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Xiong Zhang - One of the best experts on this subject based on the ideXlab platform.
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An efficient staggered grid Material Point method
Computer Methods in Applied Mechanics and Engineering, 2019Co-Authors: Yong Liang, Xiong Zhang, Yan LiuAbstract:Abstract The Material Point method (MPM) has demonstrated itself as an effective numerical method to simulate extreme events with large deformations. However, the original MPM suffers the cell crossing noise because it takes the Material Points as integration Points and employs the piecewise linear grid nodal shape functions whose gradient is discontinuous on the cell boundary. A number of techniques have been developed to alleviate the cell crossing noise. In this paper, a new staggered grid Material Point method (SGMP) is proposed to eliminate the cell crossing noise very efficiently. The volume integrals in the weak form are evaluated by cell center quadrature instead of particle quadrature as the sum of value of the integrand at each cell center of the background grid multiplied by the corresponding quadrature weight. The physical quantities and the quadrature weights at the cell centers are reconstructed efficiently based on an auxiliary grid, which is obtained by shifting the background grid half the side length of its cell in each direction. Similar to the original MPM, both grids carry no permanent information and can be reset after each time step. In addition, the SGMP evaluates the constitutive equations at the particles, just like the original MPM, to readily model the history-dependent Materials. To further reduce the cell crossing noise, a continuous strain rate/vorticity field is established based on the auxiliary grid, whose values are determined by the background grid velocity gradient. The strain rate/vorticity at each particle is interpolated from the auxiliary grid nodal values. Due to the overlap of the cell centers and the corresponding auxiliary grid nodes, a very efficient implementation is established in the SGMP. Numerical studies illustrate that the SGMP is capable of eliminating the cell crossing noise with little extra computational effort and the extra cost ratio reduces as the number of the grid cells or the particles increases.
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Coupled Shell-Material Point Method for Bird Strike Simulation
Acta Mechanica Solida Sinica, 2018Co-Authors: Zhen-peng Chen, Yan Liu, Xiong Zhang, Yanping LianAbstract:In a bird strike, the bird undergoes large deformation like flows; while most part of the structure is in small deformation, the region near the impact Point may experience large deformations, even fail. This paper develops a coupled shell-Material Point method (CSMPM) for bird strike simulation, in which the bird is modeled by the Material Point method (MPM) and the aircraft structure is modeled by the Belytschko–Lin–Tsay shell element. The interaction between the bird and the structure is handled by a particle-to-surface contact algorithm. The distorted and failed shell elements will be eroded if a certain criterion is reached. The proposed CSMPM takes full advantages of both the finite element method and the MPM for bird strike simulation and is validated by several numerical examples.
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an augmented incompressible Material Point method for modeling liquid sloshing problems
International Journal of Mechanics and Materials in Design, 2018Co-Authors: Fan Zhang, Xiong Zhang, Yan LiuAbstract:The incompressible Material Point method was proposed for modeling the free surface flow problems based on the operator splitting technique which decouples the solution of the velocity and the pressure in our previous work. To further model the coupling problems between the incompressible fluid and the moving irregular solid bodies, an augmented incompressible Material Point method is proposed in this paper based on the energy minimization form of operator splitting technique. The interaction between the fluid and the solid is taken into account via the work done by the fluid pressure on the solid bodies. By minimizing the total work done by the fluid pressure, volume-weighted pressure Poisson equations are obtained. The proposed method is validated with liquid sloshing in a rectangular tank subjected to various base-excitations, and is then used to study the optimal height of baffles mounted on the bottom of the tank to mitigate the sloshing wave.
