Efficient and robust constitutive integrators for single-crystal plasticity modeling

Simulations of the dynamic deformations of metal samples require elastic-plastic constitutive updates of the material behavior to be performed over a small time step between updates, as dictated by the Courant condition. Depending on the deformation conditions, the converged time step becomes short (~$10^{-9} s$ or less). If an implicit constitutive update is applied to this class of simulation, the benefit of the implicit update is negated, and the integration is prohibitively slow. The present work recasts an implicit update algorithm into an explicit form, for which each update step is five to six times faster, and the compute time required for a plastic update approaches that needed for a fully-elastic update. For dynamic loading conditions, the explicit model is found to perform an entire simulation up to 50 times faster than the implicit model. The performance of the explicit model is enhanced by adding a subcycling algorithm to the explicit model, by which the maximum time step between constitutive updates is increased an order of magnitude. These model improvements do not significantly change the predictions of the model from the implicit form, and provide overall computation times significantly faster than the implicit form over finite-element meshes. These modifications are also applied to polycrystals via Taylor averaging, where we also see improved model performance.Comment: 27 pages, 21 figure

Dynamic fragmentation of a brittle plate under biaxial loading: strength or toughness controlled?

The fragmentation of a brittle plate subjected to dynamic biaxial loading is investigated via numerical simulations. The aim is to extend our understanding of the dynamic processes affecting fragment size distributions. A scalable computational framework based on a hybrid cohesive zone model description of fracture and a discontinuous Galerkin formulation is employed. This enables large-scale simulations and, thus, the consideration of rich distributions of defects, as well as an accurate account of the role of stress waves. We study the dependence of the fragmentation response on defect distribution, material properties, and strain rate. A scaling law describing the dependence of fragment size on the parameters is proposed. It is found that fragmentation exhibits two distinct regimes depending on the loading rate and material defect distribution: one controlled by material strength and the other one by material toughness. At low strain rates, fragmentation is controlled by defects, whereas at high strain rates energy balance arguments dominate the fragmentation respons

A Finite Element Study of Electromagnetic Riveting

Electromagnetic riveting, used in some aerospace assembly processes, involves rapid deformation, leading to the finished rivet configuration. Analysis of this process is described for the case of an aluminum rivet joining typical aluminum structural elements. The analysis is based on a finite element method that includes the effects of heating, due to rapid plastic deformation of the material, on the material properties. Useful details of material deformation and thermal history and the final rivet and structure configuration and states of stress and strain are obtained. These results have significant implications in the design, implementation, and improvement of practical fastening processes in the aerospace industry

Direct Visualization of Laser-Driven Focusing Shock Waves

Cylindrically or spherically focusing shock waves have been of keen interest for the past several decades. In addition to fundamental study of materials under extreme conditions, cavitation, and sonoluminescence, focusing shock waves enable myriad applications including hypervelocity launchers, synthesis of new materials, production of high-temperature and high-density plasma fields, and a variety of medical therapies. Applications in controlled thermonuclear fusion and in the study of the conditions reached in laser fusion are also of current interest. Here we report on a method for direct real-time visualization and measurement of laser-driven shock generation, propagation, and 2D focusing in a sample. The 2D focusing of the shock front is the consequence of spatial shaping of the laser shock generation pulse into a ring pattern. A substantial increase of the pressure at the convergence of the acoustic shock front is observed experimentally and simulated numerically. Single-shot acquisitions using a streak camera reveal that at the convergence of the shock wave in liquid water the supersonic speed reaches Mach 6, corresponding to the multiple gigapascal pressure range 30 GPa

Dynamic fragmentation of a brittle plate under biaxial loading: strength or toughness controlled?

The fragmentation of a brittle plate subjected to dynamic biaxial loading is investigated via numerical simulations. The aim is to extend our understanding of the dynamic processes affecting fragment size distributions. A scalable computational framework based on a hybrid cohesive zone model description of fracture and a discontinuous Galerkin formulation is employed. This enables large-scale simulations and, thus, the consideration of rich distributions of defects, as well as an accurate account of the role of stress waves. We study the dependence of the fragmentation response on defect distribution, material properties, and strain rate. A scaling law describing the dependence of fragment size on the parameters is proposed. It is found that fragmentation exhibits two distinct regimes depending on the loading rate and material defect distribution: one controlled by material strength and the other one by material toughness. At low strain rates, fragmentation is controlled by defects, whereas at high strain rates energy balance arguments dominate the fragmentation response

