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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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A mesh-grading material point method and its parallelization for problems with localized extreme deformation
Computer Methods in Applied Mechanics and Engineering, 2015Co-Authors: Yanping Lian, Xiong Zhang, P.f. Yang, Fang Zhang, Yuangao Liu, P. HuangAbstract:Abstract As a kind of meshless method, material point method (MPM) applies an Eulerian Background Grid served as a finite element mesh in each time step, and therefore its accuracy and efficiency are mainly dependent on the cell size setting of Background Grid. However, the conventional MPM commonly uses a regular Background Grid with uniform cells, which is not apposite for localized extreme deformation problems from the view point of computation efficiency, where, in fact, a local refined Background Grid is preferable. Hence, a mesh-grading material point method (MGMPM) is proposed here for such problems to supply MPM with the ability for local refinement simulation. The edge displacement continuity associated with mesh grading is embedded in the nodal shape functions. Besides, the truss element is incorporated into MGMPM to model the steel reinforcement bars in reinforced concrete impacting problems, based on our previous work. Furthermore, the proposed method is parallelized using OpenMP (Open Multi-Processing) to take advantage of PC power with multi-core and hyper threading technologies for large scale engineering problems, where both loop-level parallelism and code-block parallelism are used. Several numerical examples including stress wave propagation, Taylor bar impact, and penetration problems, are studied, which show that the efficiency of MGMPM is much higher than that of conventional MPM, and with lower memory requirement.
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tied interface Grid material point method for problems with localized extreme deformation
International Journal of Impact Engineering, 2014Co-Authors: Yanping Lian, Xiong Zhang, Fusuo Zhang, X X CuiAbstract:Abstract As a meshless method, the material point method (MPM) is capable of modeling problems with extreme deformation and material fragments. MPM uses a set of Lagrangian particles to discretize a material domain. The interaction between particles is carried out via an Eulerian Background Grid which is used as a finite element mesh to integrate momentum equations and to calculate spatial derivatives in each time step. Therefore, the accuracy of MPM is mainly dependent on the cell size of the Background Grid. But, a regular mesh with uniform cells is usually employed as the Background Grid, which results in poor efficiency for problems with localized extreme deformation. In this article, a tied interface Grid material point method is proposed for such problems, in which the Background Grid with several cell sizes for different sub material domains can be used. The sub Grid with refined cell size is used to cover the material domain undergoing extreme deformation, while the sub Grid with coarse cell size used to cover the material domain elsewhere. The interaction between refined Grid and coarse Grid is implemented by a tied interface method. Several numerical examples including stress wave propagation, Taylor bar impact, and penetration problems, are studied to validate the accuracy and efficiency of the proposed method, which shows that the presented method possesses higher efficiency and lower memory requirement than MPM for problems with localized extreme deformation.
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keynote tied interface Grid material point method for problems with localized extreme deformation
The 5th International Conference on Computational Methods (ICCM2014), 2014Co-Authors: Yanping Lian, Xiong ZhangAbstract:Based on material point method (MPM), tied interface Grid material point method is proposed here for localized extreme deformation problems. MPM uses material points to discretize material domain, but uses a regular mesh with uniform cells as Background Grid to integrate momentum equations and to calculate spatial derivatives in each time step. Such type Grid used as a finite element mesh results in both time and memory consuming for problems with localized extreme deformation, where, in fact, a local refined Grid is preferable. Therefore, in the proposed method, the Background Grid with several cell sizes for different material sub domains can be used for such problems. The interaction between refined Grid and coarse Grid is implemented by a tied interface method. Several numerical examples including stress wave propagation and penetration problems are studied, which show that the proposed method is with higher efficiency and lower memory requirement than MPM.
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an adaptive finite element material point method and its application in extreme deformation problems
Computer Methods in Applied Mechanics and Engineering, 2012Co-Authors: Yanping Lian, Xiong Zhang, Yan LiuAbstract:Abstract Taking advantages of both Lagrangian and Eulerian methods, material point method (MPM) is suitable for modeling problems with extreme deformation. However, MPM is less accurate and less efficient than finite element method (FEM) for small deformation problems due to particle quadrature and mappings between particles and Background Grid applied in MPM. To take advantages of both FEM and MPM, an adaptive finite element material point method is developed for modeling the dynamic behavior of material under extreme loading. Bodies are initially discretized by finite elements, and then the elements with large strain are adaptively converted into MPM particles based on their degree of distortion or plastic strain during the solution process. The interaction between the remaining finite elements and MPM particles is implemented based on the Background Grid in MPM framework. Several numerical examples are presented to validate the efficiency and accuracy of the proposed method, and the numerical results are in good agreement with experiments, while the efficiency of the method is higher than that of both MPM and FEM.