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enhancement of the Material Point method using b spline basis functions
International Journal for Numerical Methods in Engineering, 2018Co-Authors: Xiong Zhang, Zheng Sun, Zhen Chen, Yong Gan, Yu LiuAbstract:The MPM (Material Point method) enhanced with B-spline basis functions, referred to as BSMPM (B-spline MPM), is developed and demonstrated using representative quasi-static and dynamic example problems. Smooth B-spline basis functions could significantly reduce the cell-crossing error as known for the original MPM. A Gauss quadrature scheme is designed and shown to be able to diminish the quadrature error in the BSMPM analysis of large-deformation problems for the improved accuracy and convergence, especially with the quadratic B-splines. Moreover, the increase in the order of the B-spline basis function is also found to be an effective way to reduce the quadrature error and to improve accuracy and convergence. For plate impact examples, it is demonstrated that the BSMPM outperforms the Generalized Interpolation Material Point (GIMP) and Convected Particle Domain Interpolation (CPDI) methods in term of the accuracy of representing stress waves. Thus, the BSMPM could become a promising alternative to the MPM, GIMP and CPDI in solving certain types of transient problems.
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v-p Material Point method for weakly compressible problems
Computers & Fluids, 2018Co-Authors: Zhen-peng Chen, Xiong Zhang, Kam Yim Sze, Lei Kan, Xinming QiuAbstract:Abstract The weakly compressible Material Point method (WCMPM) suffers from volumetric-locking and numerical oscillation in modeling fluid flow and fluid-structure interaction problems. In this paper, a v-pformulation of the Material Point method (vp-MPM) is proposed for weakly compressible problems based on a two-field variational principle. As only the velocity v and the pressure p are the independent variables, the v-p formulation has much less extra variables than those based on the Hu-Washizu multi-field variational principle which takes the velocity, strain and stress as independent variables. The pressure is assumed independently in the control volume of each gird node. Spurious pressure oscillation reduces but still occurs at the interface of discontinuity due to large pressure gradient difference across the interface. Therefore, a slope limiter is employed to suppress the oscillation and the general interpolation functions are used to eliminate the cell-crossing error. In order to extend the method to the fluid-structure interaction problems, the v-p formulation is incorporated into the improved coupled finite element Material Point method. Several numerical examples are presented to validate the vp-MPM.
Yong Gan - One of the best experts on this subject based on the ideXlab platform.
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Preliminary effort in developing the smoothed Material Point method for impact
Computational Particle Mechanics, 2018Co-Authors: Yong Gan, Zhen ChenAbstract:The smoothed Material Point method (SMPM) is being developed for better simulating impact problems, based on the respective strengths of the original Material Point method (MPM) and the smoothed particle hydrodynamics (SPH). The field variables of each Material Point (including velocity and stress) are re-calculated by one smoothed reconstruction procedure, while the rest of the solution steps are the same as those in the original MPM algorithm. In this preliminary study, the numerical performances of the original MPM, SPH and the SMPM are examined and compared using one-dimensional transient problems including impact. It is demonstrated that the numerical oscillations can be effectively reduced by the proposed reconstruction, showing the superiority of the SMPM over the original MPM and SPH in terms of solution accuracy and stability. As compared with the SPH, the SMPM exhibits significantly higher efficiency. Numerical results also illustrate that the proposed SMPM possesses the advantages of both the MPM and the SPH, which warrants the further development of the SMPM for general applications.
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enhancement of the Material Point method using b spline basis functions
International Journal for Numerical Methods in Engineering, 2018Co-Authors: Xiong Zhang, Zheng Sun, Zhen Chen, Yong Gan, Yu LiuAbstract:The MPM (Material Point method) enhanced with B-spline basis functions, referred to as BSMPM (B-spline MPM), is developed and demonstrated using representative quasi-static and dynamic example problems. Smooth B-spline basis functions could significantly reduce the cell-crossing error as known for the original MPM. A Gauss quadrature scheme is designed and shown to be able to diminish the quadrature error in the BSMPM analysis of large-deformation problems for the improved accuracy and convergence, especially with the quadratic B-splines. Moreover, the increase in the order of the B-spline basis function is also found to be an effective way to reduce the quadrature error and to improve accuracy and convergence. For plate impact examples, it is demonstrated that the BSMPM outperforms the Generalized Interpolation Material Point (GIMP) and Convected Particle Domain Interpolation (CPDI) methods in term of the accuracy of representing stress waves. Thus, the BSMPM could become a promising alternative to the MPM, GIMP and CPDI in solving certain types of transient problems.
