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Simulating explosions

Recently Henry talked about software that could be used to simulate explosions and introduced CartaBlanca. Luming asked whether anyone had used the software, how good it was, and whether one needed Java to implement models into CartaBlanca.

As far as I understand, CartaBlanca is the offshoot of Brian (Bucky) Kashiawa's CFDLib code and contains an implementation of Debra Sulsky's version of MPM. Our group had worked closely with Bucky in early stages of the development of the Uintah code at C-SAFE. Bucky's fluid-structure interaction ideas form the basis of our code though we have moved away from Sulsky's version of MPM.

I haven't used CartaBlanca and don't have a feel for how good it is. It is likely that a knowledge of Java is needed for further developing the code. However, anyone with some C++ (or even Python) experience will be able to pick up and start running with Java in a week. I don't think lack of Java skills will be a big barrier to adding models to CartaBlanca.



Yesterday, Guru brought my attention to a video from Seed Magazine in his blog post. That video contains visualizations of some of our simulations using Uintah. (Update: The narrator says that the exploding container ends in its "ultimate detonation". That is incorrect. The simulation is that of deflagration (steady burn) and never transitions to a detonation.)


The pool fire simulations were performed by Phil Smith and his group. The explosion simulations were performed by Jim Guilkey and Todd Harman. The solid mechanics involved in these simulations was my contribution. You can find some of the details of the fluid-structure interaction algorithm in our paper An Eulerian-Lagrangian approach for simulating explosions of energetic devices.

Which brings me to some interesting effects that I observed in my simulations a couple of years ago. When dealing with fracture of ductile materials in large simulations, people often use the concept of element death to remove failed elements. Removal of elements makes the mass, momentum, and energy balance in a simulation inaccurate. If the number of removed elements is large and the simulation is continued to long times, the results that one gets essentially cannot be trusted. The preferred method of simulating large fractures in such circumstances is not to allow failed elements to support any tension, although compressive stresses are allowed. In order, to keep the dissipation reasonable, the failed elements lose strength over a period of time determined from stress-strain curves.

The figures below show how different methods of simulating failure affect the results in our simulation. We are using the Material Point Method and instead of failed elements we have failed particles. A steel container is being blown apart by an explosive.


  • Remove failed particles: In this simulation, particles that have failed are removed from the simulation. Note how crisp the edges of the fragments are.
  • Set the stress in failed particles to zero: In this simulation, the deviatoric part of the Cauchy stress of particles that have failed is set to zero but the mass is not removed. The volumetric part of the stress is retained. This is equivalent to not allowing shear stresses.
  • Allow compressive stresses by no tensile stresses in failed particles: In this simulation, failed particles are no longer allowed to support any tensile stresses or shear stresses. However, purely compressive stresses are allowed.

Clearly, the choice of algorithm determines the shape and number of fragments. Note that the material undergoes significant plastic deformation and the usual cohesive zone approaches for brittle materials may not be applicable. If you were to do these simulations, what path would you take (keeping in mind the trade off between computational efficiency and accuracy)?

You can find a paper on the plasticity model that I used for the steel container in my paper The Mechanical Threshold Stress Model for various tempers of AISI 4340 steel, International Journal of Solids and Structures., vol 44, no. 3-4, pp. 834-859.

I'll talk a bit about the mechanical model of the explosive in a follow up post.

Plain text icon Steel4340AllData.zip_.txt2.71 MB


Henry Tan's picture

Dear Biswajit,

What is the future plan after the 10 years’ development (1998-2007) of explosion simulation at CSAFE?

We are transitioning to a range of other applications. Some examples are:

  • Modeling rocket stage separation.
  • Penetration and perforation of ceramic armor.
  • Designing better explosion resistant armor for Humvees and similar vehicles.
  • Multiscale modeling of bone and muscles.
  • Polymeric and metallic foam simulation for better characterization.
  • Flare simulation for gas well heads.