Yanping Lian - One of the best experts on this subject based on the ideXlab platform.
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A mesh-grading material point method and its parallelization for problems with localized extreme deformation
Computer Methods in Applied Mechanics and Engineering, 2015Co-Authors: Yanping Lian, Xiong Zhang, P.f. Yang, Fang Zhang, Yuangao Liu, P. HuangAbstract:Abstract As a kind of meshless method, material point method (MPM) applies an Eulerian Background Grid served as a finite element mesh in each time step, and therefore its accuracy and efficiency are mainly dependent on the cell size setting of Background Grid. However, the conventional MPM commonly uses a regular Background Grid with uniform cells, which is not apposite for localized extreme deformation problems from the view point of computation efficiency, where, in fact, a local refined Background Grid is preferable. Hence, a mesh-grading material point method (MGMPM) is proposed here for such problems to supply MPM with the ability for local refinement simulation. The edge displacement continuity associated with mesh grading is embedded in the nodal shape functions. Besides, the truss element is incorporated into MGMPM to model the steel reinforcement bars in reinforced concrete impacting problems, based on our previous work. Furthermore, the proposed method is parallelized using OpenMP (Open Multi-Processing) to take advantage of PC power with multi-core and hyper threading technologies for large scale engineering problems, where both loop-level parallelism and code-block parallelism are used. Several numerical examples including stress wave propagation, Taylor bar impact, and penetration problems, are studied, which show that the efficiency of MGMPM is much higher than that of conventional MPM, and with lower memory requirement.
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tied interface Grid material point method for problems with localized extreme deformation
International Journal of Impact Engineering, 2014Co-Authors: Yanping Lian, Xiong Zhang, Fusuo Zhang, X X CuiAbstract:Abstract As a meshless method, the material point method (MPM) is capable of modeling problems with extreme deformation and material fragments. MPM uses a set of Lagrangian particles to discretize a material domain. The interaction between particles is carried out via an Eulerian Background Grid which is used as a finite element mesh to integrate momentum equations and to calculate spatial derivatives in each time step. Therefore, the accuracy of MPM is mainly dependent on the cell size of the Background Grid. But, a regular mesh with uniform cells is usually employed as the Background Grid, which results in poor efficiency for problems with localized extreme deformation. In this article, a tied interface Grid material point method is proposed for such problems, in which the Background Grid with several cell sizes for different sub material domains can be used. The sub Grid with refined cell size is used to cover the material domain undergoing extreme deformation, while the sub Grid with coarse cell size used to cover the material domain elsewhere. The interaction between refined Grid and coarse Grid is implemented by a tied interface method. Several numerical examples including stress wave propagation, Taylor bar impact, and penetration problems, are studied to validate the accuracy and efficiency of the proposed method, which shows that the presented method possesses higher efficiency and lower memory requirement than MPM for problems with localized extreme deformation.
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keynote tied interface Grid material point method for problems with localized extreme deformation
The 5th International Conference on Computational Methods (ICCM2014), 2014Co-Authors: Yanping Lian, Xiong ZhangAbstract:Based on material point method (MPM), tied interface Grid material point method is proposed here for localized extreme deformation problems. MPM uses material points to discretize material domain, but uses a regular mesh with uniform cells as Background Grid to integrate momentum equations and to calculate spatial derivatives in each time step. Such type Grid used as a finite element mesh results in both time and memory consuming for problems with localized extreme deformation, where, in fact, a local refined Grid is preferable. Therefore, in the proposed method, the Background Grid with several cell sizes for different material sub domains can be used for such problems. The interaction between refined Grid and coarse Grid is implemented by a tied interface method. Several numerical examples including stress wave propagation and penetration problems are studied, which show that the proposed method is with higher efficiency and lower memory requirement than MPM.