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Enhancement of the Material Point method using B‐spline basis functions
International Journal for Numerical Methods in Engineering, 2017Co-Authors: Yong Gan, Xiong Zhang, Zheng Sun, Zhen Chen, Yu LiuAbstract:The MPM (Material Point method) enhanced with B-spline basis functions, referred to as BSMPM (B-spline MPM), is developed and demonstrated using representative quasi-static and dynamic example problems. Smooth B-spline basis functions could significantly reduce the cell-crossing error as known for the original MPM. A Gauss quadrature scheme is designed and shown to be able to diminish the quadrature error in the BSMPM analysis of large-deformation problems for the improved accuracy and convergence, especially with the quadratic B-splines. Moreover, the increase in the order of the B-spline basis function is also found to be an effective way to reduce the quadrature error and to improve accuracy and convergence. For plate impact examples, it is demonstrated that the BSMPM outperforms the Generalized Interpolation Material Point (GIMP) and Convected Particle Domain Interpolation (CPDI) methods in term of the accuracy of representing stress waves. Thus, the BSMPM could become a promising alternative to the MPM, GIMP and CPDI in solving certain types of transient problems.
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A multiscale Material Point method for impact simulation
Theoretical and Applied Mechanics Letters, 2012Co-Authors: Zhen Chen, Yong Gan, Yilong Han, Shan Jiang, Thomas D. SewellAbstract:To better simulate multi-phase interactions involving failure evolution, the Material Point method (MPM) has evolved for almost twenty years. Recently, a particle-based multiscale simulation procedure is being developed, within the framework of the MPM, to describe the detonation process of energetic nano-composites from molecular to continuum level so that a multiscale equation of state could be formulated. In this letter, a multiscale MPM is proposed via both hierarchical and concurrent schemes to simulate the impact response between two microrods with different nanostructures. Preliminary results are presented to illustrate that a transition region is not required between different spatial scales with the proposed approach.
Zhen Chen - One of the best experts on this subject based on the ideXlab platform.
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Preliminary effort in developing the smoothed Material Point method for impact
Computational Particle Mechanics, 2018Co-Authors: Yong Gan, Zhen ChenAbstract:The smoothed Material Point method (SMPM) is being developed for better simulating impact problems, based on the respective strengths of the original Material Point method (MPM) and the smoothed particle hydrodynamics (SPH). The field variables of each Material Point (including velocity and stress) are re-calculated by one smoothed reconstruction procedure, while the rest of the solution steps are the same as those in the original MPM algorithm. In this preliminary study, the numerical performances of the original MPM, SPH and the SMPM are examined and compared using one-dimensional transient problems including impact. It is demonstrated that the numerical oscillations can be effectively reduced by the proposed reconstruction, showing the superiority of the SMPM over the original MPM and SPH in terms of solution accuracy and stability. As compared with the SPH, the SMPM exhibits significantly higher efficiency. Numerical results also illustrate that the proposed SMPM possesses the advantages of both the MPM and the SPH, which warrants the further development of the SMPM for general applications.
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enhancement of the Material Point method using b spline basis functions
International Journal for Numerical Methods in Engineering, 2018Co-Authors: Xiong Zhang, Zheng Sun, Zhen Chen, Yong Gan, Yu LiuAbstract:The MPM (Material Point method) enhanced with B-spline basis functions, referred to as BSMPM (B-spline MPM), is developed and demonstrated using representative quasi-static and dynamic example problems. Smooth B-spline basis functions could significantly reduce the cell-crossing error as known for the original MPM. A Gauss quadrature scheme is designed and shown to be able to diminish the quadrature error in the BSMPM analysis of large-deformation problems for the improved accuracy and convergence, especially with the quadratic B-splines. Moreover, the increase in the order of the B-spline basis function is also found to be an effective way to reduce the quadrature error and to improve accuracy and convergence. For plate impact examples, it is demonstrated that the BSMPM outperforms the Generalized Interpolation Material Point (GIMP) and Convected Particle Domain Interpolation (CPDI) methods in term of the accuracy of representing stress waves. Thus, the BSMPM could become a promising alternative to the MPM, GIMP and CPDI in solving certain types of transient problems.
