Some Aspects on the Modelling of Microstructure Deformation Mechanisms with Gradient Truss Model (GTM) Bar Elements

Abstract

Unlike the classical truss model, the constitutive equation of the gradient truss model (GTM) earlier presented by the author introduces higher order strain gradient terms and a characteristic internal length parameter: Thus, considering the interaction between macroscopic and microscopic length scales in the constitutive response. Extra non-classical boundary conditions are required to solve the governing equation. In this paper, the microstructure of a material is defined in a simple manner by representing three typical underlying phenomena based on the spatial variation of strain and three combinations of extra non-classical boundary conditions of the derivative of displacement (strain) and higher order derivative of displacement (strain gradient) imposed at the bar support. To quantify the imposed strain gradient at the bar support, a simple relation is derived. Consequently, the influence of strain, strain gradient and the characteristic internal length parameter at the microstructure during deformation is readily captured and the three underlying phenomena qualitatively modelled by the three GTM bar elements. In addition, strengthening and weakening mechanisms in deformation are revealed. Numerical examples are presented as illustration.