Introduction to the Discrete Element Method (DEM) and the Applied Element Method (AEM)

INTRODUCTION

The Applied Element Method (AEM) is a new method of analysis, which combines characteristics of both the Finite Element Method (FEM) and the Discrete Element Method (DEM).?The FEM is a well-known method and is useful for the analysis of different types of structures (which have elements that are connected at the nodes) and the results are used for the sizing of different members. As FEM is well known to Structural engineers, only the other two methods, i.e. the DEM and the AEM, are discussed briefly in the following.

THE DISCRETE ELEMENT METHOD (DEM)

The Discrete Element Method (DEM) is used to study the behavior of different particles that are separated. It is a numerical method that models the motion and interaction of a large number of particles, taking into account not only the obvious geometric and material effects such as particle shape, material non-linearity, viscosity, friction, etc. but also the effects of various physical fields of surrounding media. It was first developed by?Cundall and Strack (1979)?for the analysis of rock mechanics problems. It is used to simulate the behavior of granular materials, such as sand, powders, and gravel. DEM is based on Newton's laws of motion, and it tracks the motion of each individual particle as it interacts with other particles and with boundaries.

DEM has been used to study a wide variety of phenomena in granular materials, including:

• Flow behavior
• Compaction
• ?Segregation
• Crushing
• Fracture
• Transport
• Mixing

DEM is a powerful tool for

understanding the behavior of granular materials. It has been used to predict

the behavior of granular materials in a wide variety of applications, including

the following:

• ?Powder handling
• Mining
• Construction
• Food processing
• Pharmaceutical manufacturing

It has a wide range of

applications, and it is becoming increasingly popular as computational power

increases. DEM?is not applicable to situations in which

individual particles undergo complex deformation (Matuttis, and Chen,

2014). Some examples of the applications of DEM are given below:

• The design of powder handling equipment
• The prediction of the flowability of powders
• The analysis of the stability of slopes
• The design of foundations
• The study of the fracture of rocks

DEM is a relatively new method, but it has become increasingly popular in recent years. This is due to the increasing availability of computational power, which allows DEM simulations to be performed on larger and more complex systems.

Some of the advantages of DEM include

1. It can be used to simulate the behavior of granular materials at the microscale, which can provide insights into the mechanisms of these phenomena.
2. It can be used to simulate systems with a large number of particles, which is not possible with other methods.
3. It can be used to simulate systems with complex geometries.

Some of the disadvantages of DEM are as below:

1. It can be computationally expensive, especially for large systems.
2. It can be difficult to validate DEM simulations, as there are no experimental data for many granular materials.
3. The results of DEM simulations can be sensitive to the choice of parameters, which can make it difficult to obtain accurate results.

Some software in which the Discrete Element Method (DEM) is implemented includes:

?EDEM?by Altair: This commercial software has been used in applications like powder handling, mining, and construction. It is known for its ease of use and its powerful visualization capabilities.

·????????Yade?(Yet Another DEM): This open-source software has been used in applications like granular materials, geomechanics, and biomechanics. It is known for its modular design and its ability to simulate complex systems.

·????????LIGGGHTS?(Large-scale Atomic/Molecular Massively Parallel Simulator): This open-source software has been used in a wide variety of applications, including granular materials, molecular dynamics, and biomolecular simulations. It is known for its high performance and its flexibility.

·????????DEMLab?by Itasca: This commercial software has been used for a wide range of applications, including geotechnical engineering, mining, and civil engineering. It is known for its powerful analysis capabilities and its ability to simulate complex systems.

THE APPLIED ELEMENT METHOD (AEM)?

The Applied Element Method (AEM) is capable of automatically simulating through the separation of elements to collapse and debris prediction.?AEM, which came into being after more than two decades of continuous research and development, has been found to be the only method that can automatically detect the initiation of cracks, track their progression throughout the structure, and simulate actual element separation, collision, and final collapse.

