Micromorphic Crystal Plasticity

  • Samuel ForestEmail author
  • J. R. Mayeur
  • D. L. McDowell
Reference work entry


The micromorphic approach to crystal plasticity represents an extension of the micropolar (Cosserat) framework, which is presented in a separate chapter. Cosserat crystal plasticity is contained as a special constrained case in the same way as the Cosserat theory is a special restricted case of Eringen's micromorphic model, as explained also in a separate chapter. The micromorphic theory is presented along the lines of Aslan et al. (Int J Eng Sci 49:1311–1325, 2011) and Forest et al. (Micromorphic approach to crystal plasticity and phase transformation. In: Schroeder J, Hackl K (eds) Plasticity and beyond. CISM international centre for mechanical sciences, courses and lectures, vol 550, Springer, pp 131–198, 2014) and compared to the micropolar model in some applications. These extensions of conventional crystal plasticity aim at incorporating the dislocation density tensor introduced by Kröner (Initial studies of a plasticity theory based upon statistical mechanics. In: Kanninen M, Adler W, Rosenfield A, Jaffee R (eds) Inelastic behaviour of solids. McGraw-Hill, pp 137–147, 1969). and Cermelli and Gurtin (J Mech Phys Solids 49:1539–1568, 2001) into the constitutive framework. The concept of dislocation density tensor is equivalent to that of the so-called geometrically necessary dislocations (GND) introduced by Ashby (The deformation of plastically non-homogeneous alloys. In: Kelly A, Nicholson R (eds) Strengthening methods in crystals. Applied Science Publishers, London, pp 137–192, 1971). The applications presented in this chapter deal with pile-up formation in laminate microstructures and strain localization phenomena in polycrystals.


Micromorphic medium Crystal plasticity Dislocation density tensor Geometrically necessary dislocations Strain gradient plasticity Size effect 



The first author is indebted to Dr. N.M. Cordero, Dr. S. Wulfinghoff, and Prof. E.B. Busso for their contribution to the presented micromorphic crystal plasticity theory. These contributions are duly cited in the references quoted in the text and listed below.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Centre des Materiaux, Mines ParisTech CNRSPSL Research UniversityParisFrance
  2. 2.Theoretical DivisionLos Alamos National LaboratoryLos AlamosUSA
  3. 3.Woodruff School of Mechanical Engineering, School of Materials Science and EngineeringGeorgia Institute of TechnologyAtlantaUSA

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