Comparison of a Material Point Method and a Galerkin meshfree method for the simulation of cohesive-frictional materials

The simulation of large deformation problems, involving complex history-dependent constitutive laws, is of paramount importance in several engineering fields. Particular attention has to be paid to the choice of a suitable numerical technique such that reliable results can be obtained. In this paper, a Material Point Method (MPM) and a Galerkin Meshfree Method (GMM) are presented and verified against classical benchmarks in solid mechanics. The aim is to demonstrate the good behavior of the methods in the simulation of cohesive-frictional materials, both in static and dynamic regimes and in problems dealing with large deformations. The vast majority of MPM techniques in the literature are based on some sort of explicit time integration. The techniques proposed in the current work, on the contrary, are based on implicit approaches, which can also be easily adapted to the simulation of static cases. The two methods are presented so as to highlight the similarities to rather than the differences fromPeer ReviewedPostprint (published version

Finite element modeling of free surface flow in variable porosity media

The aim of the present work is to present an overview of some numerical procedures for the simulation of free surface flows within a porous structure. A particular algorithm developed by the authors for solving this type of problems is presented. A modified form of the classical Navier–Stokes equations is proposed, with the principal aim of simulating in a unified way the seepage flow inside rockfill-like porous material and the free surface flow in the clear fluid region. The problem is solved using a semi-explicit stabilized fractional step algorithm where velocity is calculated using a 4th order Runge–Kutta scheme. The numerical formulation is developed in an Eulerian framework using a level set technique to track the evolution of the free surface. An edge-based data structure is employed to allow an easy OpenMP parallelization of the resulting finite element code. The numerical model is validated against laboratory experiments on small scale rockfill dams and is compared with other existing methods for solving similar problems.Peer ReviewedPostprint (author’s final draft

CIMNE Verification of the validation analisis of Xfinas elements database

In order to validate the Xfinas code a very comprehensive series of test examples were solved by Prof Ki-Du Kim and his co-workers. A collection of the more representative benchmarks were chosen at CIMNE for testing the good behavior of every element implemented in the software. The aim of the validation work carried out at CIMNE has been to asses the accuracy of the Xfinas program. This was done studying the whole validation process carried out by Prof Ki-Du Kim’s team in detail. For this purpose we have chosen at CIMNE randomly the different benchmarks to be reproduced between those of the validation manual (VM from now on). In every example we checked the agreement of the results with the Xfinas validation data.Postprint (author’s final draft

A modified Finite Element formulation for the imposition of the slip boundary condition over embedded volumeless geometries

This work describes a novel formulation for the simulation of Navier–Stokes problems including embedded objects. The new proposal is based on the use of a modified finite element space, which replaces the standard one within the elements intersected by the immersed geometry. The modified space is able to exactly reproduce the jumps happening at the embedded boundary while preserving the conformity across the faces intersected by the embedded object. The paper focuses particularly on the imposition of a slip boundary condition on the surface of the embedded geometry, proposing a new technique for the application of such constraint. The new proposal is carefully benchmarked using the results of a body fitted technique and of an alternative embedded approach. Potential applications of interest are also presented.Peer ReviewedPostprint (author's final draft

A discontinuous Nitsche-based finite element formulation for the imposition of the Navier-slip condition over embedded volumeless geometries

This is the peer reviewed version of the following article: [Zorrilla, R, Larese de Tetto, A, Rossi, R. A discontinuous Nitsche-based finite element formulation for the imposition of the Navier-slip condition over embedded volumeless geometries. Int J Numer Meth Fluids. 2021; 93: 2968– 3003. https://doi.org/10.1002/fld.5018], which has been published in final form at https://doi.org/10.1002/fld.5018. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-ArchivingThis work describes a novel formulation for the simulation of incompressible Navier–Stokes problems involving nonconforming discretizations of membrane-like bodies. The new proposal relies on the use of a modified finite element space within the elements intersected by the embedded geometry, which is represented by a discontinuous (or element-by-element) level set function. This is combined with a Nitsche-based imposition of the general Navier-slip boundary condition, to be intended as a wall law model. Thanks to the use of an alternative finite element space, the formulation is capable of reproducing exactly discontinuities across the embedded interface, while preserving the structure of the graph of the discrete matrix. The performance, accuracy and convergence of the new proposal is compared with analytical solutions as well as with a body fitted reference technique. Moreover, the proposal is tested against another similar embedded approach. Finally, a realistic application showcasing the possibilities of the method is also presented.European Commission, H2020-FETHPC-2016-2017-800898; International Graduate School of Science and Engineering (IGSSE)), ATMOPACE; Istituto Nazionale di Alta Matematica “Francesco Severi”, Ministero dell'Università e della Ricerca, Programma per Giovani Ricercatori “Rita Levi Mon; Secretaría de Estado de Investigación, Desarrollo e Innovación, CEX2018-000797-SPeer ReviewedPostprint (author's final draft

