Large deformation analysis using a quasi-static material point method.

The Finite Element Method (FEM) has become the standard tool for the analysis of a wide range of solid mechanics problems. However, the underlying structure of a classical updated Lagrangian FEM is not well suited for the treatment of large deformation problems, since excessive mesh distortions can lead to numerical difficulties. The Material Point Method (MPM) represents an approach in which material points moving through a fixed finite element grid are used to simulate large deformations. As the method makes use of moving material points, it can also be classifed as a point-based or meshless method. With no mesh distortions, it is an ideal tool for the analysis of large deformation problems. MPM has its origin in fluid mechanics and has only recently been applied to solid mechanics problems. It has been used successfully for impact analyses where bodies penetrate each other and for silo discharging problems. All existing MPM codes found in literature are dynamic codes with explicit time integration and only recently implicit time integration. In this study a quasi-static MPM formulation and implementation are presented. The paper starts with the description of the quasi-static governing equations and the numerical discretisation. Afterwards, the calculation process of the quasi-static MPM is explained, followed by the presentation of some geotechnical boundary value problems which have been solved with the newly developed quasi-static MPM code. The benchmark problems consist of an oedometer test and a slope. For validation, the results are compared with analytical solutions and FEM results, respectively

A laboratory-numerical approach for modelling scale effects in dry granular slides

Granular slides are omnipresent in both natural and industrial contexts. Scale effects are changes in physical behaviour of a phenomenon at different geometric scales, such as between a laboratory experiment and a corresponding larger event observed in nature. These scale effects can be significant and can render models of small size inaccurate by underpredicting key characteristics such as ow velocity or runout distance. Although scale effects are highly relevant to granular slides due to the multiplicity of length and time scales in the flow, they are currently not well understood. A laboratory setup under Froude similarity has been developed, allowing dry granular slides to be investigated at a variety of scales, with a channel width configurable between 0.25-1.00 m. Maximum estimated grain Reynolds numbers, which quantify whether the drag force between a particle and the surrounding air act in a turbulent or viscous manner, are found in the range 102-103. A discrete element method (DEM) simulation has also been developed, validated against an axisymmetric column collapse and a granular slide experiment of Hutter and Koch (1995), before being used to model the present laboratory experiments and to examine a granular slide of significantly larger scale. This article discusses the details of this laboratory-numerical approach, with the main aim of examining scale effects related to the grain Reynolds number. Increasing dust formation with increasing scale may also exert influence on laboratory experiments. Overall, significant scale effects have been identified for characteristics such as ow velocity and runout distance in the physical experiments. While the numerical modelling shows good general agreement at the medium scale, it does not capture differences in behaviour seen at the smaller scale, highlighting the importance of physical models in capturing these scale effects

Modelling of pile installation process

W pracy rozważa się zagadnienie modelowania procesu instalacji pala w gruncie. Zjawisko bardzo dużych odkształceń gruntu, występujące w tym procesie, zostało przeanalizowane za pomocą metody punktów materialnych - wariantu metody elementów skończonych, sformułowanego w dowolnym materialno-przestrzennym opisie ruchu.Modelling of the process of pile installation is considered in the paper. The problem of large strains involved in the installation process is analysed with the help of the material point method, a variant of the finite element method formulated in an arbitrary Lagrangian-Eulerian description of motion

