Existing and emerging methods in computational mechanics are rarely validated against problems with an unknown outcome. For this reason, Sandia National Laboratories, in partnership with US National Science Foundation and Naval Surface Warfare Center Carderock Division, launched a computational challenge in mid-summer, 2012. Researchers and engineers were invited to predict crack initiation and propagation in a simple but novel geometry fabricated from a common off-the-shelf commercial engineering alloy. The goal of this international Sandia Fracture Challenge was to benchmark the capabilities for the prediction of deformation and damage evolution associated with ductile tearing in structural metals, including physics models, computational methods, and numerical implementations currently available in the computational fracture community. Thirteen teams participated, reporting blind predictions for the outcome of the Challenge. The simulations and experiments were performed independently and kept confidential. The methElectronic supplementary material The online version of this article (doi:10.1007/s10704-013-9904-6) contains supplementary material, which is available to authorized users.Sandia National Laboratories, Albuquerque, NM, USA e-mail: blboyce@sandia.gov ods for fracture prediction taken by the thirteen teams ranged from very simple engineering calculations to complicated multiscale simulations. The wide variation in modeling results showed a striking lack of consistency across research groups in addressing problems of ductile fracture. While some methods were more successful than others, it is clear that the problem of ductile fracture prediction continues to be challenging. Specific areas of deficiency have been identified through this effort. Also, the effort has underscored the need for additional blind prediction-based assessments.

Reproducing kernel particle method (RKPM) has been applied to many large deformation problems. RKPM relies on polynomial reproducing conditions to yield desired accuracy and convergence properties but requires appropriate kernel support coverage of neighboring nodes to ensure kernel stability. This kernel stability condition is difficult to achieve for problems with large particle motion such as the fragment-impact processes that commonly exist in extreme events. A new reproducing kernel formulation with 'quasi-linear' reproducing conditions is introduced. In this approach, the first-order polynomial reproducing conditions are approximately enforced to yield a nonsingular moment matrix. With proper error control of the first-order completeness, nearly second-order convergence rate in L2 norm can be achieved while maintaining kernel stability. The effectiveness of this quasi-linear RKPM formulation is demonstrated by modeling several extremely large deformation and fragment-impact problems.

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.