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Microcurl Modelling of Size Effects in Single Crystals

Samuel Forest 1*, Anjan Mukherjee2, Mohamed Jebahi 2, Mohamed Abatour 3

1 Mines Paris PSL CNRS, France; 2 Arts et Métiers Institute of Technology CNRS LEM3, France; 3 Transvalor, France

Dislocations, Gradient Plasticity & Micromorphic Modeling · C223
Tuesday, 1 September 2026, 10:15–10:40 · Chair: Reuven Segev

Keywords: crystal plasticity, micromorphic, size effect

The introduction of the dislocation density tensor into the constitutive modelling of single crystalline materials is a fundamental change in the modern approach to crystal plasticity, based on the pioneering works of Nye and Kröner. It makes it possible to address the effect of grain and particle size on the local and global material responses by means of appropriate characteristic lengths. The Microcurl model, a variant of Eringen's micromorphic medium, introduces the microdeformation as an ancillary variable to total plastic deformation. It is particularly well-suited for finite element simulations with a number of additional degrees of freedom per node that does not depend on the number of involved slip systems or slip system families [1]. The proposed constitutive framework contains both energetic and dissipative contributions of the dislocation density tensor [2]. Both components are required to identify the material parameters from several data: results of dislocation dynamics simulations of cyclic plasticity and experimental results from the literature including the bending torsion of a L-beam micro-specimen under various passivation conditions [3]. The model is finally used to distinguish geometric effects from actual size effects in the compression of thin metallic layers [4].

References

  1. N. M. Cordero, A. Gaubert, S. Forest, E. Busso, F. Gallerneau, and S. Kruch, Size effects in generalised continuum crystal plasticity for two–phase laminates, Journal of the Mechanics and Physics of Solids, 58:1963–1994, 2010.
  2. Y. A. Amouzou-Adoun, M. Abatour, M. Jebahi, S. Forest, and M. Fivel, Enhanced plastic distortion based micromorphic model for flexible control of scaling effects, International Journal of Solids and Structures, 322:113568, 2025, https://doi.org/10.1016/j.ijsolstr.2025.113568.
  3. B. Zhang, K. L. Nielsen, J. W. Hutchinson, and W. J. Meng, Toward the development of plasticity theories for application to small-scale metal structures, Proc. Natl. Acad. Sci., 120(44):e2312538120, 2023.
  4. Y. Mu, X. Zhang, J. W. Hutchinson, and W. J. Meng, Dependence of confined plastic flow of polycrystalline Cu thin films on microstructure, MRS Commun., 6(3):289–294, 2016.