I notice that there appears to be little interest in such problems and other problems involving large deformations and large scale failure in this group. Also, I am yet to see any reports of significant progress in the problem of bridging of scales (both length and time). Is that lack of interest because these problems are difficult or is it because they are poorly funded at this point of time?

Interestingly, ten years after we started, we still cannot simulate the lighting of a candle, the formation of soot around a flame, and the extinction of a burning flame in a reasonable about of time! The reason is that many length and time scales (and several physical and chemical processes) are involved and we do not have good enough models that can bridge scales and still give reasonable macroscopic results.

Henry Tan's picture

Luming Shen's picture

Dear Biswajit and Henry,

Since both of you have been working in the simulation of explosion for a long time, can you please recommend any good texts on explosion science and engineering? Thanks.




I don't think there are any texts as such that cover the whole gamut of physical processes.

As far as explosives are concerned, I've found the proceedings of the detonation symposia useful. You can find the papers at the International Detonation Symposium webpage. The papers for the 2002 Det Symposium can be found here. For the 2006 symposium, the papers can be found here.

For general shock physics and other high rate physics issues, I use the proceedings of the APS Topical Group on Shock Compression of Condensed Matter. These proceedings are printed and published a couple of years after each conference and contain a wealth of material.

People usually recommend books on gas dynamics for a person starting out in shock physics. I've found the book Shock Waves And Explosions by Sachdev useful to get at the basic concepts. This book deals with exact solutions but no numerics. For the computational aspects that I'm interested in, the initial parts of Wilkins' book Computer Simulation of Dynamic Phenomena provide an excellent introduction. A book that contains a wealth of information on dynamic phenomena is Meyers' Dynamic Behavior of Materials.

We are one of the few groups who have attempted fully coupled simulations of explosion phenomena. The field could do with a textbook on explosion simulation science.


          Thanks for your helpful information.   I have not got the book "Shock Waves and Exploisions" yet.  So I don't know if there is some 3-Dimension  exact solutions or theory solutions of explosion problem in that book.  Could you introduce more book that have 3D exact solutions?  




The rule of thumb is that the blast wave becomes nearly planar and uniform at a short distance from the source.   Therefore, most analytical approaches assume that the problem is essentially one dimensional and involves uniaxial strain.  The resulting equation is usually nonlinear as it involves an exponential source term and exact solutions may not be easy to find.   For some examples of the equations involved (and probably even some exact solutions in 1-D) you can try the 1983 book by Milan Kubicek and Vladimir Hlavacek which has been republished by Dover in 2008.  The book is called "Numerical Solution of Nonlinear Boundary Value Problems with Applications ".

-- Biswajit 


       Thanks a lot.  


Dear Biswajit,

        I have a question about a parameter in JWL. 

The JWL equation as following

p=A(1-ω/(R1V))exp(-R1V)  +  B(1-ω/(R2V))exp(-R2V) + ωE/V

The pressure p is sensitive to the relative volume V in the positions near 1 or 2.  Could you tell me the approximate value of relative volume V for the TNT?    I can not find literature discuss about this value. It will be more helpful if you could give me some literature links. Thanks a lot!



If I recall correctly, V in your equation is either the specific volume (i.e., 1/density) or v/v_0 = rho_0/rho).  The units of R_1 and R_2 are determined accordingly.  The density of TNT at standard temperature and pressure is about 1600 kg/m^3.  The relative volume will decrease as the pressure increases with stiffer and stiffer responses at higher pressures.  That seems obvious - so I have probably not understood your question correctly.

The isentropic JWL EOS is  designed for the compression regime.  You have to be careful with any such model because the range of applicability is usually limited.  I believe that the model has been calibrated to approximately 1 GPa.

I don't have the values of the JWL parameters for any particular type of TNT but I'm sure that you can find that in the literature.

-- Biswajit 

I am sorry. You are right. I make a mistake in my question.  What I want know is the "the initial specific volume",   which is used in LS-DYNA.  It's the value of density of TNT devided by the density of product after detonation in some literatures.  It's hard to find this value in literatures.

