Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> D. LARGE DEFORMATION PROBLEM <s> MAGI, a three-dimensional shock and material response code which is based on smoothed particle hydrodynamics (SPH) is described. Calculations are presented and compared with experimental results. The SPH method is unique in that it employs no spatial mesh. The absence of a grid leads to some nice features such as the ability to handle large distortions in a pure Lagrangian frame and a natural treatment of voids. Both of these features are important in the tracking of debris clouds produced by hypervelocity impact—a difficult problem for which SPH seems ideally suited. We believe this is the first application of SPH to the dynamics of elastic-plastic solids. <s> BIB001 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> D. LARGE DEFORMATION PROBLEM <s> Abstract We describe a version of the smooth particle hydrodynamics (SPH) method suitable for modeling solids. The model includes strength and implements a von Mises yielding relation for stresses beyond the Hugoniot elastic limit. At lower stresses associated with brittle failure we use a rate-dependent strength based on the nucleation and growth of explicit Weibull flaws. We illustrate the capabilities of our fracture model by examining the propagation of cracks in a simple tensile rod, and by comparing simulations with laboratory experiments for high speed impacts and cratering. <s> BIB002 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> D. LARGE DEFORMATION PROBLEM <s> Abstract SPH (Smooth Particle Hydrodynamics) techniques provide the capability to perform high distortion impact computations in a Lagrangian framework. It is also possible to link SPH nodes with standard finite elements such that solutions can be obtained for problems involving both highly distorted flow and structural response. This paper presents the basic computational algorithm which includes a recently developed Normalized Smoothing Function. It discusses issues associated with smoothing functions, smoothing distances, free boundaries, material interfaces and artificial viscosity. It also presents techniques to allow SPH nodes to interact with standard finite element grids through sliding, attachment and automatic generation of SPH nodes from distorted finite elements. Examples are provided to illustrate the capabilities, algorithms and issues. <s> BIB003 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> D. LARGE DEFORMATION PROBLEM <s> The smoothed particle hydrodynamics (SPH) technique in conjunction with the macro-homogeneous, anisotropic material concept for fiber composites has been proposed for the simulation of impact damage and penetration of composite structures. To describe material behavior under high-intensity loadings, a 3-D anisotropic elasto-plasticity constitutive model, an equation of state, and a failure criterion for unidirectional composites have been developed. Furthermore, in order to maintain material frame indifference of the constitutive equations, the polar stress rate approach was employed in the stress and strain transformations for large rotations. The above physics were incorporated into the SPH. Detailed penetration process and damage progression were simulated with graphite/epoxy laminates impacted by a steel projectile. The predicted impact response and damage patterns agree fairly well qualitatively with experimental results. This study has demonstrated that SPH can be a robust and viable analytical tool for predicting the response of fiber-reinforced composite structures subjected to high-velocity impact. <s> BIB004 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> D. LARGE DEFORMATION PROBLEM <s> This paper presents an explicit 2D Lagrangian algorithm to automatically convert distorted elements into meshless particles during dynamic deformation. It also provides the contact and sliding algorithms to link the particles to the finite elements. For this approach the initial grid is composed entirely of finite elements and the response is computed with finite elements until portions of the grid become highly strained. When finite elements on the boundaries reach a user-specified plastic strain they are converted to particles and linked to the adjacent finite element grid. This approach allows for the use of accurate and efficient finite elements in the lower distortion regions, and for the use of meshless particles in the higher distortion regions. Example computations are presented to demonstrate the accuracy and utility of this approach. <s> BIB005 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> D. LARGE DEFORMATION PROBLEM <s> We use the modified smoothed-particle hydrodynamics (MSPH) method to analyze shear strain localization in elasto-thermo-viscoplastic materials that exhibit strain- and strain-rate hardening and thermal softening. A homogeneous solution of simple shearing deformations of the body is perturbed and the resulting initial-boundary-value problem analyzed by the MSPH method. It is found that the deformation localizes into a narrow region of intense plastic deformation. In materials exhibiting enhanced thermal softening, an elastic unloading shear wave emanates from this region and propagates outwards. The time when the deformation localizes decreases exponentially with an increase in the thermal softening coefficient. Results have been computed without adding an artificial viscosity and compared with those obtained by the finite element method. <s> BIB006 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> D. LARGE DEFORMATION PROBLEM <s> This paper presents the implementation of an adaptive smoothed particle hydrodynamics (ASPH) method for high strain Lagrangian hydrodynamics with material strength. In ASPH, the isotropic kernel in the standard SPH is replaced with an anisotropic kernel whose axes evolve automatically to follow the mean particle spacing as it varies in time, space, and direction around each particle. Except for the features inherited from the standard SPH, ASPH can capture dimension-dependent features such as anisotropic deformations with a more generalized elliptical or ellipsoidal influence domain. Two numerical examples, the impact of a plate against a rigid surface and the penetration of a cylinder through a plate, are investigated using both SPH and ASPH. The comparative studies show that ASPH has better accuracy than the standard SPH when being used for high strain hydrodynamic problems with inherent anisotropic deformations. <s> BIB007 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> D. LARGE DEFORMATION PROBLEM <s> This paper presents three-dimensional computational simulations of the hypervelocity impact (HVI) using standard smoothed particle hydrodynamics (SPH). The classic Taylor-Bar-Impact test is revisited with the focus on the variation of results corresponding to the different model parameters in the SPH implementation. The second example involves both normal and oblique HVIs of a sphere on the thin plate, producing large deformation of structures. Based on original experimental results and some numerical results reported previously, some comparisons are also made, in the hope of providing informative data on appropriate SPH implementation options for the software being developed. The results obtained show that the current SPH procedure is well suited for the HVI problems. <s> BIB008
High-speed impact, projectile penetration and space destruction are common phenomena in life and scientific research and production. In the calculation of the impact of such a large deformation problem, the grid method often produces a serious distortion phenomenon. The meshfree method is used to solve the difficulties encountered by the grid method. Batra and Zhang BIB006 used the modified smoothed particle hydrodynamics (MSPH) method to analyze shear strain localization in elasto-thermo-viscoelastic materials that exhibit strain-and strain-rate hardening as well as thermal softening. Libersky and Petschek  , BIB001 first considered the partial stress and elastic-plastic constitutive equation, successfully simulating the high-speed collision problem. Thereafter, Johnson et al. BIB003 , BIB005 ,  conducted a series of work on the high-speed impact problem by improving the SPH method. Benz and Asphaug BIB002 first used the SPH method with the fracture algorithm and analyzed the related problems. Chen et al. BIB004 simulated the anti-penetration of composites on the basis of the SPH method. The process was simulated, and the results were consistent to the experiment. Zhou et al. BIB008 revisited the Taylor-Bar-Impact focusing on the variation of results corresponding to different model parameters that represent varied SPH implementation in a series of three-dimensional computational simulations. The study provided informative data on appropriate SPH implementation options. The normal and oblique hypervelocity impacts of a sphere on the thin plate were likewise investigated and produced large structure deformation. Liu et al. BIB007 used the improved ASPH method to simulate the Taylor collisions and proved its superiority in dealing with large deformation problems compared with the traditional SPH method. The SPH method has been intensively used for simulating high strain hydrodynamics with material strength due to its special features of meshfree, Lagrangian, and particle nature. L.D. Libersky and his colleagues  - BIB001 carried out the pioneering work of applying the SPH method to high strain hydrodynamic problems, including hyper velocity impact (HVI), fracture, and fragmentation. The research group modeled high velocity impacts ranging from the very small to very large size.