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an adaptive finite element material point method and its application in extreme deformation problems
Computer Methods in Applied Mechanics and Engineering, 2012Co-Authors: Yanping Lian, Xiong Zhang, Yan LiuAbstract:Abstract Taking advantages of both Lagrangian and Eulerian methods, material point method (MPM) is suitable for modeling problems with extreme deformation. However, MPM is less accurate and less efficient than finite element method (FEM) for small deformation problems due to particle quadrature and mappings between particles and Background Grid applied in MPM. To take advantages of both FEM and MPM, an adaptive finite element material point method is developed for modeling the dynamic behavior of material under extreme loading. Bodies are initially discretized by finite elements, and then the elements with large strain are adaptively converted into MPM particles based on their degree of distortion or plastic strain during the solution process. The interaction between the remaining finite elements and MPM particles is implemented based on the Background Grid in MPM framework. Several numerical examples are presented to validate the efficiency and accuracy of the proposed method, and the numerical results are in good agreement with experiments, while the efficiency of the method is higher than that of both MPM and FEM.
Rainald Löhner - One of the best experts on this subject based on the ideXlab platform.
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A feature‐preserving volumetric technique to merge surface triangulations
International Journal for Numerical Methods in Engineering, 2002Co-Authors: Juan R. Cebral, Fernando Camelli, Rainald LöhnerAbstract:Several extensions and improvements to surface merging procedures based on the extraction of iso-surfaces from a distance map defined on an adaptive Background Grid are presented. The main objective is to extend the application of these algorithms to surfaces with sharp edges and corners. In order to deal with objects of different length scales, the initial Background Grids are created using a Delaunay triangulation method and local voxelizations. A point enrichment technique that introduces points into the Background Grid along detected surface features such as ridges is used to ensure that these features are preserved in the final merged surface. The surface merging methodology is extended to include other Boolean operations between surface triangulations. The iso-surface extraction algorithms are modified to obtain the correct iso-surface for multi-component objects. The procedures are demonstrated with various examples, ranging from simple geometrical entities to complex engineering applications. The present algorithms allow realistic modelling of a large number of complex engineering geometries using overlapping components defined discretely, i.e. via surface triangulations. This capability is very useful for Grid generation starting from data originated in measurements or images. Copyright © 2002 John Wiley & Sons, Ltd.
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Merging of intersecting triangulations for finite element modeling.
Journal of biomechanics, 2001Co-Authors: Juan R. Cebral, Rainald Löhner, Peter L. Choyke, Peter J. YimAbstract:Surface mesh generation over intersecting triangulations is a problem common to many branches of biomechanics. A new strategy for merging intersecting triangulations is described. The basis of the method is that object surfaces are represented as the zero-level iso-surface of the distance-to-surface function defined on a Background Grid. Thus, the triangulation of intersecting objects reduces to the extraction of an iso-surface from an unstructured Grid. In a first step, a regular Background mesh is constructed. For each point of the Background Grid, the closest distance to the surface of each object is computed. Background points are then classified as external or internal by checking the direction of the surface normal at the closest location and assigned a positive or negative distance, respectively. Finally, the zero-level iso-surface is constructed. This is the final triangulation of the intersecting objects. The overall accuracy is enhanced by adaptive refinement of the Background Grid elements. The resulting surface models are used as support surfaces to generate three-dimensional Grids for finite element analysis. The algorithms are demonstrated by merging arterial branches independently reconstructed from contrast-enhanced magnetic resonance images and by adding extra features such as vascular stents. Although the methodology is presented in the context of finite element analysis of blood flow, the algorithms are general and can be applied in other areas as well.
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Three‐dimensional parallel unstructured Grid generation
International Journal for Numerical Methods in Engineering, 1995Co-Authors: Alexander A. Shostko, Rainald LöhnerAbstract:An algorithm for the parallel generation of 3-D unstructured Grids is presented. The technique is an extension of the algorithm presented in Reference 21 for the 2-D case. The method uses a Background Grid as the means to separate spatially different regions, enabling the concurrent, parallel generation of elements in different domains and interdomain regions. The parallel 3-D Grid generator was implemented and tested on the INTEL hypercube and Touchstone Delta parallel computers. The results obtained demonstrate the effectiveness of the algorithm developed. The methodology is applicable to the parallel implementation of a wide range of problems that are, in principle, scalar by nature, and do not lend themselves to SIMD parallelization.
Michael H. Gfrerer - One of the best experts on this subject based on the ideXlab platform.
