THREE-DIMENSIONAL PRESSURE-DEPENDENT ELASTOPLASTIC COSSERAT CONTINUUM MODEL AND FINITE ELEMENT SIMULATION OF STRAIN LOCALIZATION

A pressure-dependent elastoplastic Cosserat continuum model for three-dimensional problems is presented in this paper. The nonassociated Drucker–Prager yield criterion is particularly considered. Splitting the scalar product of the stress rate and the strain rate into the deviatoric and the spherical parts, the consistent algorithm of the pressure-dependent elastoplastic model is derived in the three-dimensional framework of Cosserat continuum theory, i.e., the return mapping algorithm for the integration of the rate constitutive equation and the closed form of the consistent elastoplastic tangent modulus matrix. The matrix inverse operation usually required in the calculation of elastoplastic tangent constitutive modulus matrix is avoided, that ensures the second order convergence rate and the computational efficiency of the model in numerical solution procedure. A comparison is performed between the classical and Cosserat continuum model through the numerical results of three-dimensional shear structure, tensile specimen, footing on a soil foundation, and soil slope stability. It illustrates that mesh dependency and numerical difficulties exist in classical model, while Cosserat model possesses the capability and performance in keeping the well-posedness of the boundary value problems with strain softening behavior incorporated. The relationship between the internal length scale and the width of shear band and the load-carrying capability of the structure has also been demonstrated.

Three Dimensional Cosserat Continuum Model and its Application to Analysis for the Cantilever Beam

A basic 3D Cosserat continuum theory and corresponding finite element formulations are deduced. The deflections of a cantilever beam are analyzed by the 20-nodes solid elements based on the classical continuum theory and Cosserat continuum theory respectively. Compared with analytical solution brought forward by Timoshenko and Goodier, it illustrates that the numerical results based on Coseerat FEM are effective and more accurate and closer to the analytical solutions by choosing an appropriate value of the characteristic internal length, which also testifies the capability of reflecting the intrinsic property of the cantilever beam.