Incremental integrated modeling of dynamic viscoplastic responses of the annular sector plates exposed to shock wave loading

Abstract

An incremental integrated modeling is presented to obtain high-rate dynamic viscoplastic behavior of annular sector plates. The large amplitude shock loads are imparted uniformly over the plate’s surface. Using the first-order shear deformation theory including the nonlinear Von-Kármán system, incremental differential equations are derived for nonaxisymmetric motion of the plate. A combined strain hardening law, in conjunction with special physical-based viscoplastic models, is applied to consider the material nonlinearity. Evaluation of the viscoplastic constitutive equations is accomplished by a semi-implicit scheme of the return mapping technique. An efficient algorithm is applied by the cutting-plane iteration to enforce plasticity admissibility during evolution of yield surface. A pseudo-spectral collocation methodology is implemented based on the Chebyshev polynomials in order to calculate displacement fields stepwise. Velocity and inertia terms are discrete by the Houbolt marching method. The nonlinear terms are eliminated by the quadratic extrapolation. The aliasing phenomenon caused by collocation treatment of nonlinear terms is controlled by applying an exponential filtering. A number of sector plates with different thicknesses, angularities, sector angles and boundary conditions are examined. The maximum transverse deflections, the effective plastic strain, dynamic yield stress, plastic works and temperatures are obtained. The present modeling is validated by comparing results with other approaches available in literature.