High-rate deformation processes of metals entail intense grain refinement and special attention needs to be paid to capture the evolution of microstructure. In this article, a new formulation for coupling Cosserat crystal plasticity and phase field is developed. A common approach is to penalize kinematic incompatibility between lattice orientation and displacement-based elastic rotation. However, this can lead to significant solution sensitivity to the penalty parameter, resulting in low accuracy and convergence rates. To address these issues, a duality-based formulation is developed which directly imposes the rotational kinematic compatibility. A weak inf-sup-based skew-symmetric stress projection is introduced to suppress instabilities present in the dual formulation. An additional least squares stabilization is introduced to suppress the spurious lattice rotation with a suitable parameter range derived analytically and validated numerically. The required high-order continuity is attained by the reproducing kernel approximation. It is observed that equal order displacement-rotation-phase field approximations are stable, which allows efficient employment of the same set of shape functions for all independent variables. The proposed formulation is shown to yield superior accuracy and convergence with marginal parameter sensitivity compared to the penalty-based approach and successfully captures the dominant rotational recrystallization mechanism including block dislocation structures and grain boundary migration.
A stable and nodally integrated meshfree formulation for modeling shock waves in fluids is developed. The reproducing kernel approximation is employed to discretize the conservation equations for compressible flow, and a flux vector splitting approach is applied to allow proper numerical treatments for the advection and pressure parts, respectively, based on the characteristics of each flux term. To capture the essential shock physics in fluids, including the Rankine–Hugoniot jump conditions and the entropy condition, local Riemann enrichment is introduced under the stabilized conforming nodal integration (SCNI) framework. Meanwhile, numerical instabilities associated with the advection flux are eliminated by adopting a modified upwind scheme. To further enhance accuracy, a MUSCL-type method is introduced in conjunction with an oscillation limiter to avoid Gibbs phenomenon and ensure monotonic piecewise linear reconstruction in the smooth region. The present meshfree formulation is free from tunable artificial parameters and is capable of capturing shock and rarefaction waves without over/undershoots. Several numerical examples are analyzed to demonstrate the effectiveness of the proposed MUSCL-SCNI approach in meshfree modeling of complex shock phenomena, including shock diffraction, shock–vortex interaction, and high energy explosion processes.
A new model for determining band gaps for elastic wave propagation in a periodic composite beam structure is developed using a non-classical Bernoulli–Euler beam model that incorporates the microstructure, surface energy and rotational inertia effects. The Bloch theorem and transfer matrix method for periodic structures are employed in the formulation. The new model reduces to the classical elasticity-based model when both the microstructure and surface energy effects are not considered. The band gaps predicted by the new model depend on the microstructure and surface elasticity of each constituent material, the unit cell size, the rotational inertia, and the volume fraction. To quantitatively illustrate the effects of these factors, a parametric study is conducted. The numerical results reveal that the band gap predicted by the current non-classical model is always larger than that predicted by the classical model when the beam thickness is very small, but the difference is diminishing as the thickness becomes large. Also, it is found that the first frequency for producing the band gap and the band gap size decrease with the increase of the unit cell length according to both the current and classical models. In addition, it is observed that the effect of the rotational inertia is larger when the exciting frequency is higher and the unit cell length is smaller. Furthermore, it is seen that the volume fraction has a significant effect on the band gap size, and large band gaps can be obtained by tailoring the volume fraction and material parameters.
The Structural Reliability Partnership Workshop was held in Albuquerque, NM on August 29-30, 2017 and was hosted by Sandia National Laboratories. Attendees were present from academia, industry and several other national laboratories. The workshop kicked off with an introduction to the SRP to familiarize potential members with what the purpose, structure and benefits would be to their organization. Technical overviews were given on several topics by attendees from each sector – national labs, universities and industry – to provide a snapshot of the type of work that is currently being conducted on structural reliability. Attendees were then given the opportunity to suggest and discuss potential Challenge Scenario topics. Three were ultimately decided upon as being the most important: Additive Manufacturing, Hydrogen Pipeline Steels, and Bolted Joined Structures. These were then analyzed using Quad Charts to determine What, How, Who, and Why these areas would be further investigated. Rather than restricting future research to only one area, the option was left open to investigate both the top two, depending on interest and cost associated with hosting such an event. More informal collaboration may be undertaken for the third topic if members have time and interest. Other items discussed pertained to the organization, structure and policies of the Partnership. Topics including Data Management, IP, and mechanisms of partnering/information sharing were touched upon but final decisions were not made. Further action is needed before this can be done. Action items were outlined and assigned, where possible. The next workshop is to be held in early August 2018 in Boulder, CO and is to be hosted by NIST. In the interim, quarterly updates are to take place via WebEx to maintain a line of communication and to ensure progress on both the administrative and technical tasks.
Recent work at Sandia National Laboratories has focused on preparing strong predictive models for the simulation of ductile failure in metals. The focus of this talk is on the development of engineering-ready models that use a phenomenological approach to represent the ductile fracture processes. As such, an empirical tearing parameter that accounts for mean stress effects along the crack front is presented. A critical value of the tearing parameter is used in finite element calculations as the criterion for crack growth. Regularization is achieved with three different methods and the results are compared. In the first method, upon reaching the critical tearing, the stress within a solid element is decayed by uniformly shrinking the yield surface over a user specified amount of strain. This yields mesh-size dependent results. As a second method for regularization, cohesive surface elements are inserted using an automatic remeshing technique. In the third method, strain-localization elements are inserted with the automated remeshing.