Multiscale analysis using a coupled discrete/finite element model

Rojek, Jerzy,Onate, Eugenio Techno-Press 2008 Interaction and multiscale mechanics Vol.1 No.1

The present paper presents multiscale modelling via coupling of the discrete and finite element methods. Theoretical formulation of the discrete element method using spherical or cylindrical particles has been briefly reviewed. Basic equations of the finite element method using the explicit time integration have been given. The micr-macro transition for the discrete element method has been discussed. Theoretical formulations for macroscopic stress and strain tensors have been given. Determination of macroscopic constitutive properties using dimensionless micro-macro relationships has been proposed. The formulation of the multiscale DEM/FEM model employing the DEM and FEM in different subdomains of the same body has been presented. The coupling allows the use of partially overlapping DEM and FEM subdomains. The overlap zone in the two coupling algorithms is introduced in order to provide a smooth transition from one discretization method to the other. Coupling between the DEM and FEM subdomains is provided by additional kinematic constraints imposed by means of either the Lagrange multipliers or penalty function method. The coupled DEM/FEM formulation has been implemented in the authors' own numerical program. Good performance of the numerical algorithms has been demonstrated in a number of examples.

Vertical discretization with finite elements for a global hydrostatic model on the cubed sphere

Yi, T.H.,Park, J.R. Academic Press 2017 Journal of computational physics Vol.338 No.-

<P>A formulation of Galerkin finite element with basis-spline functions on a hybrid sigma pressure coordinate is presented to discretize the vertical terms of global Eulerian hydrostatic equations employed in a numerical weather prediction system, which is horizontally discretized with high-order spectral elements on a cubed sphere grid. This replaces the vertical discretization of conventional central finite difference that is first-order accurate in non-uniform grids and causes numerical instability in advection-dominant flows. Therefore, a model remains in the framework of Galerkin finite elements for both the horizontal and vertical spatial terms. The basis-spline functions, obtained from the de-Boor algorithm, are employed to derive both the vertical derivative and integral operators, since Eulerian advection terms are involved. These operators are used to discretize the vertical terms of the prognostic and diagnostic equations. To verify the vertical discretization schemes and compare their performance, various two- and three-dimensional idealized cases and a hindcast case with full physics are performed in terms of accuracy and stability. It was shown that the vertical finite element with the cubic basis-spline function is more accurate and stable than that of the vertical finite difference, as indicated by faster residual convergence, fewer statistical errors, and reduction in computational mode. This leads to the general conclusion that the overall performance of a global hydrostatic model might be significantly improved with the vertical finite element. (C) 2017 Elsevier Inc. All rights reserved.</P>

Compaction of Aggregated Ceramic Powders, Discrete Element and Finite Element Simulations

Pizette P.,Martin C. L.,Delette G. 한국분말야금학회 2006 한국분말야금학회 학술대회논문집 Vol.2006 No.1

In contrast with the Finite Element Method, the Discrete Element Method (DEM) takes explicitly into account the particulate nature of powders. DEM exhibits some drawbacks and many advantages. Simulations can be computationally expensive and they are only able to represent a volume element. However, these simulations have the great advantage of providing a wealth of information at the microstructural level. Here we demonstrate that the method is well suited for modelling, in coordination with FEM, the compaction of ceramic particles that have been aggregated. Aggregates of individual ceramic crystallites that are strongly bonded together are represented by porous spheres.

유한요소법에 의한 콘크리트의 진행성 파괴해석

송하원 한국콘크리트학회 1996 콘크리트학회지 Vol.8 No.1

콘크리트의 파괴진행영역은 콘크리트의 균열선단의 브리징영역과 미세균열영역으로 구성되는 비선형영역으로서 콘크리트의 파기거동을 지배한다. 파괴진행영역을 고려한 파괴역학은 콘크리트에 유용하게 적용될 수 있으며 파괴진행영역 모델의 개발은 콘크리트의 파괴현상을 규명하는데 매우 중요하다. 본 논문에서는 콘크리트의 균열진행을 해석하기 위하여 선형 인장 연화곡선을 사용한 Dugdale-Barenblatt형 모델로 콘크리트의 브리징영역을 모델링하였고 이를 이산균열방법을 사용하여 단지 요소경계면에 파괴진행영역을 발생시켜 유한요소 해석하는 방법과 요소내의 불연속 균열면을 도입한 균열요소를 사용함으로써 이산균열방법의 결점을 보완한 해석방법을 제시하였다. 또한 해석 예를 통해 균열진행해석에 사용된 유한요소모델을 검증하였다. The fracture process zone in concrete is a region ahead of a traction-free crack, in which two major mechanisms, microcracking and bridging, play important roles. The toughness due to bridging is dominant compared to toughness induced by microcracking, so that the bridging is dominani: mechanism governing the fracture process of concrete. Fracture mechanics does work for concrete provided that the fracture process zone is being considered, so that the development of model for the fracture process zone is most important to describe fracture phenomena in concrete. In this paper the bridging zone, which is a part of extended rnacrocrack with stresses transmitted by aggregates in concrete, is modelled by a Dugdale-Barenblatt type model with linear tension-softening curve. Two finite element techniques are shown for the analysis of progressive cracking in concrete based on the discrete crack approach: one with crack element, the other without crack element. The advantage of the technique with crack element is that it dees not need to update the mesh topology to follow the progressive cracking. Numerical results by the techniques are demonstrated.

