Discretized peridynamics for brittle and ductile solids

Abstract

Peridynamics is a theory of continuum mechanics expressed in forms of integral equations rather than partial differential equations. In this paper, a peridynamics code is implemented using a graphics processing unit for highly parallel computation, and numerical studies are conducted to investigate the responses of brittle and ductile material models. Stress-strain behavior with different grid sizes and horizons is studied for a brittle material model. A comparison of stresses and strains between finite element analysis (FEA) and peridynamic solutions is performed for a ductile material. By applying the proposed procedure to bridge the material model defined for peridynamic bonds and the corresponding macroscale material model for FEA, peridynamics and FEA show good agreements as regards the stresses and strains.

Peridynamic Modeling of Ruptures in Biomembranes

“…The adaptive time-step assures convergence of the fixed-point iteration. In addition to implicit integration, we employ two other means of reducing the simulation time: mass scaling (in our simulations we take the membrane density to be 1000 kg / m 3 scaled up by a factor of 10 8 ) and GPU parallelization[19, 34]. The effect of mass scaling is described in S1 File.…”

Impact fracture analysis enhanced by contact of peridynamic and finite element formulations

“…For example, a mapping strategy to determine the peridynamic material model at the bond level based on the material model at the macroscale for finite element analysis is described in Ref. [39]. In the present study, the goal is to cast a constitutive model at the peridynamic bond level that shows consistency to the experimental observation at the macroscale level.…”

“…To compare the numerical results with the analytical solutions of the projectile residual velocity, the approximate mass ratio given in Equation (40) is fitted to be 0.80. By substituting a ¼ 0.80, p ¼ 2.0 [55] and v bl ¼ 178 m=s into Equation (39), analytical values of the residual velocity are obtained. The numerical results to the analytical solutions of the residual velocity are plotted in Fig.…”

“…Compared to the finite element method, peridynamics is computationally expensive. Liu and Hong [39] used a graphics-processing unit for the highly parallel computation of peridynamics. Macek and Silling [40] implemented peridynamics in a commercial finite element code, ABAQUS, using truss elements.…”

GPU computing for accelerating the numerical Path Integration approach

“…Apparently GPU computing can be used for a number of purposes such as generating various parametric maps, basins of attractions, bifurcation diagrams, etc. Some results of GPU computing can be found in solid mechanics, see for instance [5] and references therein. In this paper we will focus on a more fundamental concept used for describing a response of a stochastic system -a probability density function (PDF).…”