SUMMARYThis paper is concerned with developing a numerical tool for detecting instabilities in elasto-plastic solids (with an emphasis on soils) and inserting a discontinuity at these instabilities allowing the boundary value problem to proceed beyond these instabilities. This consists of implementing an algorithm for detection of strong discontinuities within a finite element (FE) framework. These discontinuities are then inserted into the FE problem through the use of a displacement field enrichment technique called the extended finite element method (XFEM). The newly formed discontinuities are governed by a Mohr-Coulomb frictional law that is enforced by a penalty method. This implementation within an FE framework is then tested on a compressive soil block and a soil slope where the discontinuity is inserted and grown according to the localization detection.

The Sandia Fracture Challenges provide the mechanics community a forum for assessing its ability to predict ductile fracture through a blind, round-robin format where mechanicians are challenged to predict the deformation and failure of an arbitrary geometry given experimental calibration data. The Third Challenge, issued in 2017, required participants to predict fracture in an additively manufactured 316L stainless steel tensile-bar configuration containing through holes and internal cavities that could not have been conventionally machined. The volunteer participants were provided extensive materials data, from tensile tests of specimens printed on the same build tray to electron backscatter diffraction maps of the microstructure and micro-computed tomography scans of the Challenge geometry. The teams were asked to predict a number of quantities of interest in the response, including predictions of variability in the resulting fracture response, as the basis for assessment of the predictive capabilities of the modeling and simulation strategies. This paper describes the Third Challenge, compares the experimental results to the predictions, and identifies successes and gaps in capabilities in both the experimental procedures and the computational analyses to inform future investigations.

Ductile failure of structural metals is relevant to a wide range of engineering scenarios. Computational methods are employed to anticipate the critical conditions of failure, yet they sometimes provide inaccurate and misleading predictions. Challenge scenarios, such as the one presented in the current work, provide an opportunity to assess the blind, quantitative predictive ability of simulation methods against a previously unseen failure problem. Rather than evaluate the predictions of a single simulation approach, the Sandia Fracture Challenge relies on numerous volunteer teams with expertise in computational mechanics to apply a broad range of computational methods, numerical algorithms, and constitutive models to the challenge. This exercise is intended to evaluate the state of health of technologies available for failure prediction. In the first Sandia Fracture Challenge, a wide range of issues were raised in ductile failure modeling, including a lack of consistency in failure models, the importance of shear calibration data, and difficulties in quantifying the uncertainty of prediction [see Boyce et al. (Int J Fract 186:5-68, 2014) for details of these observations]. This second Sandia Fracture Challenge investigated the ductile rupture of a Ti-6Al-4V sheet under both quasi-static and modest-rate dynamic loading (failure in ∼0.1 s). Like the previous challenge, the sheet had an unusual arrangement of notches and holes that added geometric complexity and fostered a competition between tensile-and shear-dominated failure modes. The teams were asked to predict the fracture path and quantitative far-field failure metrics such as the peak force and displacement to cause crack initiation. Fourteen teams contributed blind predictions, and the experimental outcomes were quantified in three independent test labs. Additional shortcomings were revealed in this second challenge such as inconsistency in the application of appropriate boundary conditions, need for a thermomechanical treatment of the heat generation in the dynamic loading condition, and further difficulties in model calibration based on limited realworld engineering data. As with the prior challenge, this work not only documents the 'state-of-the-art' in computational failure prediction of ductile tearing scenarios, but also provides a detailed dataset for non-blind assessment of alternative methods.

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