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A $$C^1$$ C 1 -continuous Trace-Finite-Cell-Method for linear thin shell analysis on implicitly de
Computational Mechanics, 2020Co-Authors: Michael H. GfrererAbstract:A Trace-Finite-Cell-Method for the numerical analysis of thin shells is presented combining concepts of the TraceFEM and the Finite-Cell-Method. As an underlying shell model we use the Koiter model, which we re-derive in strong form based on first principles of continuum mechanics by recasting well-known relations formulated in local coordinates to a formulation independent of a parametrization. The field approximation is constructed by restricting shape functions defined on a structured Background Grid on the shell surface. As shape functions we use on a Background Grid the tensor product of cubic splines. This yields $$C^1$$ C 1 -continuous approximation spaces, which are required by the governing equations of fourth order. The parametrization-free formulation allows a natural implementation of the proposed method and manufactured solutions on arbitrary geometries for code verification. Thus, the implementation is verified by a convergence analysis where the error is computed with an exact manufactured solution. Furthermore, benchmark tests are investigated.
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A $$C^1$$-continuous Trace-Finite-Cell-Method for linear thin shell analysis on implicitly defined surfaces
Computational Mechanics, 2020Co-Authors: Michael H. GfrererAbstract:A Trace-Finite-Cell-Method for the numerical analysis of thin shells is presented combining concepts of the TraceFEM and the Finite-Cell-Method. As an underlying shell model we use the Koiter model, which we re-derive in strong form based on first principles of continuum mechanics by recasting well-known relations formulated in local coordinates to a formulation independent of a parametrization. The field approximation is constructed by restricting shape functions defined on a structured Background Grid on the shell surface. As shape functions we use on a Background Grid the tensor product of cubic splines. This yields $$C^1$$ -continuous approximation spaces, which are required by the governing equations of fourth order. The parametrization-free formulation allows a natural implementation of the proposed method and manufactured solutions on arbitrary geometries for code verification. Thus, the implementation is verified by a convergence analysis where the error is computed with an exact manufactured solution. Furthermore, benchmark tests are investigated.
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A $C^1$-continuous Trace-Finite-Cell-Method for linear thin shell analysis on implicitly defined surfaces
arXiv: Computational Engineering Finance and Science, 2020Co-Authors: Michael H. GfrererAbstract:A Trace-Finite-Cell-Method for the numerical analysis of thin shells is presented combining concepts of the TraceFEM and the Finite-Cell-Method. As an underlying shell model we use the Koiter model, which we re-derive in strong form based on first principles of continuum mechanics by recasting well-known relations formulated in local coordinates to a formulation independent of a parametrization. The field approximation is constructed by restricting shape functions defined on a structured Background Grid on the shell surface. As shape functions we use on a Background Grid the tensor product of cubic splines. This yields $C^1$-continuous approximation spaces, which are required by the governing equations of fourth order. The parametrization-free formulation allows a natural implementation of the proposed method and manufactured solutions on arbitrary geometries for code verification. Thus, the implementation is verified by a convergence analysis where the error is computed with an exact manufactured solution. Furthermore, benchmark tests are investigated.
X X Cui - One of the best experts on this subject based on the ideXlab platform.
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tied interface Grid material point method for problems with localized extreme deformation
International Journal of Impact Engineering, 2014Co-Authors: Yanping Lian, Xiong Zhang, Fusuo Zhang, X X CuiAbstract:Abstract As a meshless method, the material point method (MPM) is capable of modeling problems with extreme deformation and material fragments. MPM uses a set of Lagrangian particles to discretize a material domain. The interaction between particles is carried out via an Eulerian Background Grid which is used as a finite element mesh to integrate momentum equations and to calculate spatial derivatives in each time step. Therefore, the accuracy of MPM is mainly dependent on the cell size of the Background Grid. But, a regular mesh with uniform cells is usually employed as the Background Grid, which results in poor efficiency for problems with localized extreme deformation. In this article, a tied interface Grid material point method is proposed for such problems, in which the Background Grid with several cell sizes for different sub material domains can be used. The sub Grid with refined cell size is used to cover the material domain undergoing extreme deformation, while the sub Grid with coarse cell size used to cover the material domain elsewhere. The interaction between refined Grid and coarse Grid is implemented by a tied interface method. Several numerical examples including stress wave propagation, Taylor bar impact, and penetration problems, are studied to validate the accuracy and efficiency of the proposed method, which shows that the presented method possesses higher efficiency and lower memory requirement than MPM for problems with localized extreme deformation.