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Enhancement of the Material Point method using B‐spline basis functions
International Journal for Numerical Methods in Engineering, 2017Co-Authors: Yong Gan, Xiong Zhang, Zheng Sun, Zhen Chen, Yu LiuAbstract:The MPM (Material Point method) enhanced with B-spline basis functions, referred to as BSMPM (B-spline MPM), is developed and demonstrated using representative quasi-static and dynamic example problems. Smooth B-spline basis functions could significantly reduce the cell-crossing error as known for the original MPM. A Gauss quadrature scheme is designed and shown to be able to diminish the quadrature error in the BSMPM analysis of large-deformation problems for the improved accuracy and convergence, especially with the quadratic B-splines. Moreover, the increase in the order of the B-spline basis function is also found to be an effective way to reduce the quadrature error and to improve accuracy and convergence. For plate impact examples, it is demonstrated that the BSMPM outperforms the Generalized Interpolation Material Point (GIMP) and Convected Particle Domain Interpolation (CPDI) methods in term of the accuracy of representing stress waves. Thus, the BSMPM could become a promising alternative to the MPM, GIMP and CPDI in solving certain types of transient problems.
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The Material Point method
The Material Point Method, 2017Co-Authors: Xiong Zhang, Zhen Chen, Jianhui Liao, Yan LiuAbstract:Chapter 3 establishes the MPM formulation by discretizing a continuum body into a set of Material Points (particles). Both explicit and implicit formulations are presented. The Generalized Interpolation Material Point (GIMP) method, contact algorithm, adaptive MPM, incompressible MPM, non-reflecting boundary are discussed in detail.
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A multiscale Material Point method for impact simulation
Theoretical and Applied Mechanics Letters, 2012Co-Authors: Zhen Chen, Yong Gan, Yilong Han, Shan Jiang, Thomas D. SewellAbstract:To better simulate multi-phase interactions involving failure evolution, the Material Point method (MPM) has evolved for almost twenty years. Recently, a particle-based multiscale simulation procedure is being developed, within the framework of the MPM, to describe the detonation process of energetic nano-composites from molecular to continuum level so that a multiscale equation of state could be formulated. In this letter, a multiscale MPM is proposed via both hierarchical and concurrent schemes to simulate the impact response between two microrods with different nanostructures. Preliminary results are presented to illustrate that a transition region is not required between different spatial scales with the proposed approach.
Yu Liu - One of the best experts on this subject based on the ideXlab platform.
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enhancement of the Material Point method using b spline basis functions
International Journal for Numerical Methods in Engineering, 2018Co-Authors: Xiong Zhang, Zheng Sun, Zhen Chen, Yong Gan, Yu LiuAbstract:The MPM (Material Point method) enhanced with B-spline basis functions, referred to as BSMPM (B-spline MPM), is developed and demonstrated using representative quasi-static and dynamic example problems. Smooth B-spline basis functions could significantly reduce the cell-crossing error as known for the original MPM. A Gauss quadrature scheme is designed and shown to be able to diminish the quadrature error in the BSMPM analysis of large-deformation problems for the improved accuracy and convergence, especially with the quadratic B-splines. Moreover, the increase in the order of the B-spline basis function is also found to be an effective way to reduce the quadrature error and to improve accuracy and convergence. For plate impact examples, it is demonstrated that the BSMPM outperforms the Generalized Interpolation Material Point (GIMP) and Convected Particle Domain Interpolation (CPDI) methods in term of the accuracy of representing stress waves. Thus, the BSMPM could become a promising alternative to the MPM, GIMP and CPDI in solving certain types of transient problems.
