In this work, we have developed nonlinear peridynamics models of drained and saturated geomaterials, and applied them to simulations of dynamic fragmentation and ejecta formation due to impulse loads. First, we have re-phrased and re-interpreted the non-local state-based peridynamics formulation to connect the non-local integral operator with the local differential operator. Second, we have implemented the Drucker-Prager plasticity model in state-based peridynamics at finite strain. A peridynamics version of the Hughes and Winget algorithm is derived for the constitutive update. Third, we have developed a peridynamics U-p formulation for saturated geomaterials. Fourth, numerical simulations have been carried out to verify the proposed peridynamics formulations in the simulation of geomaterial fragmentation induced by impulse loads. Comparisons of analytical and numerical results indicate that the peridynamics model has the ability to both match traditional continuum compression examples, as well as simulate complex geomaterial fragmentation processes resulting from impulse loads. PERIDYNAMICS SIMULATION OF GEOMATERIAL FRAGMENTATION 1305 particle method [2]. In CZM, the cohesive zone is embedded at the edges or facets of the original FE mesh, [3]. In the literature, many researchers have studied the fragmentation processes of solids using CZM, [4][5][6]. In these studies, usually phenomenological elastic or inelastic traction-separation cohesive laws are used to control the fracture behavior. Extended FEM adopts an enrichment of the field, in which discontinuous shape functions are used to represent the evolving discontinuous/fracturing domain, [7]. The meshfree methods use the parametric visibility condition to cut off the particle connections that cross the crack [8]. These approaches require precise calculation and representation of the crack surfaces, which have been successfully implemented for the single-crack and multiple-crack problems. However, tracking the crack surfaces can become complex and cumbersome when simulating fragmentation processes, which involve huge numbers of crack surfaces interwoven at different length scales. It is difficult to develop a numerical algorithm to deal with these complex geometric evolutions in three-dimensional (3D) space, including crack initiation and growth, crack surface description, and geometric data bookkeeping. In particular, geomaterials are multiphase materials composed of solids, liquids, and gases that are spatially heterogeneous, and as a result, simulating their dynamic failure process is complex.In recent years, peridynamics has emerged as a viable and efficient numerical method for solving many material and structural failure problems in engineering mechanics applications. This is due to its ability to represent and capture discontinuous deformation in solids and structures during their failure processes. The state-based peridynamics theory uses a non-local integral formulation to approximate the partial differential equations representing the local physica...

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A B S T R A C TIn this work, we employ both the state-based peridynamics and the smoothed particle hydrodynamics (SPH) to simulate soil fragmentation/ejection induced by the blast of buried explosives. We use peridynamics representation to model soil medium, and we use SPH representation to model explosive gas. The key of the simulation is the coupling of the two. In the peridynamics-SPH computational domain, there is an interphase zone, in which a peridynamic particle can have SPH particles within its own horizon, while an SPH particle can have peridynamic particles within its supporting domain. The interactions of the peridynamic and SPH particles in this interphase zone are discussed. By assuming the equivalence of the two methods in the current configuration, we study how to choose simulation parameters that can seamlessly couple the two methods. A Drucker-Prager plasticity soil model at finite strain is used for soil medium and a charge model of equation of state is used to model the buried explosive. Numerical examples are carried out to simulate soil fragmentation/ejection induced by the shock waves from the buried explosive. It is shown that the numerical results are in general agreement with that of the experiment.

In this work, a nonlocal peridynamics-smoothed particle hydrodynamics (SPH) coupling formulation has been developed and implemented to simulate soil fragmentation induced by buried explosions. A peridynamics-SPH coupling strategy has been developed to model the soilexplosive gas interaction by assigning the soil as peridynamic particles and the explosive gas as SPH particles. Artificial viscosity and ghost particle enrichment techniques are utilized in the simulation to improve computational accuracy. A Monaghan type of artificial viscosity function is incorporated into both the peridynamics and SPH formulations in order to eliminate numerical instabilities caused by the shock wave propagation. Moreover, a virtual or ghost particle method is introduced to improve the accuracy of peridynamics approximation at the boundary. Three numerical simulations have been carried out based on the proposed peridynamics-SPH theory: (1) a 2D explosive gas expansion using SPH, (2) a 2D peridynamics-SPH coupling example, and (3) an example of soil fragmentation in a 3D soil block due to shock wave expansion. The simulation results reveal that the peridynamics-SPH coupling method can successfully simulate soil fragmentation generated by the shock wave due to buried explosion.

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