Multisurface plasticity for Cosserat materials: plate element implementation and validation

International audienceThe 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 non-associative 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

Three-dimensional shakedown solutions for anisotropic cohesive-frictional materials under moving surface loads

Previous work on three-dimensional shakedown analysis of cohesive-frictional materials under moving surface loads has been entirely for isotropic materials. As a result, the effects of anisotropy, both elastic and plastic, of soil and pavement materials are ignored. This paper will, for the first time, develop three-dimensional shakedown solutions to allow for the variation of elastic and plastic material properties with direction. Melan's lower-bound shakedown theorem is used to derive shakedown solutions. In particular, a generalised, anisotropic Mohr–Coulomb yield criterion and cross-anisotropic elastic stress fields are utilised to develop anisotropic shakedown solutions. It is found that shakedown solutions for anisotropic materials are dominated by Young's modulus ratio for the cases of subsurface failure and by shear modulus ratio for the cases of surface failure. Plastic anisotropy is mainly controlled by material cohesion ratio, the rise of which increases the shakedown limit until a maximum value is reached. The anisotropic shakedown limit varies with frictional coefficient, and the peak value may not occur for the case of normal loading only

Shakedown solutions for pavements with materials following associated and non-associated plastic flow rules

Existing lower-bound shakedown solutions for pavement problems are generally obtained by assuming that materials obey an associated flow rule, whereas plasticity of real materials is more inclined to a non-associated flow. In this paper, a numerical step-by-step approach is developed to estimate shakedown limits of pavements with Mohr–Coulomb materials. In particular, influences of a non-associated flow rule on the shakedown limits are examined by varying material dilation angle in the numerical calculations. It is found that the decrease of dilation angle will lead to accelerated reduction of pavement shakedown limits, and the reduction is most significant when the material friction angle is high. Furthermore, existing lower-bound shakedown solutions for pavements are extended, in an approximate manner, to account for the change of material dilation angle and the shakedown results obtained in this way agree well with those obtained through the numerical step-by-step approach. An example of pavement design using shakedown theory is also presented

Effect of Material Stiffness Variation on Shakedown Solutions of Soils Under Moving Loads

Shakedown limits of pavements and railway foundations can be calculated based on shakedown theorems. These values can be used to guide the thickness designs of pavement and railway constructions considering material plastic properties. However, most existing shakedown analyses were carried out by assuming a unique stiffness value for each material. This paper mainly concentrates on the influence of stiffness variation on the shakedown limits of pavements and railway foundations under moving loads. Finite element models as well as a user-defined material subroutine UMAT are first developed to obtain the elastic responses of soils considering a linearly increasing stiffness modulus with depth. Then, based on the lower-bound shakedown theorem, shakedown solutions are obtained by searching for the most critical self-equilibrated residual stress field. It is found that for a single-layered structure, the rise of a stiffness changing ratio will give a larger shakedown limit; and the increase is more pronounced when the friction angle is relatively high. For multi-layered pavement and railway systems, neglecting the stiffness variation may overestimate the capacity of the structures

A Multi-phase Mesoscopic Simulation Model for the Long-term Chloride ingress and Electrochemical Chloride Extraction

Electrochemical chloride extraction (ECE) is one of the effective methods to remove chloride and prolong the service life of reinforced concrete (RC) structures. To fully understand the mechanisms of the long-term chloride ingress and subsequent ECE treatment of RC structure, a multi-phase mesoscopic numerical model is proposed. Unlike most of existing models, the long-term chloride ingress and the effect of chloride binding are considered in the proposed model, and the transport of chloride is simulated through a novel diffusion-migration-reaction process. The numerical simulation results show that the adsorption capacity of concrete to chloride decreases with the increase of chloride ingress time. Interestingly, the free chloride concentration on the surface of concrete decreases dramatically, and the maximum value appears in the concrete protective cover after ECE treatment. Furthermore, ECE treatment time, current density and concrete protective cover have significant influences on ECE treatment efficiency. Besides, the quantitative relationship models between these factors and ECE treatment efficiency have been developed. Moreover, the use of stirrup can improve the efficiency of ECE treatment. The research outcomes reveal previously ignored fundamental aspects of the ECE treatment and provide insights for the durability prediction of RC structures