Abstract
Micropolar field theory represents an extension of the classical Cauchy continuum theory. In this paper, a topology optimization procedure for maximum stiffness is applied to structural elements made of micropolar (Cosserat) solids. Some special problems are dealt with and particular attention is given to models that refer to structural interfaces. The results are in good agreement with the real behavior of some biological tissues.
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References
Bendsøe MP, Sigmund O (2002) Topology optimization: theory, methods and applications. Springer, Berlin Heidelberg New York
Chen Y, Lee JD, Eskandarian A (2004) Atomistic viewpoint of the applicability of microcontinuum theories. Int J Solids Struct 41:2085–2097
Cheng KT, Olhoff N (1982) Regularized formulation for optimal design of axisymmetric plates. Int J Solids Struct 18:153–169
Eringen AC (1966) Linear theory of micropolar elasticity. J Math Mech 15(6):909–923
Eringen AC (1999) Microcontinuum field theories, vol 1. Springer, Berlin Heidelberg New York
Eschenauer HA, Olhoff N (2001) Topology optimization of continuum structures: a review. Appl Mech Rev 54(4):331–390
Fatemi J, van Keulen F (2003) Identification of elastic constants of micropolar solids using an optimization approach. WCSMO5, Venice Italy, 2003
Fatemi J, Van Keulen F, Onck PR (2002) Generalized continuum theories: application to stress analysis in bone. Meccanica 37:385–396
Gauthier RD, Jahsman WE (1975) A quest for micropolar elastic constants. J Appl Mech ASME 42:369–374
Hutapea P, Qiao P (2001) Micropolar in-plane shear and rotation moduli of unidirectional fiber composites with fiber-matrix interfacial debonding. J Comp Mech 36(11)
Koiter WT (1964) Couple stress in the theory of elasticity, parts I and II. Mech 67:17–44
Lakes RS (1986) Experimental microelasticity of two porous solids. Int J Solids Struct 22:55–63
Lakes RS (1995) Experimental methods for study of Cosserat elastic solids and other generalized elastic continua. In: Mühlhaus H (ed) Continuum models for materials with micro-structure. Wiley, New York, pp 1–25
Lakes RS, Benedict RL (1982) Noncentrosymmetry in micropolar elasticity. Int J Eng Sci 20(10):1161–1167
Novacki W (1986) Theory of asymmetric elasticity. Pergamon, New York
Providas E, Kattis MA (2002) Finite element method in plane Cosserat elasticity. Comp Struct 80:2059–2069
Rosenberg J, Cimrman R (2001) Microcontinuum in biomechanical medelling. Mathematics and Computers in simulation. Proceedings of the Conference Modelling, Plzen, 2001
Walsh SDC, Tordesillas A (2003) A thermomechanical approach to the development of micropolar costitutive models of granular media. Acta Mech 167(3–4):145–169
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Rovati, M., Veber, D. Optimal topologies for micropolar solids. Struct Multidisc Optim 33, 47–59 (2007). https://doi.org/10.1007/s00158-006-0031-0
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DOI: https://doi.org/10.1007/s00158-006-0031-0