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Enhancement of the Material Point method using B‐spline basis functions
International Journal for Numerical Methods in Engineering, 2017Co-Authors: Yong Gan, Xiong Zhang, Zheng Sun, Zhen Chen, Yu LiuAbstract:The MPM (Material Point method) enhanced with B-spline basis functions, referred to as BSMPM (B-spline MPM), is developed and demonstrated using representative quasi-static and dynamic example problems. Smooth B-spline basis functions could significantly reduce the cell-crossing error as known for the original MPM. A Gauss quadrature scheme is designed and shown to be able to diminish the quadrature error in the BSMPM analysis of large-deformation problems for the improved accuracy and convergence, especially with the quadratic B-splines. Moreover, the increase in the order of the B-spline basis function is also found to be an effective way to reduce the quadrature error and to improve accuracy and convergence. For plate impact examples, it is demonstrated that the BSMPM outperforms the Generalized Interpolation Material Point (GIMP) and Convected Particle Domain Interpolation (CPDI) methods in term of the accuracy of representing stress waves. Thus, the BSMPM could become a promising alternative to the MPM, GIMP and CPDI in solving certain types of transient problems.
Biswajit Banerjee - One of the best experts on this subject based on the ideXlab platform.
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A Material Point Method Formulation for Plasticity
arXiv: Computational Physics, 2012Co-Authors: Biswajit BanerjeeAbstract:This paper discusses a general formulation of the Material Point method in the context of additive decomposition rate-independent plasticity. The process of generating the weak form shows that volume integration over deforming particles can be major source of error in the MPM method. Several useful identities and other results are derived in the appendix.
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Simulation of impact and fragmentation with the Material Point method
arXiv: Computational Physics, 2012Co-Authors: Biswajit Banerjee, James E. Guilkey, Todd Harman, John A. Schmidt, Patrick McmurtryAbstract:The simulation of high-rate deformation and failure of metals is has traditionally been performed using Lagrangian finite element methods or Eulerian hydrocodes. Lagrangian mesh-based methods are limited by issues involving mesh entanglement under large deformation and considerable complexity in handling contact. On the other hand, Eulerian hydrocodes are prone to Material diffusion. In the Material Point Method (MPM), the Material state is defined on solid Lagrangian particles. The particles interact with other particles in the same body, with other solid bodies, or with fluids through a background mesh. Thus, some of the problems associated with finite element codes and hydrocodes are alleviated. Another attractive feature of the Material Point method is the ease with which large deformation, fully coupled, fluid-structure interaction problems can be handled. In this work, we present MPM simulations that involve large plastic deformations, contact, Material failure and fragmentation, and fluid-structure interaction.
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Material Point method simulations of fragmenting cylinders
arXiv: Computational Physics, 2012Co-Authors: Biswajit BanerjeeAbstract:Most research on the simulation of deformation and failure of metals has been and continues to be performed using the finite element method. However, the issues of mesh entanglement under large deformation, considerable complexity in handling contact, and difficulties encountered while solving large deformation fluid-structure interaction problems have led to the exploration of alternative approaches. The Material Point method uses Lagrangian solid particles embedded in an Eulerian grid. Particles interact via the grid with other particles in the same body, with other solid bodies, and with fluids. Thus, the three issues mentioned in the context of finite element analysis are circumvented. In this paper, we present simulations of cylinders which fragment due to explosively expanding gases generated by reactions in a high energy Material contained inside. The Material Point method is the numerical method chosen for these simulations discussed in this paper. The plastic deformation of metals is simulated using a hypoelastic-plastic stress update with radial return that assumes an additive decomposition of the rate of deformation tensor. Various plastic strain, plastic strain rate, and temperature dependent flow rules and yield conditions are investigated. Failure at individual Material Points is determined using porosity, damage and bifurcation conditions. Our models are validated using data from high strain rate impact experiments. It is concluded that the Material Point method possesses great potential for simulating high strain-rate, large deformation fluid-structure interaction problems.
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Simulation of thin hyperelastic shells with the Material Point Method
arXiv: Materials Science, 2005Co-Authors: Biswajit BanerjeeAbstract:A non-linear shell theory that includes transverse shear strains and its implementation in the Material Point method framework are discussed. The applicability of the shell implementation to model large deformations of thin shells is explored. Results suggest that an implicit time stepping scheme may be required for improved modeling of thin shells by the Material Point method.
