A mixed three-node triangular element with continuous nodal stress for fully dynamic consolidation of porous media

Abstract

A mixed three-node triangular element with continuous nodal stresses (mixed T3-MINI-CNS) is presented for dynamics of porous media based on the three-variable u-w-p Biot model and the numerical manifold method (NMM). The displacement and velocity approximations are derived using the constrained and orthonormalized least-square (CO-LS) scheme, which possess continuous derivatives and Delta property at nodes. The pressure approximation takes linear piecewise interpolation. Relative to higher-order element, the mixed quadratic six-node triangle, mixed T3-MINI-CNS can model dynamic response of porous media more precisely with fewer unknowns, especially the short-term transient response. Moreover, mixed T3-MINI-CNS is immune from locking in both undrained and rigid skeleton limits and achieves more accurate pressure results than other characteristic locking-free elements. Based on NMM and u-w-p formulation, the most versatile three-node triangular mesh can always be used, avoiding difficulties in mesh generation. As fluid acceleration is involved, mixed T3-MINI-CNS is capable of totally predicting dynamic response of porous mixture, especially under rapid loading condition. In addition, reliability and precision of the time integration are assessed in terms of the energy balance condition. Through calculating benchmark problems, convergence, accuracy, and reliability of the mixed T3-MINI-CNS are thoroughly investigated and validated.