Granular flow modelling by the materiał point method

Red. serii : Wodziński, PiotrModelowanie komputerowe procesu przepływu materiału sypkiego ma duże znaczenie praktyczne, ponieważ pozwala wyznaczyć profil i prędkość przepływu oraz oddziaływania materiału na ściany zbiornika znacznie mniejszym kosztem niż badania eksperymentalne. Modelowanie numeryczne może również w znacznym stopniu zredukować koszt eksperymentu, jeśli zostanie on poprzedzony odpowiednio przygotowaną analizą numeryczną. Niniejsze opracowanie poświęcone jest temu zagadnieniu, przy czym analizowano procesy zarówno opróżniania, jak i napełniania zbiornika. Opis mechaniczny przepływu materiału sypkiego charakteryzuje się silnymi nieliniowościami związanymi z dużymi odkształceniami, nieliniowymi związkami fizycznymi oraz zjawiskiem kontaktu z tarciem. Jako narzędzie analizy zastosowano metodę punktów materialnych - wykorzystaną w analizie zagadnień mechaniki ciała stałego implementację metody cząstki w komórce ( ang. particle-in-cell method). Metodę punktów materialnych można także interpretować jako metodę elementów skończonych, sformułowaną w mieszanym, materialno- przestrzennym opisie ruchu. W opracowaniu porównano kilka modeli konstytutywnych materiału sypkiego. Metodę analizy zastosowano do zbiorników o złożonych kształtach - analizowano przepływ płaski i osiowosymetryczny.[...]Dynamie processes of granular flow have been analysed using the materiał point method. Piane strain and axi-symmetric flows have been investigated. Dynamie, strongly non-linear problems including large strains, materiał non-linearity and frictional contact have been solved. The materiał point method (MPM) has been proved to be a reliable numerical tool in the analysis of highly complex problems as discharging and filling containers (silos). The materiał point method is a variant of the finite element method formulated in an arbitrary Lagrangian-Eulerian description of motion. Although MPM uses the computational element mesh, it can also be regarded as a pointbased (meshless) method as the history of state variables is traced at the materiał points that are defined independently of the computational mesh used in the method. The point-based methods including MPM are more efficient in an analysis of large strain problems than the finite element method (FEM) formulated in the purely Lagrangian format as the latter method suffers from the excessive distortions of the element mesh used in calculations. The dynamie problem of granular flow has been formulated variationally and solved in the incrementa! way. The dynamie equations of MPM have been integrated in time by an explicit procedure. The mechanical behaviour of the granular materiał has been described by the use of several constitutive models: elastic-ideal plastic model, elastic-viscoplastic one, and several hypoplastic models. The Drucker-Prager yield condition and the non-associative (plastic incompressible) flow rule have been utilised in the case of the first two models. The constitutive relations have been integrated with respect to time by implicit algorithms. Problems of granular flow in silos of different shapes have been analysed. The silos with flat bottoms and trapezoidal or conical outlets have been considered. Two basie kinds of flow pattem (in the siło discharge process) have been modelled: the mass and funnel ones. The problem of granular flow around inserts has also been investigated including the flow in a container of the "silo-in-silo" type. In the case of the analysis of siło filling problem, an additional algorithm of mass density field calculation has been added to the MPM procedure. The density field has been determined on the base of the masses and current position of the materiał points. This approach is more accurate than the calculation of the density field by time integration of the constitutive relations, and also allows to determine the density in the stress-free state when the materiał grains are separated. A combination of viscous and non-linear elastic terms has been used to relate the volumetric strain and pressure in the constitutive equations. To avoid the mesh dependency of the numerical solution, the viscoplastic regularisation in the constitutive model has been used. This approach allows to obtain the thickness of shear bands - occurring in granular flow problems - related to the materiał model parameter, not to the size of element mesh. The mesh independence of the materiał point solution has been shown in the work. The phenomenon of dome which can be created over an outlet of a siło has also been investigated in the book. The phenomenon can appear when the granular materiał reveals some cohesion which can be an effect of materiał moistness. The small materiał cohesion can lead to an unreliable flow or flow suspension. MPM allows to analyse this problem. The minimum values of cohesion have been found for which the flow is stopped in the cases of siło discharge and stock-pile reclaim problems. To reduce the real time of computations, the parallel programming has been used by means of OpenMP. The loop-level parallelism has been applied for the main loops of the computer program. Although the approach is rather straightforward, the significant value of 2.6 has been achieved for the speed-up factor when 4 threads are used in the calculations. Some numerical results have been compared with those obtained from empirical formulae; good agreement has been noticed. The materiał point modelling of the granular flow seems to have the practical significance as it allows to find the flow profile, flow rate and the interaction between the flowing materiał and siło walls by means of smaller cost than an experiment. This does not mean that the modelling can entirely replace the experiment. However, the cost of the experimental research can be remarkably reduced when the computer modelling is utilised in preparing the experiment