Finite element modelling for materials with size effect

Abstract

This paper involves the formulation of the C0 finite elements incorporating the conventional mechanism-based strain gradient plasticity theory. Higher-order variables and consequently higher-order continuity conditions are not required allowing the direct applications of conventional plasticity algorithms in the existing finite element package. Implementation of the model whether analytically or computationally is efficient and straightforward as the strain gradient effect is confined in the material constitutive relation. The accuracy of the proposed elements in simulating the response of materials with strong size effect is verified through several numerical examples. The approach is applicable and valid to any materials with non-uniform plastic deformation larger than about 100 nm onwards. The proposed model becomes imperative when the deformation is less than 10 µm as classical plasticity is unable to describe the phenomenon comprehensively at this low level of deformation.