Simplified Anisotropic Plasticity Model for Analyzing the Postyield Behavior of Cold-Formed Sheet-Metal Shear Panel Structures
Publication: Journal of Structural Engineering
Volume 141, Issue 7
Abstract
A simplified anisotropic constitutive model for orthotropic metal sheets is developed herein to analyze the off-axial stress-strain response of cold-formed metal sheets, where the material plastic anisotropy is induced by work hardening during the forming process. Hill’s 1948 anisotropic yield criterion is used to determine the material initial yielding, and the strain hardening is modeled using a mixed kinematic-isotropic hardening law along with constantly changing material principal directions as a result of the off-axial plastic loading. The isotropic hardening parameters were expressed using Fourier series and are functions of the loading directions. The expression of hardening parameters using Fourier series allows the model to be adaptively calibrated to the current state of stress using as few as three sets of off-axial stress-strain data. The proposed model is able to predict the direction-dependent strain hardening behavior of orthotropic metal sheets, as well as account for the progressive changing in material principal directions as a result of the off-axial plastic loading. The predicted results were validated using published experimental data of AA7018-T1 aluminum alloy. Finally, as an illustrative example, the anisotropic plasticity model was implemented, along with the simplified analytical approach, to analyze the push-over responses of a sheet-metal shear wall structure with a cold-rolled infill plate. The results predicted by the simplified model match closely with those of finite element analysis and indicate that the performance of the shear wall system depends on the installation direction of the infill metal sheet with respect to its rolling direction.
Get full access to this article
View all available purchase options and get full access to this article.
References
ABAQUS. (2010). Version 6.10 user’s manual, Dassault Systemes, Providence, RI.
Barlat, F., and Lian, J. (1989). “Plastic behavior and stretchability of sheet metals. Part I: A yield function for orthotropic sheets under plane stress conditions.” Int. J. Plast., 5(1), 51–66.
Bathe, K. J., and Montans, F. J. (2004). “On modeling mixed hardening in computational plasticity.” Comput. Struct., 82(6), 535–539.
Berman, J., and Bruneau, M. (2003). “Plastic analysis and design of steel plate shear walls.” J. Struct. Eng., 1448–1456.
Brando, G., and De Matteis, G. (2011). “Experimental and numerical analysis of a multi-stiffened pure aluminum shear panel.” Thin-Walled Struct., 49(10), 1277–1287.
Dafalias, Y. F. (1984). “The plastic spin concept and a simple illustration of its role in finite plastic transormations.” Mech. Mater., 3(3), 223–233.
Dafalias, Y. F. (2000). “Orientation evolution of plastic orthotropy in sheet metals.” J. Mech. Phys. Solids, 48(11), 2231–2255.
De Matteis, G., Brando, G., and Mazzolani, F. M. (2012). “Pure aluminum: An innovative material for structural applications in seismic engineering.” Constr. Build. Mater., 49(1), 1277–1287.
De Matteis, G., Formisano, A., Mazzolani, F. M., and Panico, S. (2008a). “Numerical and experimental analysis of pure aluminum shear panels with welded stiffeners.” Comput. Struct., 86(6), 545–555.
De Matteis, G., Mazzolani, F. M., and Panico, S. (2004). “Seismic protection of steel buildings by pure aluminum shear panels.” Proc., 13th World Conf. on Earthquake Engineering, Paper No. 2704, Vancouver, BC.
De Matteis, G., Mazzolani, F. M., and Panico, S. (2007). “Pure aluminium shear panels as dissipative devices in moment-resisting steel frames.” Earthquake Eng. Struct. Dyn., 36(7), 841–859.
De Matteis, G., Mazzolani, F. M., and Panico, S. (2008b). “Experimental tests on pure aluminum shear panels with welded stiffeners.” Eng. Struct., 30(6), 1734–1744.
Driver, R. G., Kulak, G. L., Elwi, A. E. E., and Kennedy, D. J. L. (1998a). “FE and simplified models of steel plate shear wall.” J. Struct. Eng., 121–130.
Driver, R. G., Kulak, G. L., Kennedy, D. J. L., and Elwi, A. E. E. (1998b). “Cyclic test of four-story steel plate shear wall.” J. Struct. Eng., 112–120.
Drucker, D. C. (1951). “A more fundamental approach to plastic stress-strain relations.” Proc., 1st US National Congress of Applied Mechanics, ASME, 487–491.
Eisenberg, M. A., and Yen, C. F. (1984). “The anisotropic deformation of yield surface.” J. Eng. Mater. Tech. Trans., 106(4), 355–360.
Hill, R. (1948). “A theory of yielding and plastic flow of anisotropic metals.” Proc. R. Soc. A, 193(1033), 281–297.
Hill, R. (1950). The mathematical theory of plasticity, Clarendon Press, Oxford, U.K.
Hill, R. (1979). “Theoretical plasticity of textured aggregates.” Math. Proc. Cambridge Philos. Soc., 85(01), 179–191.
