In this two-part paper we begin the development of a new class of methods for modeling fluid-structure interaction (FSI) phenomena for air blast. We aim to develop accurate, robust, and practical computational methodology, which is capable of modeling the dynamics of air blast coupled with the structure response, where the latter involves large, inelastic deformations and disintegration into fragments. An immersed approach is adopted, which leads to an a-priori monolithic FSI formulation with intrinsic contact detection between solid objects, and without formal restrictions on the solid motions. In Part I of this paper, the core air-blast FSI methodology suitable for a variety of discretizations is presented and tested using standard finite elements. Part II of this paper focuses on a particular instantiation of the proposed framework, which couples isogeometric analysis (IGA) based on non-uniform rational B-splines and a reproducing-kernel particle method (RKPM), which is a meshfree technique. The combination of IGA and RKPM is felt to be particularly attractive for the problem class of interest due to the higher-order accuracy and smoothness of both discretizations, and relative simplicity of RKPM in handling fragmentation scenarios. A collection of mostly 2D numeri-B Y. Bazilevs
In the conventional Newmark family for time integration of hyperbolic problems, both explicit and implicit methods are inherently sequential in the time domain and not well suited for parallel implementations due to unavoidable processor communication at every time step. In this work we propose a Waveform Relaxation Newmark (WRN β ) algorithm for the solution of linear second-order hyperbolic systems of ODEs in time, which retains the unconditional stability of the implicit Newmark scheme with the advantage of the lower computational cost of explicit time integration schemes. This method is unstructured in the time domain and is well suited for parallel implementation. We consider a Jacobi and Gauss-Seidel type splitting and study their convergence and stability. The performance of the WRN β algorithm is compared to a standard implicit Newmark method and the obtained results confirm the effectiveness of the Waveform Relaxation Newmark algorithm as a new class of more efficient time integrators, which is applicable, as shown in the numerical examples, to both the finite element method and meshfree methods (e.g. the reproducing kernel particle method).
Meshfree methods such as the reproducing kernel particle method (RKPM) are well suited for modeling materials and solids undergoing fracture and damage processes, and nodal integration is a natural choice for modeling this class of problems. However, nodal integration suffers from spatial instability, and the excessive material deformation and damage process could also lead to kernel instability in RKPM. This paper reviews the recent advances in nodal integration for meshfree methods that are stable, accurate, and with optimal convergence. A variationally consistent integration (VCI) is introduced to allow correction of low order quadrature rules to achieve optimal convergence, and several stabilization techniques for nodal integration are employed. The application of the stabilized RKPM with nodal integration for shock modeling, fracture to damage multiscale mechanics, and materials modeling in extreme events, are demonstrated. These include the modeling of man-made disasters such as fragmentimpact processes, penetration, shock, and blast events will be presented to demonstrate the effectiveness of the new developments.
This special issue is dedicated to Steve Attaway, who passed away on February 28, 2019. Steve Attaway worked at Sandia National Laboratories in Albuquerque, NM, for over 30 years making significant contributions in highperformance computing, shock physics, meshfree methods, the geosciences, concrete mechanics, and blast effects on structures. Steve's early contributions in meshfree methods included stability analysis of smoothed particle hydrodynamics (SPH) (Swegle, J.
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