Micromechanics-based elasto-plastic–damage energy formulation for strain gradient solids with granular microstructure

• Published in: Continuum mechanics and thermodynamics Vol. 33; no. 5; pp. 2213 - 2241
• Main Authors: Placidi, Luca, Barchiesi, Emilio, Misra, Anil, Timofeev, Dmitry
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2021; Springer; Springer Nature B.V
• Subjects: Classical and Continuum Physics; Cyclic loads; Damage; Deformation; Energy; Engineering; Engineering Thermodynamics; Evolution; Heat and Mass Transfer; Kinematics; Micromechanics; Microstructure; Morphology; Original Article; Physics; Physics and Astronomy; Plastic deformation; Plastic properties; Plasticity; Strain; Structural Materials; Theoretical and Applied Mechanics; Variables; Granular microstructures; Damage; KKT conditions; Variational procedure; Strain gradient; Plasticity
• ISSN: 0935-1175; 1432-0959
• DOI: 10.1007/s00161-021-01023-1

This paper is devoted to the development of a continuum theory for materials having granular microstructure and accounting for some dissipative phenomena like damage and plasticity. The continuum description is constructed by means of purely mechanical concepts, assuming expressions of elastic and dissipation energies as well as postulating a hemi-variational principle, without incorporating any additional postulate like flow rules. Granular micromechanics is connected kinematically to the continuum scale through Piola’s ansatz. Mechanically meaningful objective kinematic descriptors aimed at accounting for grain–grain relative displacements in finite deformations are proposed. Karush–Kuhn–Tucker (KKT)-type conditions, providing evolution equations for damage and plastic variables associated with grain–grain interactions, are derived solely from the fundamental postulates. Numerical experiments have been performed to investigate the applicability of the model. Cyclic loading–unloading histories have been considered to elucidate the material hysteretic features of the continuum, which emerge from simple grain–grain interactions. We also assess the competition between damage and plasticity, each having an effect on the other. Further, the evolution of the load-free shape is shown not only to assess the plastic behavior, but also to make tangible the point that, in the proposed approach, plastic strain is found to be intrinsically compatible with the existence of a placement function.