Porcine Head Response to Blast

Recent studies have shown an increase in the frequency of traumatic brain injuries related to blast exposure. However, the mechanisms that cause blast neurotrauma are unknown. Blast neurotrauma research using computational models has been one method to elucidate that response of the brain in blast, and to identify possible mechanical correlates of injury. However, model validation against experimental data is required to ensure that the model output is representative of in vivo biomechanical response. This study exposes porcine subjects to primary blast overpressures generated using a compressed-gas shock tube. Shock tube blasts were directed to the unprotected head of each animal while the lungs and thorax were protected using ballistic protective vests similar to those employed in theater. The test conditions ranged from 110 to 740 kPa peak incident overpressure with scaled durations from 1.3 to 6.9 ms and correspond approximately with a 50% injury risk for brain bleeding and apnea in a ferret model scaled to porcine exposure. Instrumentation was placed on the porcine head to measure bulk acceleration, pressure at the surface of the head, and pressure inside the cranial cavity. Immediately after the blast, 5 of the 20 animals tested were apneic. Three subjects recovered without intervention within 30 s and the remaining two recovered within 8 min following respiratory assistance and administration of the respiratory stimulant doxapram. Gross examination of the brain revealed no indication of bleeding. Intracranial pressures ranged from 80 to 390 kPa as a result of the blast and were notably lower than the shock tube reflected pressures of 300–2830 kPa, indicating pressure attenuation by the skull up to a factor of 8.4. Peak head accelerations were measured from 385 to 3845 G’s and were well correlated with peak incident overpressure (R2 = 0.90). One SD corridors for the surface pressure, intracranial pressure (ICP), and head acceleration are presented to provide experimental data for computer model validation

A Second-Order Linear Newmark Method for Lagrangian Navier-Stokes Equations

[Abstract]: In this paper we propose a second-order pure Lagrange-Galerkin method for the numerical solution of free surface problems in fluid mechanics. We consider a viscous, incompressible Newtonian fluid in a time dependent domain which may present large deformations but no topological changes at interfaces. Pure-Lagrangian methods are useful for solving these problems because the convective term disappears, the computational domain is independent of time and modelling and tracking of the free surface is straightforward as far as there is no solid walls preventing the free motion of surface particles. Unfortunately, for moderate to high-Reynolds number flows and as a consequence of high distortion of the moved mesh, it can be necessary to re-mesh and re-initialize the motion each certain time. In this paper, a Newmark algorithm is considered for both, the time semi-discretization of equations in Lagrangian coordinates and the computation of initial conditions. The proposed scheme is pure-Lagrangian and can be written in terms of either material velocity and pressure or material acceleration and pressure or material displacement and pressure. The three formulations are stated. In order to assess the performance of the overall numerical method, we solve different problems in two space dimensions. In particular, numerical results of a dam break problem and a flow past a cylinder are presented.This work was partially funded by FEDER and the Spanish Ministry of Science and Innovation under research projects ENE2013-47867-C2-1-R and MTM2013-43745-R, and by FEDER and Xunta de Galicia under research project GRC2013/014.Xunta de Galicia; GRC2013/01

A scalable 3D fracture and fragmentation algorithm based on a hybrid, discontinuous Galerkin, Cohesive Element Method

A scalable algorithm for modeling dynamic fracture and fragmentation of solids in three dimensions is presented. The method is based on a combination of a discon- tinuous Galerkin (DG) formulation of the continuum problem and Cohesive Zone Models (CZM) of fracture. Prior to fracture, the flux and stabilization terms aris- ing from the DG formulation at interelement boundaries are enforced via interface elements, much like in the conventional intrinsic cohesive element approach, albeit in a way that guarantees consistency and stability. Upon the onset of fracture, the traction-separation law (TSL) governing the fracture process becomes operative without the need to insert a new cohesive element. Upon crack closure, the rein- statement of the DG terms guarantee the proper description of compressive waves across closed crack surfaces. The main advantage of the method is that it avoids the need to propagate topo- logical changes in the mesh as cracks and fragments develop, which enables the indistinctive treatment of crack propagation across processor boundaries and, thus, the scalability in parallel computations. Another advantage of the method is that it preserves consistency and stability in the uncracked interfaces, thus avoiding issues with wave propagation typical of intrinsic cohesive element approaches. A simple problem of wave propagation in a bar leading to spall at its center is used to show that the method does not affect wave characteristics and as a consequence properly captures the spall process. We also demonstrate the ability of the method to capture intricate patterns of radial and conical cracks arising in the impact of ceramic plates which propagate in the mesh impassive to the presence of processor boundaries