28
M. Tabatabaei and S. N. Atluri
element with 12 DOF, and the nonlinear coupling of axial, bidirectional-bending, and
torsional deformations is studied for each spatial beam element. For the large elasticplastic deformation analysis of micro-architected cellular metallic materials, the plastic
hinge method is utilized in such a way that plastic hinges can be formed everywhere
along the beam when the plasticity condition is satisfied. For the large deformation
analysis of the cuboct cellular composite with flexible connections, the standardized
Ramberg-Osgood function is employed to introduce the moment-rotation relation at
flexible nodes. One of the fabricated nickel-based cellular microstructures is modeled
using an RVE with 36 nodes and 64 elements, and its mechanical properties under
compression are calculated and compared with the corresponding experimental results.
Moreover, a series of fabricated cuboct cellular composites with different thickness-tolength ratio are simulated using an RVE with 21 nodes and 48 elements, and the calculated
Young’s moduli are compared with the corresponding experimental measurements. We
find a very good agreement between our computational results and experimental reports
available in the literature.
References
1. Schaedler, T.A., Carter, W.B.: Architected cellular materials. Annu. Rev. Mater. Res. 46,
187–210 (2016)
2. Schaedler, T.A., Jacobsen, A.J., Torrents, A., Sorensen, A.E., Lian, J., Greer, J.R., Valdevit,
L., Carter, W.B.: Ultralight Metallic Microlattices. Science 334, 962–965 (2011)
3. Torrents, A., Schaedler, T.A., Jacobsen, A.J., Carter, W.B., Valdevit, L.: Characterization
of nickel-based microlattice materials with structural hierarchy from the nanometer to the
millimeter scale. Acta Mater. 60, 3511–3523 (2012)
4. Cheung, K.C., Gershenfeld, N.: Reversibly assembled cellular composite Materials. Science
13, 1219–1221 (2013)
5. Lakes, R.: Materials with structural hierarchy. Nature 361, 511–515 (1993)
6. Evans, A.G., He, M.Y., Deshpande, V.S., Hutchinson, J.W., Jacobsen, A.J., Carter, W.B.:
Concepts for enhanced energy absorption using hollow micro-lattices. Int. J Imp Eng. 37,
947–959 (2010)
7. Christensen, J., Kadic, M., Wegener, M., Kraft, O., Wegener, M.: Vibrant times for mechanical
metamaterials. MRS Commun. 5(3), 453–462 (2015)
8. Hutmacher, D.W.: Scaffolds in tissue engineering bone and cartilage. Biomaterials 21, 2529–
2543 (2000)
9. Hutchinson, R.G., Wicks, N., Evans, A.G., Fleck, N.A., Hutchinson, J.W.: Kagome plate
structures for actuation. Int. J. Solids Struct. 40, 6969–6980 (2002)
10. Hodge, P.G.: Plastic Analysis of Structures, Series in Engineering Sciences, McGraw-Hill,
New York (1959)
11. Ueda, Y., Yao, T.: The plastic node method: a new method of plastic analysis. Comp. Meth.
Appl. Mech. Eng. 34, 1089–1104 (1982)
12. Ramberg, W., Osgood, W.R.: Description of stress-strain curves by three parameters. National
Advisory Committee for Aeronautics, Technical Note 902. Washington DC. (1943)
13. Reissner, E.: On a variational theorem for finite elastic deformations. J. Math. Phys. 32,
129–135 (1953)
14. Liu, C.S., Yeih, W., Kuo, C.L., Atluri, S.N.: A scalar homotopy method for solving an
over/under determined system of non-linear algebraic equations. CMES: Comput. Model.
Eng. Sci. 53, 47–71 (2009)
M. Tabatabaei and S. N. Atluri
element with 12 DOF, and the nonlinear coupling of axial, bidirectional-bending, and
torsional deformations is studied for each spatial beam element. For the large elasticplastic deformation analysis of micro-architected cellular metallic materials, the plastic
hinge method is utilized in such a way that plastic hinges can be formed everywhere
along the beam when the plasticity condition is satisfied. For the large deformation
analysis of the cuboct cellular composite with flexible connections, the standardized
Ramberg-Osgood function is employed to introduce the moment-rotation relation at
flexible nodes. One of the fabricated nickel-based cellular microstructures is modeled
using an RVE with 36 nodes and 64 elements, and its mechanical properties under
compression are calculated and compared with the corresponding experimental results.
Moreover, a series of fabricated cuboct cellular composites with different thickness-tolength ratio are simulated using an RVE with 21 nodes and 48 elements, and the calculated
Young’s moduli are compared with the corresponding experimental measurements. We
find a very good agreement between our computational results and experimental reports
available in the literature.
References
1. Schaedler, T.A., Carter, W.B.: Architected cellular materials. Annu. Rev. Mater. Res. 46,
187–210 (2016)
2. Schaedler, T.A., Jacobsen, A.J., Torrents, A., Sorensen, A.E., Lian, J., Greer, J.R., Valdevit,
L., Carter, W.B.: Ultralight Metallic Microlattices. Science 334, 962–965 (2011)
3. Torrents, A., Schaedler, T.A., Jacobsen, A.J., Carter, W.B., Valdevit, L.: Characterization
of nickel-based microlattice materials with structural hierarchy from the nanometer to the
millimeter scale. Acta Mater. 60, 3511–3523 (2012)
4. Cheung, K.C., Gershenfeld, N.: Reversibly assembled cellular composite Materials. Science
13, 1219–1221 (2013)
5. Lakes, R.: Materials with structural hierarchy. Nature 361, 511–515 (1993)
6. Evans, A.G., He, M.Y., Deshpande, V.S., Hutchinson, J.W., Jacobsen, A.J., Carter, W.B.:
Concepts for enhanced energy absorption using hollow micro-lattices. Int. J Imp Eng. 37,
947–959 (2010)
7. Christensen, J., Kadic, M., Wegener, M., Kraft, O., Wegener, M.: Vibrant times for mechanical
metamaterials. MRS Commun. 5(3), 453–462 (2015)
8. Hutmacher, D.W.: Scaffolds in tissue engineering bone and cartilage. Biomaterials 21, 2529–
2543 (2000)
9. Hutchinson, R.G., Wicks, N., Evans, A.G., Fleck, N.A., Hutchinson, J.W.: Kagome plate
structures for actuation. Int. J. Solids Struct. 40, 6969–6980 (2002)
10. Hodge, P.G.: Plastic Analysis of Structures, Series in Engineering Sciences, McGraw-Hill,
New York (1959)
11. Ueda, Y., Yao, T.: The plastic node method: a new method of plastic analysis. Comp. Meth.
Appl. Mech. Eng. 34, 1089–1104 (1982)
12. Ramberg, W., Osgood, W.R.: Description of stress-strain curves by three parameters. National
Advisory Committee for Aeronautics, Technical Note 902. Washington DC. (1943)
13. Reissner, E.: On a variational theorem for finite elastic deformations. J. Math. Phys. 32,
129–135 (1953)
14. Liu, C.S., Yeih, W., Kuo, C.L., Atluri, S.N.: A scalar homotopy method for solving an
over/under determined system of non-linear algebraic equations. CMES: Comput. Model.
Eng. Sci. 53, 47–71 (2009)