Toward robust scalar-based gradient plasticity modeling and simulation at finite deformations

• Published in: Acta mechanica 2023-03, Vol.234 (3), p.911-958
• Main Authors: Abatour, Mohamed, Forest, Samuel, Ammar, Kais, Ovalle, Cristian, Osipov, Nikolay, Quilici, Stéphane
• Format: Article
• Language: English
• Subjects: Bending; Classical and Continuum Physics; Control; Cyclic loads; Dynamical Systems; Edge dislocations; Engineering; Engineering Fluid Dynamics; Engineering Sciences; Engineering Thermodynamics; Exact solutions; Heat and Mass Transfer; Localization; Mechanics; Mechanics of materials; Modelling; Original Paper; Plastic deformation; Plastic properties; Shear bands; Simulation; Size effects; Solid Mechanics; Strain localization; Theoretical and Applied Mechanics; Vibration
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-022-03411-3

Strain gradient plasticity has been the subject of extensive research in the past 40 years in order to model size effects in metal plasticity, on the one hand, and provide finite width shear bands in the simulation of localization phenomena, on the other hand. However, the use of the emerging models is still limited to academic applications and has not yet been adopted by industry practitioners. The present paper systematically reviews the pros and the cons of gradient plasticity at finite strains based on the gradient of scalar plastic variables, in particular the gradient of the cumulative plastic strain. It proposes benchmark tests addressing both size effect modeling and plastic strain localization simulation. It includes new analytical solutions for validation of FE implementation. It focuses on the micromorphic approach to gradient plasticity, as a convenient method for implementation in FE codes. New features of the analysis include the comparison of three distinct formulations of rate-independent gradient plasticity at finite deformations, based on the multiplicative decomposition of the deformation gradient and on quadratic potentials with respect to gradient terms. The performance of micromorphic and Lagrange-multiplier-based strain gradient plasticity models is evaluated for various monotonic and cyclic loading conditions including confined plasticity in simple glide and tension, bending and torsion at large deformations. Limitations are pointed out in the case of bending and torsion, which can be overcome for instance by the use of the gradient of equivalent plastic strain model.