Multisurface plasticity for Cosserat materials: Plate element implementation and validation

Abstract

SUMMARYThe macroscopic behaviour of materials is affected by their inner micro-structure. Elementary considerations based on the arrangement, and the physical and mechanical features of the micro-structure may lead to the formulation of elastoplastic constitutive laws, involving hardening/softening mechanisms and nonassociative properties. In order to model the non-linear behaviour of micro-structured materials, the classical theory of time-independent multisurface plasticity is herein extended to Cosserat continua. The account for plastic relative strains and curvatures is made by means of a robust quadratic-convergent projection algorithm, specifically formulated for non-associative and hardening/softening plasticity. Some important limitations of the classical implementation of the algorithm for multisurface plasticity prevent its application for any plastic surfaces and loading conditions. These limitations are addressed in this paper, and a robust solution strategy based on the Singular Value Decomposition technique is proposed. The projection algorithm is then implemented into a finite element formulation for Cosserat continua. A specific finite element is considered, developed for micropolar plates. The element is validated through illustrative examples and applications, showing able performance.

The importance of Thermo-Hydro-Mechanical couplings and microstructure to strain localization in 3D continua with application to seismic faults. Part II: Numerical implementation and post-bifurcation analysis

“…They are then completed with the necessary constitutive 90 equations, i.e. a three dimensional elasto-plastic constitutive law considering a Drucker-Prager yield surface extended for Cosserat continua with a single plastic multiplier (Godio et al, 2016).…”

“…Moreover, mesh refinement leads towards zero en-45 ergy dissipation, which is nonphysical. However, the Cosserat FE formulation followed herein does not suffer from the above issues as it possesses a material parameter with dimension of length which regularizes the numerical problem (see also de Borst (1991), Godio et al (2016), Stefanou et al (2017)). …”

“…are compared to the ones already published (de Borst, 1991, Tejchman, 2008, Godio et al, 2016. The methodology for the evaluation of the shear band thickness is presented.…”

Localisation of Deformation for Shearing of a Fault Gouge with Cosserat Microstructure and Different Couplings

“…The full system of equations is integrated numerically using a displacement-rotation incremental finite element formulation [2]. The integration in time is implicit using the solver provided by Redback [5] (Moose framework).…”

The importance of Thermo-Hydro-Mechanical couplings and microstructure to strain localization in 3D continua with application to seismic faults. Part I: Theory and linear stability analysis

“…Furthermore, the effect of grain crushing inside the shear band is explored by varying the internal length of the constitutive law. 45 the fact that it has been recognized to play an important role on fault gouge behavior (Anthony and Marone, 2005, Cashman et al, 2007, Phillips and White, 2017).Cosserat continuum (Cosserat and Cosserat, 1909) is a special case of micromorphic continua (Germain, 1973, Godio et al, 2016, also called generalized 50 or higher order continua. In addition to the translational degrees of freedom of the Cauchy continuum, Cosserat theory considers rotational degrees of freedom at the material point that allow for a better representation of the physics and the mechanical behavior of heterogeneous solids with non-negligible microstructure.…”