**65**, 1, pp. 31–38, 2017

**10.24423/engtrans.759.2017**

### Two-Phase Isotropic Composites of Extremal Moduli. The Inverse Homogenization Problem

**Keywords**: laminates; isotropic composites; inverse-homogenization

**Full Text:**PDF

#### References

Bendsøe M.P., Kikuchi N., Generating optimal topologies in optimal design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, 71(2): 197–224, 1988, doi: 10.1016/0045-7825(88)90086-2.

Bendsøe M.P., Sigmund O., Material interpolation schemes in topology optimization, Archive of Applied Mechanics, 69(9): 635–654,1999, doi: 10.1007/s004190050248.

Cherkaev A.V., Gibiansky L.V., Coupled estimates for the bulk and shear moduli of a two-dimensional isotropic elastic composite, Journal of the Mechanics and Physics of Solids, 41(5): 937–980, 1993, doi: 10.1016/0022-5096(93)90006-2.

Czarnecki S., Isotropic material design, Computational Methods in Science and Technology, 21(2): 49–64, 2015, doi: 10.12921/cmst.2015.21.02.001.

Dzierżanowski G., On the comparison of material interpolation schemes and optimal composite properties in plane shape optimization, Structural and Multidisciplinary Optimization, 46(5): 693–710, 2012, doi: 10.1007/s00158-012-0788-2.

Dierżanowski G.: Optimization of material layout in thin elastic plates [in Polish], Oficyna Wydawnicza Politechniki Warszawskiej, Warszawa, 2010.

Hassani B., Hinton E.. Homogenization and structural topology optimization: theory, practice and software, Springer, New York, 1998.

Lewiński T., Telega J.J.: Plates, laminates, and shells: asymptotic analysis and homogenization, World Scientific, Singapore, 2000.

Łukasiak T., Two-phase isotropic composites with prescribed bulk and shear moduli, [in:] Recent Advances in Computational Mechanics, Łodygowski T., Rakowski J., Litewka P. (Eds.), pp. 213–222, CRC Press, London, 2014, doi: 10.1201/b16513-29.

Łukasiak T., HSρ – an isotropic interpolation scheme based on Hashin-Shtrikman variational bounds, [in:] Advances in Mechanics: Theoretical, Computational and Interdisciplinary Issues, Proceedings of the 3rd Polish Congress of Mechanics (PCM) and 21st International Conference on Computer Methods in Mechanics (CMM), Gdansk, Poland, 8-11 September 2015, Kleiber M., Burczyński T., Wilde K., Górski J., Winkelmann K., Smakosz Ł. (Eds.), pp. 355–360, CRC Press, London 2016, doi: 10.1201/b20057-77.

Sigmund O., A new class of extremal composites, Journal of the Mechanics and Physics of Solids, 48(2): 397–428, 2000, doi: 10.1016/S0022-5096(99)00034-4.

Stolpe M., Svanberg K., An alternative interpolation scheme for minimum compliance optimization, Structural and Multidisciplinary Optimization, 22(2): 116–124, 2001, doi: 10.1007/s001580100129.

DOI: 10.24423/engtrans.759.2017