Could you tell me what's "the compression regime" and which kind of EOS you used for product of TNT detonation.  Which software do you used for simulation of detonation and interaction with ambient air?  Is the initial specific volume is a essential parameter in such software?   I am a newbee of explosions simulation. Any suggestion and comments will be greatly appreciated.  Thanks a lot.




I haven't used LS-DYNA for any detonation calculations.  The only detontation calculations that I have performed have been using Uintah (for a copper clad rate stick calculation with ANFO).  Most of my work has been on deflagration type problems which do not involve very strong shocks.

In our ANFO calculations we have used a Murnaghan EOS for the reactant and a JWL++ EOS for the product and treated both as fluids.   The STP density of the product gases was assumed to be 1160 kg/m^3 (which was the same as that of the reactant.  In your case you will have to assume rho_0 =~ 1600 kg/m^3.

If your numerical method is velocity driven then the current density is chosen by you (based on the amount of deformation) and the ratio of the initial to the current density gives you the V that you need.  On the other hand, if the numerical method is pressure driven then you have to do a Newton solve to get the current density (and hence the current V).  That is the reason that you won't find a value for V is the literature - it is either a primary variable or a secondary one and not a parameter.

The initial specific volume is 1/(rho_0).  You have to estimate the value of rho_0 based on the temperature and pressure.  Hope that helps.

-- Biswajit 

DR. Biswajit,

    Thanks a lot. Your reply is helpful.  Could you introduce some book or literature about numerical implement of Murnaghan EOS JWL, and  JWL++?  Thanks.




I think the first step is to understand the basics shock wave theory, i.e., the meanings of isentropic compression, the Hugoniot, the Rayleigh line, etc - in particular, what assumptions are made when we talk about those things.   I would suggest a book on gas dynamics such as "Gas Dynamics" by James E. John for the basis ideas followed by "Detonation: Theory and Experiment" by Wildon Fickett and William C. Davis.

Once you understand the basic theory well (and it takes a bit of time to understand the current dogma), you have to decide whether you want to use a Eulerian hydrocode (i.e., compressible CFD code) to solve your problem or a Lagrangian code (e.g. finite elements).  If you use a CFD code you will start of with a ceratin pressure, use a Newton-Raphson method to find the  corresponding volume (i.e., density, keeping the mass fixed), and iterate until you reach some sort of equilibriation condition.  On the other hand, if you use lagrangian finite elements, you will be able to compute the volume change directly.  Therefore, you can just take that value, plug it into the EOS and get the pressure.

The literature on these EOSs is diffuse and often classified. You will find some references in

-- Biswajit 


Luming Shen's picture


Thanks for your quick response. These information is very helpful. Hope to see a textbook on simulation of explosion from your group in the near future.




You can some more information in Numerical modeling of Explosives and Propellants by Charles Mader. The book deals primarily with Eulerian simulations. There is a lot of information and examples of verification problems that are useful. However, the numerics are not discussed in any great detail (as in convergence issues and such). The book deals primarily with detonation while I was more interested in deflagration related issues. Also, modern plasticity models, burn models, and even detonation/EOS models such as JWL++ are not discussed in any detail. The appendices in the book are quite useful because they summize the models and lay out differencing schemes used that can be used in Eulerian simulations.

Henry Tan's picture

As pointed out by Biswajit that explosion is a multiscale phenomenon involving multiscales in both time and space, and multiphysics including solid deformation, fluid dynamics, combustion, and much more.

There exist two approaches in modeling explosions. One is through multiscale complicated simulation; the other is through simplified theoretical analysis.

Concerning the theory of the detonation, I would recommend the book Introduction to Detonation Theory by Wildon Fickett. Unfortunately, this book is currently unavailable in The book is a systematic study of a simple mathematical analog of the equations of motion for compressible flow with chemical reaction, with emphasis on detonation. The use of analog as a vehicle for the presentation allows considerable simplification, and gives better exposure to the main ideas. The newcomer to detonation theory will find this book a simpler introduction.

Luming Shen's picture



Thanks for the information. