Meshfree Methods for Fracture and High-Velocity Impact Simulation

The study of projectile penetration has a long history with a great military research interest for various applications such as projectile’s design to maximize depth of penetration into different materials, or penetration depth prediction for munitions removal for military training sites. The nature of the problem involves complex physics and mechanics, leading to extremely large deformations, high velocity penetration, and highly fragmented configurations, which in turn posts immense challenges in computational simulations. The aims of this study is to develop computational tools, addressing challenges at micro- and macro-scales, to simulate and study mechanisms of projectile penetration into soils. Within a hierarchical multiscale framework, a microscale model accounting micro defeats and their evolution can be simulated in detail in order to develop physically based constitutive models for geomaterials. However, simulating an excessive amount of defeats and how they propagate, branch, and nuclear, remains a big challenge in computation. The phase-field variational approaches have gained considerable amount of interest to address challenges abovementioned. However, phase-field becomes a computationally expensive method when narrow-width crack with a small value for length-scale parameter is required, which demands an extremely fine mesh close to the crack initiation location and on its propagation path. Moreover, Galerkin methods require quadrature rule for numerical integration which leads to either integration inaccuracy and instability or excessively high computational cost. To overcome domain integration issues and mesh-size dependency of the phase-field approach, two new methods are introduced within the Reproducing Kernel (RK) collocation method. A high-order gradient reproducing kernel collocation method (HGRKCM) is introduced for solving higher order phase-field formulation, such as the fourth-order formulation which increases the regularity of the phase-field solution. The method provides stable and accurate solutions by solving the determined system of equations and gradient derivatives of RK shape functions, which boost the computational efficiency compared to regular RK collocation methods. Besides, a Harmonic RK (HRK) method is introduced to address the mesh-decency of the phase-field problem. The method provides exact approximation for the phase-field solution up to machine limit with considerably coarser nodal distant size compared to other methods. Harmonic-enriched RK in the HGRKCM framework provide a robust method for solving the phase-field problem in term of both accuracy and efficiency. To simulate the penetration process at the macroscale, a two-field (u - p) formulation based on the Biot theory has been developed and implemented under the semi-Lagrangian RK framework, where displacement and pressure fields are independently approximated by the semi-Lagrangian RK shape functions. A Drucker-Prager type constitutive model including a one-parameter damage model is employed to simulate the material behavior as well as the separation phenomenon. For numerical stability, Modified Stabilized Non-conforming Nodal Integration (MSNNI) within an explicit temporal dynamic algorithm is used. The method is validated for penetration simulation into dry and fully saturated soils.