The group led by Parsons and Hjelmstad, aided by Hales, Namazifard, Taciroglu and Schranz, has developed a scaleable parallel finite element code capable of forming the backbone for structural model development of the solid rocket motor. The code is based on a linear multigrid solver, and is capable of solving nonlinear transient problems using an implicit time integrator. The code executes in parallel on shared or distributed memory machines using the standard MPI library. Preliminary benchmarking studies demonstrate that the procedure is scaleable. These data were fit to the standard Amdahl’s law curve, indicating that about 98% of the code executes in parallel. This figure is expected to increase when larger problems are considered (partly because the communication time will represent a smaller fraction of the total execution time).
Additional work of this group has focused on development of mesh generation procedures for the multigrid solver. We currently use TrueGrid to produce the sequence of meshes required by the multigrid solver. This allows us to generate nested meshes for complicated parts. Domain decomposition is then performed on the coarsest mesh using Metis. This ensures that we have optimal load balance among all processors on all levels. Data are finally output in the form required by our analysis code. The figure above shows some representative meshes and partitions for the rocket simulation. Other work has considered advanced solid element formulations (e.g., based on assumed strain methods) and material model development (linear and nonlinear viscoelastic models).
In the immediate future, the Structural Analysis group will continue benchmarking studies to determine whether the code scales well on the multiprocessor ASCI computers when extremely large problems (10 million or more elements) are considered. Element and material model development will also continue. Meshing algorithms will be modified to treat the complications introduced by moving boundaries (specifically, a combustion front moving through the propellant). Contact algorithms will be combined with our multigrid solver so that details such as joints may be incorporated into the model. Studies on fluid-structure interaction will be conducted to help determine the most suitable algorithm for coupling fluid and structural calculations in an integrated code.
The group led by Haber and Tortorelli, with Acharya, Sobh, Lin and Palaniappan has been working this year on the formulation and implementation of advanced numerical methods for rigorous modeling of the response of the solid grain as it interacts with the moving combustion front. Part of this effort involved the formulation on nonlinear viscoelastic constitutive models for the bulk response of the solid propellant. This group has also actively participated in the on-going effort to use rigorous balance laws and constitutive relations to formulate the jump conditions at a sharp combustion interface, including the effects of finite deformation of the solid. The requirement to maintain independent descriptions of the velocities of the combustion front and the adjacent solid material is a significant outcome that distinguished the numerical solid model we are developing from the models used in earlier versions (GEN0 and GENH) of the CSAR code. This group has worked specifically on the development of space-time finite element methods that can continuously track the motion of the combustion interface. This work includes investigation of novel discontinuous Galerkin finite element formulations and 4-D space-time mesh generation with colleagues in Computer Science (Edelsbrunner and Teng). This group is exploring variants of Finite Element Tearing and Interconnecting method (FETI) algorithms as a means of enforcing the jump conditions across the combustion interface in the coupled system, as well as domain decomposition techniques for parallel computation within the solid region.
In the coming year, the Solid-Combustion-Fluid Interface group will develop new codes based on these formulations to describe the response of the solid propellant during a normal burn scenario. The resulting code will be integrated with codes for the response of the fluid, combustion and case regions. Scalability will play a central role in the software design. Work will also be done on adaptive procedures to take advantage of unstructured meshing over the space-time domain.
In addition to research activities directly concerned with the development of the fully integrated (GEN1) code, a series of research efforts related to the GEN2 code are currently underway. Most of these activities are aimed at modeling the constitutive and failure behaviors of the solid propellant and the case, and involve a wide variety of numerical tools.
At the continuum level, Sofronis and Meyer are developing a 3-D phenomenological model for the behavior of the polymeric binder in the viscoelastic regime. The model, which accounts for large strains and for the effect of strain rate and temperature, has recently been implemented into an ABAQUS UMAT subroutine and is currently being tested under various loading conditions. Future efforts include combining this model with a special form of Hill’s approach aimed at capturing the failure behavior of the solid propellant. After the constitutive law for nonlinear response is established, the issue of hot spot generation will be addressed. The idea is that intense shear deformation within the material may result in rapid energy generation that can trigger a localized reaction leading to a hot spot. These phenomena of plastic instability in solid propellants are investigated in collaboration with Professor Aravas of the University of Thessaly, Greece, who visited CSAR this past summer.
Also at the continuum level, Geubelle and members of his group are developing a special form of the cohesive volumetric finite element (CVFE) scheme to study spontaneous crack propagation in the solid propellant. Special emphasis is put on the incorporation of rate dependence in the failure model and in the adequate treatment of contact between the crack faces. Kubair currently investigates the importance of rate-dependence in spontaneous dynamic cohesive fracture with the aid of a spectral scheme. Lin has developed a quasi-static CVFE scheme, which includes a local contact component. To validate the code, numerical and experimental results a fiber pushout test performed on a model polyester/epoxy composite system have been compared. Excellent agreement has been shown, as illustrated in Fig. 3.5 (TO BE INSERTED). Future plans for this part of the project include the addition of a global contact algorithm in both the quasi-static and dynamic CVFE codes.
Beaudoin, Dodds, Acharya, and Schalk are currently working on the formulation and implementation of a physically motivated gradient single crystal plasticity model to explain size effects in metallic single crystal response. Special emphasis has been put so far on the implementation of the Mechanical Stress Threshold (MTS) model. At present, a material subroutine has been written for rate-dependent, isothermal yield behavior, incorporated into ABAQUS and used to simulate stress relaxation for aluminum alloys (Fig. 3.6)(TO BE INSERTED). A literature search for the D6AC steel used in the Space Shuttle has provided a report on biaxial testing, authored by the Defense Science and Technology Organization of Australia. The experimental data available in that report will be used to fit the parameters to the MTS model for D6AC. Future plans involve extending the formulation to polycrystalline plasticity and incorporating the final model in existing 3-D ductile fracture codes such as WARP3D. This part of the project also involves close collaboration with Dr. Stout’s group at LANL where Beaudoin and one of his students (Michael Bange) spent a substantial part of this past summer collecting high strain rate and high temperature data on aluminum alloys.
At a much smaller scale, Averback, Sofronis, and Albe have recently started to develop a coupled continuum/molecular dynamics scheme to study the debonding of polymeric-ceramic interfaces. As a first step, interfacial fracture between metals and their native oxides will be studied as model for interfacial fracture in a rigid/plastic system. Work is currently underway to develop the appropriate potentials for this system.
Finally, molecular dynamics (MD) simulations are also used by Schweizer to study the tracer diffusion of penetrants in dense polymeric materials. This phenomenon is of fundamental importance in a variety of material reliability and aging problems. It is a slow process, and thus difficult or impossible to simulate at the atomistic level via classical MD techniques. A project has been initiated to develop a novel hybrid theory-simulation approach that combines short time MD results with nonequilibrium statistical dynamical theory for long time motion. The goal is to predict for specific material systems both the macroscopic penetrant diffusion constant and anomalous non-Fickian transport at intermediate times. In collaboration with scientists at Sandia National Laboratory, future work will continue to focus on methodology development, and also quantitative tests of the hybrid approach by comparing its predictions against massive simulations for model systems consisting of small spherical penetrant particles diffusing in polymer melts of variable local structures.