Hill, R. (1990). “Constitutive modeling of orthotropic plasticity in sheet metals.” J. Mech. Phys. Solids, 38(3), 405–417.
Hill, R. (1993). “A user-friendly theory of orthotropic plasticity in sheet metals.” Int. J. Mech. Sci., 35(1), 19–25.
Hosford, W. F. (1972). “A generalized isotropic yield criterion.” J. Appl. Mech., 39(2), 607–609.
Khan, A. S., and Huang, S. J. (1995). Continuum theory of plasticity, John Wiley & Sons, New York.
Kharrazi, M. H. K., Ventura, C. E., and Prion, G. L. (2011). “Analysis and design of steel plate shear walls: Analytical model.” Can. J. Civ. Eng., 38(1), 49–59.
Kharrazi, M. H. K., Ventura, C. E., Prion, G. L., and Sabouri-Ghomi, S. (2004). “Bending and shear analysis and design of ductile steel plate shear walls.” Proc., 13th World Conf. on Earthquake Engineering, Paper No. 77, Vancouver, BC.
Kim, K. H. (1992). “Evolution of anisotropy during twisting of cold drawn tubes.” J. Mech. Phys. Solids, 40(1), 127–139.
Kim, K. H., and Yin, J. J. (1997). “Evolution of anisotropy under plane stress.” J. Mech. Phys. Solids, 45(5), 841–851.
Kissell, J. R., and Ferry, R. L. (2002). Aluminum structures, Wiley, New York.
Lademo, O. G., Hopperstad, O. S., and Langseth, M. (1999). “An evaluation of yield criteria and flow rules for aluminum alloys.” Int. J. Plast., 15(2), 191–208.
Matteis, D. M. (2005). “Effect of lightweight cladding panels on the seismic performance of moment resisting steel frames.” Eng. Struct., 27(11), 1662–1676.
Nithyadharan, M., and Kalyanaraman, V. (2012). “Behaviour of cold-formed steel shear wall panels under monotonic and reversed cyclic loading.” Thin-Walled Struct., 60, 12–23.
Pan, C. L., and Shan, M. Y. (2011). “Monotonic shear tests of cold-formed steel wall frames with sheathing.” Thin-Walled Struct., 49(2), 363–370.
Pinelli, J. P., Moor, C., Graig, J. I., and Goodno, B. J. (1996). “Testing of energy dissipating cladding connections.” Earthquake Eng. Struct. Dyn., 25(2), 129–147.
Prager, W. (1955). “The theory of plasticity: A survey of recent achievements.” Proc. Inst. Mech. Eng., 169(1955), 41–57.
Qu, B., Bruneau, M., Lin, C. H., and Tsai, K. C. (2008). “Testing of full-scale two-story steel plate shear wall with reduced beam section connections and composite floors.” J. Struct. Eng., 364–373.
Sabouri-Ghomi, S., and Roberts, T. M. (1992). “Nonlinear dynamic analysis of steel plate shear walls including shear and bending deformations.” Eng. Struct., 14(5), 309–317.
Sabouri-Ghomi, S., Ventura, C. E., and Kharrazi, M. H. K. (2005). “Shear analysis and design of ductile steel plate shear walls.” J. Struct. Eng., 878–889.
Shishkin, J. J., Driver, R. G., and Grondin, G. Y. (2009). “Analysis of steel plate shear walls using the modified strip model.” J. Struct. Eng., 1357–1366.
Simo, J. C., and Hughes, T. J. R. (1998). Computational inelasticity, Springer, New York.
Thorburn, L. J., Kulak, G. L., and Montgomery, C. J. (1983). “Analysis of steel plate shear walls.”, Dept. of Civil Engineering, Univ. of Alberta, Edmonton, AB.
Timler, P. A., and Kulak, G. L. (1983). “Experimental study of steel plate shear walls.”, Dept. of Civil Engineering, Univ. of Alberta, Edmonton, AB.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability, Dover Publications, New York.
Wu, H. C. (2002). “Anisotropic plasticity for sheet metals using the concept of combined isotropic-kinematic hardening.” Int. J. Plast., 18(12), 1661–1682.
Wu, H. C., Hong, H. K., and Shiao, Y. P. (1999). “Anisotropic plasticity with application to sheet metals.” Int. J. Plast., 41(1), 703–724.
Yu, C. (2010). “Shear resistance of cold-formed steel framed shear walls with 0.686 mm, 0.762 mm, and 0.838 mm steel sheet sheathing.” Eng. Struct., 32(6), 1522–1529.
Zhao, Q., and Astaneh-Asl, A. (2004). “Cyclic behavior of traditional and innovative composite shear walls.” J. Struct Eng., 271–284.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 141 • Issue 7 • July 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Sep 25, 2013
Accepted: Jul 10, 2014
Published online: Aug 20, 2014
Discussion open until: Jan 20, 2015
Published in print: Jul 1, 2015
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.