MICROMECHANICS BASED CONSTITUTIVE MODEL FOR GRANULAR SOLIDS AND ITS IMPLEMENTATION INTO MESHFREE NUMERICAL METHOD

Abstract

To capture the fracture process and non-linear behavior at the element and structural level of granular materials, concrete, under the presence of pre-existing imperfections, a constitutive model and a mesh free method is derived in this study. For the constitutive model, a micromechanical approach with 2nd gradient theory is used to derive the stress-strain and double stress - strain gradient response of the material. For the mesh-free method, an element-free-Galerkin formulation is used. Results of the simulations show that the model qualitatively describes the failure mechanism and processes at the element and structural level. At the element level, the model describes the failure mechanisms, evolution, and behavior of concrete for different loading conditions (uniaxial, bi-axial, tri-axial, and shear). In addition, the model parameters are related to the material's mechanical properties and geometry, and therefore they have physical meaning. This model can be used to study the material's properties that need to be enhanced and/or modified for a particular interest. At the structural level, the mesh-free method captures the fracture process and evolution of a 2D concrete plate under the presence of two types of inclusions subjected to tensile and compressive loading. Moreover, simulation results show that the proposed element-free-Galerkin mesh-free method overcomes the mesh-subjectivity and does not need adaptive analysis as it is observed in finite element methods