Implementation and Verification of RKPM in the Sierra/SolidMechanics Analysis Code

Abstract

The reproducing kernel particle method (RKPM) is a meshfree method for computational solid mechanics that can be tailored for an arbitrary order of completeness and smoothness. The primary advantage of RKPM relative to standard finite-element (FE) approaches is its capacity to model large deformations, material damage, and fracture. Additionally, the use of a meshfree approach offers great flexibility in the domain discretization process and reduces the complexity of mesh modifications such as adaptive refinement. We present an overview of the RKPM implementation in the Sierra/SolidMechanics analysis code, with a focus on verification, validation, and software engineering for massively parallel computation. Key details include the processing of meshfree discretizations within a FE code, RKPM solution approximation and domain integration, stress update and calculation of internal force, and contact modeling. The accuracy and performance of RKPM are evaluated using a set of benchmark problems. Solution verification, mesh convergence, and parallel scalability are demonstrated using a simulation of wave propagation along the length of a bar. Initial model validation is achieved through simulation of a Taylor bar impact test. The RKPM approach is shown to be a viable alternative to standard FE techniques that provides additional flexibility to the analyst community.

Verification and large deformation analysis using the reproducing kernel particle method

“…The grey, horizontal line is the measured height from the experiment and the other lines are the predictions given by the simulations. Three discretizations are considered: a coarse discretization with 938 nodes, a medium discretization with 26 488 nodes, and a fine discretization with 46 592 nodes [12]. The medium and fine refinements have a nearly identical response and predict the final height very well.…”

“…Instead of considering a characteristic element length, the RKPM uses the support distance instead as well as the wave speed of the material given by the effective lamé parameters and material density. The integration method (SCNI, SNNI, VCSNNI) also affects the critical time step [1,12]. In the foam crush analysis, significant oscillation could be observed, shown in Currently, RKPM is implemented using a Lagrangian formulation.…”

“…Computed final height of taylor bar[12] Traction patch test of RKPM simulation movement in the x-direction only to ensure a linear displacement field was achieved in all directions. To remove transient motion from the analysis the explicit analysis employs a halver-cosine ramp function with a duration of 1.0 × 10 −3 s to limit the amount of oscillation in the bar.…”