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Xiong Zhang - One of the best experts on this subject based on the ideXlab platform.
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a critical assessment and contact algorithm for the staggered grid Material Point Method
International Journal of Mechanics and Materials in Design, 2021Co-Authors: Lei Kan, Yong Liang, Xiong ZhangAbstract: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 several defects caused by the particle quadrature, including cell crossing noise, low spatial integration accuracy, and loss of spatial convergence. Our newly developed staggered grid Material Point Method (SGMP) employs the cell center quadrature to efficiently eliminate the cell crossing noise and to recover the spatial convergence. In this paper, the SGMP is further formulated with the updated stress last, updated stress first and modified updated stress last schemes. The energy errors of the SGMP with different schemes are derived analytically to study their accuracy and stability. The performance of the SGMP is critically assessed by investigating its performance in terms of convergence, stability, dissipation and efficiency theoretically and numerically. This study shows that the SGMP performs much better than the MPM. In addition, a contact algorithm is also developed for the SGMP to model the contact-impact problems, and is verified by several numerical examples.
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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, Zhen Chen, Zheng Sun, 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.
Yan Liu - 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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Material Point Method with enriched shape function for crack problems
Computer Methods in Applied Mechanics and Engineering, 2017Co-Authors: Yong Liang, Xiong Zhang, Tamas Benedek, Yan LiuAbstract:Abstract A Material Point Method (MPM)/generalized interpolation Material Point Method (GIMP) with enriched shape function (EMPM/EGIMP for short) is proposed for modelling crack problems in the MPM/GIMP framework. The EMPM/EGIMP enriches the nodal degrees of freedom based on the idea of the extended finite element Method (XFEM). This improvement allows the crack problem, whose displacement and velocity are discontinuous, to be simulated by only one set of background grid meshes, so multigrid and multiple velocity fields are unnecessary. In addition, the technique we developed to lump the mass matrix makes the EMPM/EGIMP can be implemented easily in a conventional MPM/GIMP code. If there is no crack, the EMPM/EGIMP degenerates to the conventional MPM/GIMP. The Level Set Method (LSM) is employed in the EMPM/EGIMP for easily tracking crack surfaces. The crack moves with the Material Points physically, so that the LSM function is carried by particles. In each time step, the LSM function value is mapped to the grid nodes from the particles, and the nodes to be enriched can be identified conveniently from the grid nodal LSM function values. Numerical experiments for stress fields distribution, fracture parameters calculation and crack propagation are provided to validate the proposed EMPM/EGIMP.
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investigation on high velocity impact of micron particles using Material Point Method
International Journal of Impact Engineering, 2015Co-Authors: Ping Liu, Xiong Zhang, Yan Liu, Yu GuanAbstract:Abstract Continuous high-velocity impact of micro space debris and micro-meteroids may cause significant accumulative damages to spacecrafts. The process of high-velocity impact of micron aluminum particles on the aluminum target is investigated with the Material Point Method (MPM). As a meshfree particle Method, MPM is very suitable for solving high-velocity impact problems owing to its prominent advantages of dealing with fracture, fragmentation and moving Material interface over the traditional mesh-based Methods. The target plate is modeled as semi-infinite media since its thickness is much larger than the characteristic length of the projectile particles. The micron particles are projected to the target individually and in group with different angles and different velocities. The predicted impact responses and dimensions of the craters agree well with the experimental results and the empirical equations. The influences of the flux density, the projectile angle and the impact velocity are thoroughly investigated, and the morphology modes of the crater group are concluded. Finally, an empirical formula is proposed for the crater depth under impact of particle group.
Yanping Lian - One of the best experts on this subject based on the ideXlab platform.
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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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incompressible Material Point Method for free surface flow
Journal of Computational Physics, 2017Co-Authors: Fan Zhang, Xiong Zhang, Yanping LianAbstract:To overcome the shortcomings of the weakly compressible Material Point Method (WCMPM) for modeling the free surface flow problems, an incompressible Material Point Method (iMPM) is proposed based on operator splitting technique which splits the solution of momentum equation into two steps. An intermediate velocity field is first obtained by solving the momentum equations ignoring the pressure gradient term, and then the intermediate velocity field is corrected by the pressure term to obtain a divergence-free velocity field. A level set function which represents the signed distance to free surface is used to track the free surface and apply the pressure boundary conditions. Moreover, an hourglass damping is introduced to suppress the spurious velocity modes which are caused by the discretization of the cell center velocity divergence from the grid vertexes velocities when solving pressure Poisson equations. Numerical examples including dam break, oscillation of a cubic liquid drop and a droplet impact into deep pool show that the proposed incompressible Material Point Method is much more accurate and efficient than the weakly compressible Material Point Method in solving free surface flow problems. An incompressible MPM is proposed to simulate free surface flow.A scheme for calculating pressure gradients at nodes in semi-staggered grid is proposed.Hourglass damping is employed to suppress spurious velocity modes.
