China
Africa
Explore chapters and articles related to this topic
On the use of the material point method to model problems involving large rotational deformation
Published in António S. Cardoso, José L. Borges, Pedro A. Costa, António T. Gomes, José C. Marques, Castorina S. Vieira, Numerical Methods in Geotechnical Engineering IX, 2018
L. Wang, W.M. Coombs, C.E. Augarde, M. Brown, J. Knappett, A. Brennan, C. Davidson, D. Richards, A. Blake
The Material Point Method (MPM) is a numerical method used to simulate massive deformation of solids combining advantages of both Eulerian and Lagrangian approaches for solving solid mechanics problems. In the MPM a body is described by a number of Lagrangian material points, at which state variables are stored and tracked. Computation for an incremental loading is then carried out on a background computational mesh. As demonstrated in Figure 1 for a simple shear problem, the total deformation and other state variables are stored at the material points, while the background mesh is extended with the incremental displacment, thus avoiding the mesh distortion seen with the standard FEM for large deformation problems. In fact, the background mesh can be any mesh at the beginning of each load step. Because of this attraction the MPM has been applied to several large deformation problems particularly in the area of geotechnical engineering, e.g. (Ceccato et al. 2016, among others).
On the use of the material point method to model problems involving large rotational deformation
Published in António S. Cardoso, José L. Borges, Pedro A. Costa, António T. Gomes, José C. Marques, Castorina S. Vieira, Numerical Methods in Geotechnical Engineering IX, 2018
L. Wang, W.M. Coombs, C.E. Augarde, Sachin Brown, J. Knappett, A. Brennan, C. Davidson, A. Blake, D. Richards
The Material Point Method (MPM) is a numerical method used to simulate massive deformation of solids combining advantages of both Eulerian and Lagrangian approaches for solving solid mechanics problems. In the MPM a body is described by a number of Lagrangian material points, at which state variables are stored and tracked. Computation for an incremental loading is then carried out on a background computational mesh. As demonstrated in Figure 1 for a simple shear problem, the total deformation and other state variables are stored at the material points, while the background mesh is extended with the incremental displacment, thus avoiding the mesh distortion seen with the standard FEM for large deformation problems. In fact, the background mesh can be any mesh at the beginning of each load step. Because of this attraction the MPM has been applied to several large deformation problems particularly in the area of geotechnical engineering, e.g. (Ceccato et al. 2016, among others).
Finite Difference and Numerical Methods
Published in K.T. Chau, Theory of Differential Equations in Engineering and Mechanics, 2017
A numerical technique called the material point method (MPM) is particularly useful in modelling large deformation problems, such as landslides, runouts, or dynamic fragmentations. This formulation uses a dual description of the media by using Lagrangian material points and a Eulerian numerical mesh. The MPM is an extension of the particle-in-cell method (a method developed in Los Alamos National Laboratory in 1957) in computational fluid dynamics to computational solid dynamics, and is a finite element method (FEM)-based particle method. It is primarily used for multiphase simulations, because of the ease of detecting contact without inter-penetration. It can also be used as an alternative to dynamic FEM methods in simulating large material deformations, because there is no re-meshing required by the MPM. It was originally proposed by Sulsky et al. (1995).
Experimental and numerical investigation of the behavior of three-dimensional orthogonal woven composite plates under high-velocity impact
Published in Mechanics of Advanced Materials and Structures, 2023
Hao Su, Xuena Si, Yan Liu, Ming-ming Xu, Guang-yan Huang, Jiacong Pan
We established a point-based mesocopic modeling scheme of 3DOWC in our previous research [24]. Complex mesoscopic structures can be easily discretized with points. Meanwhile, the material point method (MPM) has great advantages in simulating impact problems because it is natural to describe fracture in MPM framework and no mesh distortion exists. Therefore, it is very effective to simulate the impact problem of 3DOWC by combining the point-based mesocopic model and MPM [24, 25]. In this research, a combined experimental and numerical research based on point model and MPM is carried out to investigate the responses and the failure mechanisms of 3DOWC.