Nonlinear soil-structure interaction analysis in poroelastic soil using mid-point integrated finite elements and perfectly matched discrete layers

Elsevier 2018 Soil dynamics and earthquake engineering Vol.108 No.-

<P><B>Abstract</B></P> <P>A numerical approach for a nonlinear analysis of soil-structure interaction in poroelastic soil is proposed. Nonlinear behavior in the near-field region of soil is considered by conventional finite elements. The far-field region of soil is represented by mid-point integrated finite elements and perfectly matched discrete layers (PMDLs) in order to consider the energy radiation into infinity. The mid-point integrated finite elements can be formulated identically to conventional finite elements. Thus, PMDLs for poroelastic media are formulated in this study. A means by which to represent a layered poroelastic half-space with conventional finite elements, mid-point integrated finite elements, and the developed PMDLs is proposed. The proposed numerical approach is verified from various perspectives. The approach is applied to a nonlinear analysis of the earthquake responses of a structural system on poroelastic soil. It is demonstrated via the application that the proposed approach can be applied successfully to nonlinear dynamic soil-structure interaction problems.</P> <P><B>Highlights</B></P> <P> <UL> <LI> A numerical approach for nonlinear soil-structure interaction in poroelastic soil is proposed. </LI> <LI> Perfectly matched discrete layers (PMDLs) for poroelastic media are formulated. </LI> <LI> A layered poroelastic half-space can be represented accurately and effectively. </LI> <LI> Linear/nonlinear dynamic problems in a layered poroelastic half-space are solved. </LI> </UL> </P>

A discrete particle model for reinforced concrete fracture analysis

Azevedo, N. Monteiro,Lemos, J.V.,Almeida, J.R. Techno-Press 2010 Structural Engineering and Mechanics, An Int'l Jou Vol.36 No.3

The Discrete Element Method adopting particles for the domain discretization has recently been adopted in fracture studies of non-homogeneous continuous media such as concrete and rock. A model is proposed in which the reinforcement is modelled by 1D rigid-spring discrete elements. The rigid bars interact with the rigid circular particles that simulate the concrete through contact interfaces. The DEM enhanced model with reinforcement capabilities is evaluated using three point bending and four point bending tests on reinforced concrete beams without stirrups. Under three point bending, the model is shown to reproduce the expected final crack pattern, the crack propagation and the load displacement diagram. Under four point bending, the model is shown to match the experimental ultimate load, the size effect and the crack propagation and localization.

ON DISCRETENESS OF MÖBIUS GROUPS

Fu, Xi Korean Mathematical Society 2013 대한수학회보 Vol.50 No.3

It's known that one could use a fixed loxodromic or parabolic element in $M(\bar{\mathbb{R}}^n)$ as a test map to test the discreteness of a non-elementary M$\ddot{o}$bius group G. In this paper, we discuss the discreteness of G by using a fixed elliptic element.

Damage prediction in the vicinity of an impact on a concrete structure: a combined FEM/DEM approach

Jessica Rousseau,Emmanuel Frangin,Philippe Marin,Laurent Daudeville 사단법인 한국계산역학회 2008 Computers and Concrete, An International Journal Vol.5 No.4

This article focuses on concrete structures submitted to impact loading and is aimed at predicting local damage in the vicinity of an impact zone as well as the global response of the structure. The Discrete Element Method (DEM) seems particularly well suited in this context for modeling fractures. An identification process of DEM material parameters from macroscopic data (Young’s modulus, compressive and tensile strength, fracture energy, etc.) will first be presented for the purpose of enhancing reproducibility and reliability of the simulation results with DE samples of various sizes. The modeling of a large structure by means of DEM may lead to prohibitive computation times. A refined discretization becomes required in the vicinity of the impact, while the structure may be modeled using a coarse FE mesh further from the impact area, where the material behaves elastically. A coupled discrete-finite element approach is thus proposed: the impact zone is modeled by means of DE and elastic FE are used on the rest of the structure. The proposed approach is then applied to a rock impact on a concrete slab in order to validate the coupled method and compare computation times.

A discrete particle model for reinforced concrete fracture analysis

N. Monteiro Azevedo,J.V. Lemos,J.R. Almeida 국제구조공학회 2010 Structural Engineering and Mechanics, An Int'l Jou Vol.36 No.3

The Discrete Element Method adopting particles for the domain discretization has recently been adopted in fracture studies of non-homogeneous continuous media such as concrete and rock. A model is proposed in which the reinforcement is modelled by 1D rigid-spring discrete elements. The rigid bars interact with the rigid circular particles that simulate the concrete through contact interfaces. The DEM enhanced model with reinforcement capabilities is evaluated using three point bending and four point bending tests on reinforced concrete beams without stirrups. Under three point bending, the model is shown to reproduce the expected final crack pattern, the crack propagation and the load displacement diagram. Under four point bending, the model is shown to match the experimental ultimate load, the size effect and the crack propagation and localization.

이산요소법을 이용한 화강암의 선형절삭 시뮬레이션

전철웅(Chul-Woong Jun),손정현(Jeong-Hyun Sohn),이재욱(Jae-Wook Lee) 한국기계가공학회 2016 한국기계가공학회지 Vol.15 No.4

The pick cutter, which directly contacts and crushes the rock, is the expendable part of a roadheader. The arrangement and angle of attachment of the pick cutter are important factors that determine excavator performance. It is necessary to numerically calculate the contact between the pick cutter and rock. The rock is defined as a set of particles using the discrete element method. The parallel bond model is used to define the bonds between particles. The properties of granite that are measured by the uniaxial compressive test are applied to the numerical rock model. The pick cutter is defined by the polygon elements. The linear cutting simulation is considered to simulate the contact between the pick cutter and rock. The results of the simulation show the rock breaking due to contact with the pick cutter.