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improved coupling of finite element Method with Material Point Method based on a particle to surface contact algorithm
Computer Methods in Applied Mechanics and Engineering, 2015Co-Authors: Zhen-peng Chen, Xiong Zhang, Xinming Qiu, Yanping LianAbstract:Abstract For extreme deformation problems, Material Point Method (MPM) takes competitive advantages compared with finite element Method (FEM) which often encounters mesh distortion. However, for small deformation problems, FEM is still more efficient and accurate than MPM in most cases. Hence, a coupled finite element Material Point (CFEMP) Method and an adaptive finite element Material Point Method (AFEMP) have been proposed by our group to take advantages of both Methods. Because the coupling between MPM particles and FEM elements was implemented based on the MPM grid-based contact Method, both CFEMP and AFEMP demand a high degree of consistence of meshing between FEM domain and MPM domain. This may lead to over meshing in FEM domain, thus significantly decreases the time step size and increases computational cost as well as data storage. In order to allow arbitrary inconsistent meshing, the CFEMP and AFEMP Methods are further improved in this article. The coupling between the MPM particles and FEM elements is implemented based on a particle-to-surface contact algorithm rather than the MPM grid-based contact Method, so that the consistent meshing is no more needed. Thus, the meshing of FEM body can be much coarser than the MPM grid. Numerical studies illustrate that the robustness, efficiency and accuracy of the improved CFEMP (ICFEMP) Method and the improved AFEMP (IAFEMP) Method are much higher than MPM, CFEMP and AFEMP.
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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.
Chenfanfu Jiang - One of the best experts on this subject based on the ideXlab platform.
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lagrangian eulerian multi density topology optimization with the Material Point Method
arXiv: Computational Physics, 2020Co-Authors: Yixin Zhu, Chenfanfu Jiang, Bo ZhuAbstract:In this paper, a hybrid Lagrangian-Eulerian topology optimization (LETO) Method is proposed to solve the elastic force equilibrium with the Material Point Method (MPM). LETO transfers density information from freely movable Lagrangian carrier particles to a fixed set of Eulerian quadrature Points. The transfer is based on a smooth radial kernel involved in the compliance objective to avoid the artificial checkerboard pattern. The quadrature Points act as MPM particles embedded in a lower-resolution grid and enable a sub-cell multi-density resolution of intricate structures with a reduced computational cost. A quadrature-level connectivity graph-based Method is adopted to avoid the artificial QR patterns commonly existing in multi-resolution topology optimization Methods. Numerical experiments are provided to demonstrate the efficacy of the proposed approach.
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A Hybrid Material Point Method for Frictional Contact with Diverse Materials
Proceedings of the ACM on Computer Graphics and Interactive Techniques, 2019Co-Authors: Theodore Gast, Stephanie J. Wang, Chenfanfu Jiang, Joseph TeranAbstract:We present a new hybrid Lagrangian Material Point Method for simulating elastic objects like hair, rubber, and soft tissues that utilizes a Lagrangian mesh for internal force computation and an Eulerian mesh for self collision as well as coupling with external Materials. While recent Material Point Method (MPM) techniques allow for natural simulation of hyperelastic Materials represented with Lagrangian meshes, they utilize an updated Lagrangian discretization where the Eulerian grid degrees of freedom are used to take variations of the potential energy. This often coarsens the degrees of freedom of the Lagrangian mesh and can lead to artifacts. We develop a hybrid approach that retains Lagrangian degrees of freedom while still allowing for natural coupling with other Materials simulated with traditional MPM, e.g. sand, snow, etc. Furthermore, while recent MPM advances allow for resolution of frictional contact with codimensional simulation of hyperelasticity, they do not generalize to the case of volumetric Materials. We show that our hybrid approach resolves these issues. We demonstrate the efficacy of our technique with examples that involve elastic soft tissues coupled with kinematic skeletons, extreme deformation, and coupling with multiple elastoplastic Materials. Our approach also naturally allows for two-way rigid body coupling.
