A 3D fractional elastoplastic constitutive model for concrete material

Abstract

The core mission to establish elastoplastic constitutive model is how to determine the magnitude and direction of plastic strain increment for material under the given load. Fractional derivative provides a powerful tool for determining the nonorthogonal direction of a certain differentiable function. A three-dimensional (3D) fractional plastic flow rule suitable for concrete material is presented for the first time utilizing fractional derivative. The direction of plastic strain increment is determined by the proposed fractional plastic flow rule. A closed form yield function is developed in the transformed stress (TS) space based on the nonlinear unified strength criterion, and further used to describe the plastic strain induced by hydrostatic loading. A united hardening/softening function proposed by the authors in previous works is adopted to describe the pre-peak hardening and post-peak softening behaviour of concrete. Furthermore, a 3D fractional elastoplastic constitutive model for concrete material is presented. Only nine material parameters with the clear physical meaning are need for the proposed model, and the determination method of each material parameter is given. A series of test results of concrete with different strength under biaxial and triaxial stress conditions are used to assess the performance of proposed model.