Coupled soil-structure interaction modeling and simulation of landslide protective structures

Within the past two decades, mass movements hazards involving fast and large soil deformation have increased significantly in frequency and magnitude due to their strong relation to climate changes and global warming. These phenomena often bring along rocks, debris, and heavy materials that can extensively damage and destroy the landscape and infrastructures, causing devastating economic loss, and often, human casualties. The risk of future disasters continues to escalate with the increase of real estate development in suburban areas, including mountainous regions. Further assessment and prediction on such disasters and their countermeasures are, therefore, in high economic demands. One of the most intuitive ways is to install protective structures in mountain slopes and valleys that can hold the materials brought by the moving landslides. While the current state of the art of landslide prediction using numerical methods has been mainly dominated by the development of advanced geomechanical models suited for different types of soil materials, e.g. multi-phase unsaturated soil model, this study focuses more on the interaction of such phenomena with the installed protective structures. Here, an implicit formulation of material point method (MPM) is implemented to model the landslides considering finite strain assumption. Furthermore, a staggered coupling scheme with traditional Finite Element Method (FEM) is proposed to simulate accurately and robustly the dynamic force and displacement coupling of soil-structure interaction (SSI). All developments of the method are implemented within the Kratos-Multiphysics framework [1] and available under the BSD license (https://github.com/KratosMultiphysics/Kratos/wiki). In the future works, more adequate consideration of coupling scheme and material models considering damage and fracture will be investigated before conducting a real-scale landslide simulation

PFEM application in fluid structure interaction problems

In the current paper the Particle Finite Element Method (PFEM), an innovative numerical method for solving a wide spectrum of problems involving the interaction of fluid and structures, is briefly presented. Many examples of the use of the PFEM with GiD support are shown. GiD framework provides a useful pre and post processor for the specific features of the method. Its advantages and shortcomings are pointed out in the present work.Peer ReviewedPostprint (published version

A coupled Eulerian-PFEM model for the simulation of overtopping in rockfill dams

Postprint (published version

A mixed Lagrangian and Eulerian FSI approach for simulation of overtopping on embankment dams

The present work is concerned with some recent advances in FSI simulations with particular emphasis on the simulation of rockfill dams during extreme phenomena. The final objective is the study of the consequences of an overtopping on the stability of such structure and its possible failure mode. A mixed Lagrangian and Eulerian approach is used. The fluid behavior is described using a modified form of the Navier Stokes equations in order to consider the effect of a variable porosity. A non linear Darcy law is included in the momentum equation. A level set function is chosen to follow the movement of the free surface inside and outside the porous medium. The structure is described using a purely lagrangian PFEM formulation. The specific features of PFEM make it appropriate to treat the rockfill material and its large deformations and shape changes. A projection technique allows to perform the data transfer between the fluid and the structure non matching meshes.Peer ReviewedPostprint (published version

Analysis of stability of earth dams in overtopping scenarios with the particle finite element method

The aim of this work is to study the consequences of an overtopping on the stability of earth dams and its possible failure mode. Rehabilitation and safety analysis of existing dams is nowadays an open field of research. The possibility to define a numerical instrument to provide support for analyzing the failure of a dam is a big step ahead for organizing the intervention measures and for optimizing the economic plan. In fact many existing dams have now to be modified due to the revision of previous design criteria in order to increase their safety. The objective of our work is to develop and validate a new computational method of general applicability that allows treating the above problems. The method will combine advanced finite element and particle techniques. Fluid-structure interaction effects and non-linear geometrical and mechanical effects in the dam material are considered. A mixed Lagrangian and Eulerian approach is used. The fluid behavior is described using a modified form of the Navier Stokes equations in order to consider the effect of a variable porosity. A non linear Darcy law is included in the momentum equation. A level set function is chosen to follow the movement of the free surface inside and outside the porous medium. The structure is described using a purely lagrangian PFEM formulation [1] and [2]. The specific features of PFEM make it appropriate to treat the rockfill material and its large deformations and shape changes. A projection technique allows to perform the data transfer between the fluid and the structure non matching meshes.Peer ReviewedPostprint (published version