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simulation and visualization of ductile fracture with the Material Point Method
Proceedings of the ACM on Computer Graphics and Interactive Techniques, 2019Co-Authors: Stephanie Wang, Theodore Gast, Chenfanfu Jiang, Mengyuan Ding, Leyi Zhu, Steven Gagniere, Joseph TeranAbstract:We present novel techniques for simulating and visualizing ductile fracture with the Material Point Method (MPM). We utilize traditional particle-based MPM [Stomakhin et al. 2013; Sulsky et al. 1994] as well as the Lagrangian energy formulation of [Jiang et al. 2015] that utilizes a tetrahedron mesh, rather than particle-based estimation of the deformation gradient and potential energy. We model failure and fracture via elastoplasticity with damage. Material is elastic until its deformation exceeds a Rankine or von Mises yield condition, at which Point we use a softening model that shrinks the yield surface until a damage threshold is reached. Once damaged, the Material Lame coefficients are modified to represent failed Material. We design visualization techniques for rendering the boundary of the Material and its intersections with evolving crack surfaces. Our approach uses a simple and efficient element splitting strategy for tetrahedron meshes to represent crack surfaces that utilizes an extrapolation technique based on the MPM simulation. For traditional particle-based MPM we use an initial Delaunay tetrahedralization to connect randomly initialized MPM particles. Our visualization technique is a post-process and can be run after the MPM simulation for efficiency. We demonstrate our Method with a number of challenging simulations of ductile failure with considerable and persistent self-contact.
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silly rubber an implicit Material Point Method for simulating non equilibrated viscoelastic and elastoplastic solids
ACM Transactions on Graphics, 2019Co-Authors: Yu Fang, Ming Gao, Chenfanfu JiangAbstract:Simulating viscoelastic polymers and polymeric fluids requires a robust and accurate capture of elasticity and viscosity. The computation is known to become very challenging under large deformations and high viscosity. Drawing inspirations from return mapping based elastoplasticity treatment for granular Materials, we present a finite strain integration scheme for general viscoelastic solids under arbitrarily large deformation and non-equilibrated flow. Our scheme is based on a predictor-corrector exponential mapping scheme on the principal strains from the deformation gradient, which closely resembles the conventional treatment for elastoplasticity and allows straightforward implementation into any existing constitutive models. We develop a new Material Point Method that is fully implicit on both elasticity and inelasticity using augmented Lagrangian optimization with various preconditioning strategies for highly efficient time integration. Our Method not only handles viscoelasticity but also supports existing elastoplastic models including Drucker-Prager and von-Mises in a unified manner. We demonstrate the efficacy of our framework on various examples showing intricate and characteristic inelastic dynamics with competitive performance.
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a moving least squares Material Point Method with displacement discontinuity and two way rigid body coupling
International Conference on Computer Graphics and Interactive Techniques, 2018Co-Authors: Yuanming Hu, Yu Fang, Ziheng Ge, Ziyin Qu, Andre Pradhana, Chenfanfu JiangAbstract:We introduce the Moving Least Squares Material Point Method (MLS-MPM) and the Compatible Particle-In-Cell algorithm for efficient simulation of Material cutting, dynamic open boundaries, and two-way coupling with rigid bodies.
Deborah Sulsky - One of the best experts on this subject based on the ideXlab platform.
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Improving the Material Point Method
Innovative Numerical Approaches for Multi-Field and Multi-Scale Problems, 2016Co-Authors: Deborah Sulsky, Ming GongAbstract:The Material-Point Method (MPM) was introduced about 20 years ago and is a versatile Method for solving problems in continuum mechanics. The flexibility of the Method is achieved by combining two discretizations of the Material. One is a Lagrangian description based on representing the continuum by a set of Material Points that are followed throughout the calculation. The second is a background grid that is used to solve the continuum equations efficiently. In its original form, some applications of the Method appeared to be second order accurate while other tests showed poor or no convergence. This paper provides a framework for analyzing the errors in MPM. Moreover, the analysis suggests modifications to the algorithm to improve accuracy. The analysis also Points to connections between MPM and other meshfree Methods.