Table 1 summarizes the key differences between the AEM, FEM, and DEM:

The AEM is a powerful numerical analysis method that can be used to predict the behavior of structures under a variety of loading conditions. The AEM is particularly well-suited for predicting the behavior of structures that are likely to experience progressive collapse.

History of AEM

AEM took shape in 1995 at the University of Tokyo as part of Dr. Hatem Tagel Din’s research studies on the analysis and visualization of structures subjected to the extreme loading conditions generated during an earthquake.?Since 1995 the research and validation of AEM has been undertaken. Because of these efforts, many validation tests were conducted and research papers were published on the Applied Element Method.?The term ‘applied element method’ itself, however, was first coined only in 2000 in a paper published by Meguro and Tagel-Din. Research has been conducted since then to verify its accuracy for elastic analysis(Meguro and Tagel-Din, 2000); crack initiation and propagation, estimation of failure loads for reinforced concrete structures(Tagel-Din and Meguro,2000), reinforced concrete structures under cyclic loading (Tagel-Din and Meguro,2001), buckling and post-buckling behavior(Tagel-Din and Meguro,2002); nonlinear dynamic analysis of structures subjected to severe earthquakes(Tagel-Din and Meguro 2002); fault-rupture propagation (Tagel-Din and Meguro, 2000b); nonlinear behavior of brick structures(Tagel-Din and Meguro, 2004); and the analysis of glass reinforced polymers (GFRP) walls under blast loads(Paola and Meguro, 2003).

BRIEF DESCRIPTION OF THE APPLIED ELEMENT METHOD

The Applied Element Method (AEM) is a numerical analysis method used in predicting the continuum and discrete behavior of structures. The modeling method in AEM adopts the concept of discrete cracking, allowing it to automatically track structural collapse behavior passing through all stages of loading: elastic, crack initiation and propagation in tension-weak materials, reinforcement yield, element separation, element contact, and collision, as well as collision with the ground and adjacent structures.

In AEM, the structure is divided virtually and modeled as an assemblage of relatively small elements. The elements are then connected through a set of normal and shear springs located at contact points distributed along with the element faces. Normal and shear springs are responsible for the transfer of normal and shear stresses from one element to the other adjacent element.

The AEM has several advantages over the Finite Element Method (FEM) and the Discrete Element Method (DEM). These advantages include:

1.?????The AEM can accurately simulate the behavior of structures through all stages of loading, from elastic to collapse.

2.?????The AEM can automatically track the propagation of cracks in structures.

3.?????The AEM is relatively easy to implement and use.

4.?????The AEM is a relatively new numerical analysis method, but it has been shown to be effective in predicting the behavior of structures under a variety of loading conditions.

5.?????The AEM is particularly well-suited for predicting the behavior of structures that are likely to experience progressive collapse.

Element Generation and Formulation in AEM

The modeling of objects in AEM is similar to the modeling of objects in?conventional FEM. Each structure is divided into a series of elements connected to each other and forming a mesh. The main difference between AEM and FEM, however, is how the elements are joined together. In AEM the elements are connected by a series of?non-linear?springs representing the material behavior.

There are three types of springs used in AEM:

1. ?Matrix Springs: Matrix springs connect two elements together representing the main?material properties?of the object.
2. Reinforcing Bar Springs: Reinforcement springs are used to implicitly represent additional reinforcement bars running through the object without adding additional elements to the analysis.
3. Contact Springs: Contact Springs are generated when two elements collide with each other or the ground. When this occurs three springs are generated (Shear Y, Shear X, and Normal).

Automatic Element Separation

When the average strain value at the element face reaches the separation strain, all springs at this face are removed and elements are no longer connected until a collision occurs, at which point they collide together as rigid bodies.

Separation strain is considered the strain at which adjacent elements are totally separated at the connecting face. For concrete, all springs between the adjacent faces including reinforcement bar springs are cut. If the elements meet again, they will behave as two different rigid bodies that have now contacted each other. For steel, the bars are cut if the stress point reaches?ultimate stress?or if the concrete reaches the?separation strain.

