors appeared in Eqs. (45) and (A.12) which did not influence the obtained results. The corrected equations should be P ¼ J TFT ;
ð45Þ "(
bðt2 Þ ¼ bðt1 Þ þ Dt
# ) r1 r3 þ r2 e_ r5 Cðt2 Þbde ðt2 Þ r4 fbðt1 Þg : r3 þ e_
ðA:12Þ
Also, the authors would like to thank Prof. E. Mazza for correcting the computer program that was used to simulate the material response. This led to an error in the integration of the hardening variable with the consequence that three of the derived material constants were not appropriate for matching the test data. Table C1 exhibits the corrected values of these three material constants. All other material constants remain the same as those in the original Table 1. Figs. C1 and C2 exhibit the corrected versions of the original Figs. 1 and 2. The other figures were also recalculated and were found to be very similar to the original figures so that all of the conclusions remain the same.
q
PII of original article S0020-7683(02)00237-8 Corresponding author. Tel.: +972-4-8293188; fax: +972-4-8295711. E-mail address: [email protected] (M.B. Rubin).
*
doi:10.1016/j.ijsolstr.2003.11.001
1740
Corrigendum / International Journal of Solids and Structures 41 (2004) 1739–1740
Table C1 Corrected material constants for SMAS and facial skin l0 (MPa) r1 r2
Facial skin
2.7 100.0 1.3
1.5 1000.0 2.2
3.0
(a) SMAS-5 (Loading)
2.0
Cycle 1 Cycle 2 Cycle 3 Theory
Π11 (MPa)
Π11 (MPa)
3.0
SMAS
1.0 0.0 0.0
(b) SMAS-4 (Relaxation) Exp.
Theory
2.0 1.0 0.0
0.1
ε11
0.2
0.3
0.0
500.0 1000.0 t (sec)
1500.0
Fig. C1. Response of SMAS.
1.5
2.0
(a) SKIN-6 (Loading) Cycle 1 Cycle 2
Cycle 3 Theory
1.0 0.5 0.0 0.0
Π11 (MPa)
Π11 (MPa)
2.0
(b) SKIN-6 (Relaxation) Exp.
1.5
Theory
1.0 0.5 0.0
0.1
ε11
0.2
0.3
0.0
Fig. C2. Response of facial skin.
1000.0 t (sec)
2000.0
Corrigendum
‘‘Modeling nonlinear dissipative response of biological tissues’’ by M.B. Rubin and S.R. Bodner [Int. J. Solids Struct. 39 (2002) 5081–5099] q M.B. Rubin *, S.R. Bodner Technion, Faculty of Mechanical Engineering, Technion City, 32000 Haifa, Israel Received 4 November 2003; received in revised form 4 November 2003
Typographical errors appeared in Eqs. (45) and (A.12) which did not influence the obtained results. The corrected equations should be P ¼ J TFT ;
ð45Þ "(
bðt2 Þ ¼ bðt1 Þ þ Dt
# ) r1 r3 þ r2 e_ r5 Cðt2 Þbde ðt2 Þ r4 fbðt1 Þg : r3 þ e_
ðA:12Þ
Also, the authors would like to thank Prof. E. Mazza for correcting the computer program that was used to simulate the material response. This led to an error in the integration of the hardening variable with the consequence that three of the derived material constants were not appropriate for matching the test data. Table C1 exhibits the corrected values of these three material constants. All other material constants remain the same as those in the original Table 1. Figs. C1 and C2 exhibit the corrected versions of the original Figs. 1 and 2. The other figures were also recalculated and were found to be very similar to the original figures so that all of the conclusions remain the same.
q
PII of original article S0020-7683(02)00237-8 Corresponding author. Tel.: +972-4-8293188; fax: +972-4-8295711. E-mail address: [email protected] (M.B. Rubin).
*
doi:10.1016/j.ijsolstr.2003.11.001
1740
Corrigendum / International Journal of Solids and Structures 41 (2004) 1739–1740
Table C1 Corrected material constants for SMAS and facial skin l0 (MPa) r1 r2
Facial skin
2.7 100.0 1.3
1.5 1000.0 2.2
3.0
(a) SMAS-5 (Loading)
2.0
Cycle 1 Cycle 2 Cycle 3 Theory
Π11 (MPa)
Π11 (MPa)
3.0
SMAS
1.0 0.0 0.0
(b) SMAS-4 (Relaxation) Exp.
Theory
2.0 1.0 0.0
0.1
ε11
0.2
0.3
0.0
500.0 1000.0 t (sec)
1500.0
Fig. C1. Response of SMAS.
1.5
2.0
(a) SKIN-6 (Loading) Cycle 1 Cycle 2
Cycle 3 Theory
1.0 0.5 0.0 0.0
Π11 (MPa)
Π11 (MPa)
2.0
(b) SKIN-6 (Relaxation) Exp.
1.5
Theory
1.0 0.5 0.0
0.1
ε11
0.2
0.3
0.0
Fig. C2. Response of facial skin.
1000.0 t (sec)
2000.0