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using the Material Point Method to model sea ice dynamics
Journal of Geophysical Research, 2007Co-Authors: Deborah Sulsky, H L Schreyer, Kara J Peterson, R Kwok, Max D CoonAbstract:[1] The Material-Point Method (MPM) is a numerical Method for continuum mechanics that combines the best aspects of Lagrangian and Eulerian discretizations. The Material Points provide a Lagrangian description of the ice that models convection naturally. Thus properties such as ice thickness and compactness are computed in a Lagrangian frame and do not suffer from errors associated with Eulerian advection schemes, such as artificial diffusion, dispersion, or oscillations near discontinuities. This desirable property is illustrated by solving transport of ice in uniform, rotational and convergent velocity fields. Moreover, the ice geometry is represented by unconnected Material Points rather than a grid. This representation facilitates modeling the large deformations observed in the Arctic, as well as localized deformation along leads, and admits a sharp representation of the ice edge. MPM also easily allows the use of any ice constitutive model. The versatility of MPM is demonstrated by using two constitutive models for simulations of wind-driven ice. The first model is a standard viscous-plastic model with two thickness categories. The MPM solution to the viscous-plastic model agrees with previously published results using finite elements. The second model is a new elastic-decohesive model that explicitly represents leads. The model includes a mechanism to initiate leads, and to predict their orientation and width. The elastic-decohesion model can provide similar overall deformation as the viscous-plastic model; however, explicit regions of opening and shear are predicted. Furthermore, the efficiency of MPM with the elastic-decohesive model is competitive with the current best Methods for sea ice dynamics.
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using the Material Point Method to model sea ice dynamics
Journal of Geophysical Research, 2007Co-Authors: Deborah Sulsky, H L Schreyer, Kara J Peterson, R Kwok, Max D CoonAbstract:[1] The Material-Point Method (MPM) is a numerical Method for continuum mechanics that combines the best aspects of Lagrangian and Eulerian discretizations. The Material Points provide a Lagrangian description of the ice that models convection naturally. Thus properties such as ice thickness and compactness are computed in a Lagrangian frame and do not suffer from errors associated with Eulerian advection schemes, such as artificial diffusion, dispersion, or oscillations near discontinuities. This desirable property is illustrated by solving transport of ice in uniform, rotational and convergent velocity fields. Moreover, the ice geometry is represented by unconnected Material Points rather than a grid. This representation facilitates modeling the large deformations observed in the Arctic, as well as localized deformation along leads, and admits a sharp representation of the ice edge. MPM also easily allows the use of any ice constitutive model. The versatility of MPM is demonstrated by using two constitutive models for simulations of wind-driven ice. The first model is a standard viscous-plastic model with two thickness categories. The MPM solution to the viscous-plastic model agrees with previously published results using finite elements. The second model is a new elastic-decohesive model that explicitly represents leads. The model includes a mechanism to initiate leads, and to predict their orientation and width. The elastic-decohesion model can provide similar overall deformation as the viscous-plastic model; however, explicit regions of opening and shear are predicted. Furthermore, the efficiency of MPM with the elastic-decohesive model is competitive with the current best Methods for sea ice dynamics.
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Implicit dynamics in the Material-Point Method
Computer Methods in Applied Mechanics and Engineering, 2004Co-Authors: Deborah Sulsky, A. KaulAbstract:Abstract A time-implicit discretization is derived and validated for the Material-Point Method (MPM). The resulting non-linear, discrete equations are solved using Newton's Method combined with either the conjugate gradient Method or the generalized minimum residual Method. These Newton–Krylov solvers are implemented in a matrix-free fashion for numerical efficiency. A description of the algorithms and evaluation of their performance is presented. On all test problems, if the time step is chosen appropriately, the implicit solution technique is more efficient than an explicit Method without loss of desired features in the solutions. In a dramatic example, time steps 10,000 times the explicit step size are possible for the large deformation compression of a cylindrical billet at 1.2% the computational cost.
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modeling delamination as a strong discontinuity with the Material Point Method
Computer Methods in Applied Mechanics and Engineering, 2002Co-Authors: H L Schreyer, Deborah Sulsky, S J ZhouAbstract:Decohesion is an important failure mode associated with layered composite Materials. Here, the energy implications of Material softening are explored in a thermodynamic framework with the result that the dissipated energy (fracture energy) is greater than the plastic work of the traction on the failure surface. It is also argued that if the traction and continuum constitutive equations are solved simultaneously, the resulting algorithm is as simple as that for conventional plasticity. For numerical simulations, the Material Point Method displays the attributes of no mesh deformation so that remeshing is not necessary and the continuous tracking of Material Points avoids the need for remapping history variables such as decohesion. Compatibility is invoked in a weak sense with the result that no special algorithms are needed for mesh realignment along crack surfaces or for double nodes. Example solutions exhibit no sensitivity of delamination propagation with mesh orientation.