Modeling Of Saturated Soil Dynamic Response And Generalized Hill's Lemma For Higher-order Continuum

This thesis includes two major works. As the first one, an iterative, incremental pressure-stabilized fractional step algorithm in saturated soil dynamics is proposed, besides which a generalized Hill's lemma for computational homogenization of gradient-enhanced Cosserat continuum is presented.Work I:The thesis presents an iterative, incremental pressure-stabilized fractional step algorithm in saturated soil dynamics by the introduction of both an iteration procedure and a finite increment calculus (FIC) process into the existing fractional step algorithm, with the aim to ensure the stabilization of pressure field as equal low order u-p mixed finite elements are used. The introduction of the iterative procedure makes the velocity term satisfy the momentum conservation equation in an implicit sense and allows much larger time step sizes to be used than those limited in existing explicit and semi-implicit versions of the algorithm. The introduction of the FIC process removes the dependence of the stability of the proposed algorithm on the time step size, as the results, it allows to using the incremental version of the algorithm and evades the minimum time step size requirement presented in existing versions of the fractional step algorithm, that restricts the application of the algorithm to saturated soil dynamics problems with high frequencies. Consequently, the proposed algorithm is robust not only to the low frequency response problems, for which large time step sizes should be used to enhance the computational efficiency, but also to the high frequency response problems, for which small time step sizes have to be used to ensure the computational accuracy.Workâ…¡: Based on the Hill's lemmas for classical Cauchy continuum and classical Cosserat continuum, a generalized Hill's lemma for micro-macro homogenization modeling of gradient-enhanced Cosserat continuum is proposed in the frame of the average-field theory. In this context not only the strain and stress tensors defined in classical Cosserat continuum but also their gradients at each macroscopic sampling point are attributed to representative volume element (RVE). In addition, according to the presented generalized Hill's lemma the admissible boundary conditions prescribed in the strong form and the weak form for the representative volume element of gradient-enhanced Cosserat continuum are proposed with the satisfaction of both the enhanced Hill-Mandel energy condition and the average-field theory.