Automatic Element Contact/Collision

Contact or collision is detected without any user intervention. Elements are able to separate, contract and/or make contact with other elements. In AEM three contact methods include Corner-to-Face, Edge-to-Edge, and Corner-to-Ground

?Software for AEM

Some of the software that can be used to analyze structures using the Applied Element Method (AEM) are given below:

1.?????Extreme Loading for Structures (ELS)?by ASI: This commercial software has been used in a wide range of applications, including progressive collapse analysis, impact analysis, and blast analysis. It is known for its ability to simulate complex structures and its ability to handle large deformations.

2.?????AEM-Solver?by ASI: This commercial software has been used in several applications, including structural analysis, crash analysis, and impact analysis. It is known for its accuracy and its ability to handle large deformations.

3.?????ADINA?by ADINA R&D, Inc.: This commercial software has been used in a number of applications, including structural analysis, crash analysis, and impact analysis. It is known for its accuracy and its ability to handle large deformations.

4.?????LS-DYNA?by Livermore Software Technology Corporation: This is commercial software has been used in a wide range of applications, including structural analysis, crash analysis, and impact analysis. It is known for its speed and its ability to handle large deformations.

5.?????Abaqus?by Dassault Systèmes: This commercial software has been used in several applications, including structural analysis, crash analysis, and impact analysis. It is known for its versatility and its ability to handle complex geometries.

References

1. Cundall, P.A. and?Strack, O.D.L.(1979) "A discrete numerical model for granular assemblies", Geotechnique, Vol 29, No.1, Mar. pp. 47-65.
2. Matuttis, H.-G., and Chen, J., (2014) Understanding the Discrete Element Method: Simulation of Non‐Spherical Particles for Granular and Multi‐Body Systems, John Wiley & Sons, Singapore Pte. Ltd., 448 pp.
3. Meguro, K. and Tagel-Din, H. (2000).?"Applied element method for structural analysis: Theory and application for linear materials".?Structural Engineering/Earthquake Engineering. Japan Society of Civil Engineers,?Vol.17, No.1, pp. 21–35.
4. Tagel-Din, H. and Meguro, K. (2000).?"Applied Element Method for Simulation of Nonlinear Materials: Theory and Application for RC Structures",?Structural Engineering/ Earthquake Engineering, Japan Society of Civil Engineers, Vol.?17, No. 2, pp. 137–148.
5. Tagel-Din, H. and Meguro, K. (2001).?"Applied Element Simulation of RC Structures under Cyclic Loading".?Journal of Structural Engineering, ASCE, Vol.?127, No.11, pp. 137-148. ?https://ascelibrary.org/doi/10.1061/%28ASCE%290733-9445%282001%29127%3A11%281295%29
6. ?Tagel-Din, H. and Meguro, K. (2002).?"AEM Used for Large Displacement Structure Analysis"?,?Journal of Natural Disaster Science, Japan, Vol.?24, No.1, pp. 25–34.
7. Tagel-Din, H. and Meguro, K. (2000b).?“Analysis of a Small Scale RC Building Subjected to Shaking Table Tests using Applied Element Method”, Proc. of the 12th World Conference on Earthquake Engineering, New Zealand, pp.?25–34.
8. Tagel-Din, H. and Meguro, K. (2004).?“Dynamic Modeling of Dip-Slip Faults for Studying Ground Surface Deformation Using Applied Element Method”, Proc. of the 13th World Conference on Earthquake Engineering, Vancouver, Canada.
9. Paola, M., and Meguro, K. (2003).?"Modeling Masonry Structures using the Applied Element Method",?Seisan Kenkyu, Japan: Institute of Industrial Science, The University of Tokyo.?55?(6): 123–126.?
10. ?Paola, M., and Meguro, K. (2005).?“Blast Testing and Research Bridge at the Tenza Viaduct. Japan”, University of Missouri-Rolla, Final Report of Task 1.
11. ?en.wikipedia.org/wiki/Applied_element_method
12. ?https://en.wikipedia.org/wiki/Discrete_element_method
13. https://www.appliedelementmethod.o