Material point method

The material point method (MPM) is a numerical technique used to simulate the behavior of solids, liquids, gases, and any other continuum material. Especially, it is a robust spatial discretization method for simulating multi-phase (solid-fluid-gas) interactions. In the MPM, a continuum body is described by a number of small Lagrangian elements referred to as 'material points'. These material points are surrounded by a background mesh/grid that is used to calculate terms such as the deformation gradient. Unlike other mesh-based methods like the finite element method, finite volume method or finite difference method, the MPM is not a mesh based method and is instead categorized as a meshless/meshfree or continuum-based particle method, examples of which are smoothed particle hydrodynamics and peridynamics. Despite the presence of a background mesh, the MPM does not encounter the drawbacks of mesh-based methods (high deformation tangling, advection errors etc.) which makes it a promising

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MATERIAL POINT METHOD A numerical evaluation for elastic problems

Mathilde Metral

Frozen, the movie, released in 2013, made a big impression on many people: some children were no doubt amazed by the talking snowman, others by the film’s music, the designers were probably more interesed in the reproduction quality of the snow modelled, by the Material Point Method (MPM). Many paperspraise the effectiveness of this method for simulating complex phenomena. However, very few studies have been carried out to verify the method on very simple academic problems; that is precisely what we will try to study throughout this paper. We will see that simple problem modeling is not so easy with MPM. We will try to present as well as possible the different factors influencing the results, before concluding on its advantages and disadvantages

2020

Sharp transition in modes of dynamic crack propagation in dry-snow slab avalanche

Bertil Trottet

Dry-snow slab avalanche release can be separated in four distinct phases : (i) failure initiation in a weak snow layer, (ii) onset, (iii) dynamics of crack propagation in the weak layer and eventually (iv)slab release. While a lot has been done to study the first two phases, less is known about dynamic crack propagation, especially at slope scale.In this study, we used the Material Point Method and elastoplasticity to simulate the dynamics of20 m long Centered Propagation Saw Tests (PST). We improved the recent constitutive snow model of Gaume et al. (2018) by developing a new softening law based on the total plastic deformation (volumetric and deviatoric parts) to account for damages caused by shearing the weak layer. Interestingly, several regimes of propagations are observed depending on slope angle. For slope angles smaller than the friction angle (θφ), a sharp transition is observed once the crack reaches a critical length (lf). We interpret this transition as a change from slab bending to slab tension due to the increasing load in the downstream direction. An estimation of this critical length (lf) is proposed using a basic analytical shear model with residual friction similar to the one developped by McClung in 1979. The crack speed seems only bounded by the elastic wave speed in the slab. By this study, we explain the gap between propagation speeds based on 2 m PSTs and slope scale observations. Finally, our results bring back to light the pioneer work of McClung which appears sufficient to model slab avalanche release on steep terrain.

2020

Application of Material Point Method

Selimcan Ozden

The main goal of this project is by using MPM which is in continuum formulation to reproduce the wear mechanism in larger scale simulation which is performed in atomistic scale by Professor Jean-François Molinari. Then, having experience and getting information about the Material Point Method (MPM) which is used for computational fluid dynamics and solid dynamics based on weak formulation which is also case for Finite Element Method (FEM). Short information about methods, mathematical aspects and algorithm are provided in this report. Then, comparison of MPM and FEM is included in terms of advantages and points for both methods. MATLAB is the tool for first and second examples. The code that developed by Tsinghua University is implemented for second and third examples. At the end, conclusion about the MPM is presented.

2019

PHYS-100: Advanced physics I (mechanics)

La Physique Générale I (avancée) couvre la mécanique du point et du solide indéformable. Apprendre la mécanique, c'est apprendre à mettre sous forme mathématique un phénomène physique, en modélisant la situation et appliquant les lois de la physique.

PHYS-101(k): General physics : mechanics

Le but du cours de physique générale est de donner à l'étudiant.e les notions de base nécessaires à la compréhension des phénomènes physiques. L'objectif est atteint lorsque l'étudiant.e est capable de prévoir quantitativement les conséquences de ces phénomènes avec des outils théoriques appropriés.

PHYS-101(d): General physics : mechanics

Le but du cours de physique générale est de donner à l'étudiant les notions de base nécessaires à la compréhension des phénomènes physiques. L'objectif est atteint lorsque l'étudiant est capable de prévoir quantitativement les conséquences de ces phénomènes avec des outils théoriques appropriés.