Modelling rainfall-induced mudflows using FEMLIP and a unified hydro-elasto-plastic model with solid-fluid transition
Published in European Journal of Environmental and Civil Engineering, 2018
Smooth particle hydrodynamics (SPH) (Cascini, Cuomo, Pastor, Sorbino, & Piciullo, 2014) is a well-known technique in which the studied domain is discretised into particles that have a spatial distance or so-called smoothing length. Within this distance, material properties are “smoothed” using a kernel function. Because of its formulation, SPH can be adapted for problems that are dynamically driven and that require a specific solution in the treatment of boundary conditions. In addition, the material point method (MPM) combines the capacities of the Eulerian and Lagrangian methods. The domain is first discretised into a series of mobile particles, Newton’s second law is then solved to determine global displacement in the fixed mesh. While this method is frequently used to describe landslides (Abe, Soga, & Bandara, 2014; Bandara, Ferrari, & Laloui, 2016; Soga, Alonso, Yerro, Kumar, & Bandara, 2015), it suffers from several weaknesses:The linear shape functions frequently induce numerical noises in large displacements cases, when material points cross the background mesh (Abe et al., 2014; Bardenhagen & Kober, 2004), While the Generalised Interpolation Material Point Method has ameliorated this issue, a very fine mesh can still reveal this problem (Abe et al., 2014).The numerical weight of the material particles reflects the particle’s representative volume which is updated according to the continuum transformation. However, this volume update does not account for the number of particles in a cell. Furthermore, Beuth, Wieckowski, and Vermeer (2011) proposed a new version based on a re-computation of the numerical weight, such as the cell weight when constant in time. It should be pointed out that this contribution was first proposed by Moresi et al. (Moresi & Solomatov, 1995) in 1995.Higher dimensional shape functions demand additional computational time.
Mechanism, influencing factors and research methods for soil desiccation cracking: a review
Published in European Journal of Environmental and Civil Engineering, 2023
Shuoshuo Xu, Hossein Nowamooz, Jinxing Lai, Huitian Liu
These traditional continuous methods are based on certain assumptions, which brings many limitations to the complex cracking process, especially, it is obviously discontinuous at the crack location where the presence of a pre-existing embedded cracks needs to be set in advance. Therefore, some upgrade methods, such as extended finite element method (XFEM) (Mohammadnejad & Khoei, 2013), mesh fragmentation technique (MFT) and smoothed particle hydrodynamics method (SPH), have attracted attentions. Vahab et al. (2019) built an XFEM model of non-permeable media hydrodynamically driven viscous cracks containing naturally cemented cracks. However, the functions are needed in the XFEM model to track the propagation of the crack which make it is difficult to simulate complex cracking patterns. On the contrary, there is no need to establish function in the mesh fragmentation technique (MFT) model (Sánchez et al., 2014), which has a better prospect in simulating the formation of drying cracks. The smoothed particle hydrodynamics (SPH) method for meshless technology performs well in dealing with large material deformation and destruction which does not require any background mesh. Bui et al. (2007, 2015) proposed the smoothed particle hydrodynamics (SPH) for the first time to simulate shrinkage-induced soil cracking. And a simple tension damage model was adopted in the promising numerical approach. The basic equations used to describe the motion of soil in the SPH framework are the continuity equation and the momentum equation. The former describes the change in density and void ratio of soil undergoing large deformation, while the momentum equation simulates soil deformation subjected to external loading (Bui et al., 2008). Tran et al. (2019b) proposed a size-dependent SPH framework to investigation of soil cracking problems that combines the mesh-free SPH method with a size-dependent constitutive model governed by an embedded cohesive fracture process zone. The biggest advantage of this model is that it does not need to define the crack location in advance, which is of great help to the prediction of cracks. Jihen et al. (2021) developed a continuum-based particle method (FEM-MPM) to simulate the initiation and propagation of desiccation crack. The constitutive equation of the method considered a hydro-mechanical model including cohesion suction and porosity evolution. Material point method (MPM) have the advantages of both Lagrangian and Eulerian description (Yerro et al., 2015; Bhandari et al., 2016) and it allows the use of fully coupled hydromechanical process into the multiphase problems.