A Finite Element Formulation for Nonlinear Viscoplastic Material Using a Q Model

Keywords: Soil Models, Finite Element Discretization, Time Integration Methods, and Nonlinear Viscoplastic Materials.

Abstract: A direct comparison of the rheological behavior of a mass supported by a complex spring and a mass supported by a spring-dashpot arrangement provides a means of establishing a relationship between material damping in the frequency domain and the frequency dependent Q (omega). For the special case where Q (omega) is constant over a given frequency range, the expansion of Q-1 (omega), i.e., the measure of energy dissipation per cycle, into a Laurent Series yields a set of damping coefficients whose values are determined by minimizing the mean square error of the series over the prescribed frequency range. The resulting damping expression is used in conjunction with an elastoplastic constitutive matrix in finite element discretization to produce a viscoplastic model suitable for a direct step by step time integration. The proposed model is very convenient for use in finite element descretization for the analyses of earthquake, blast, shock, and other soil-structure interaction problems involving cyclic loading.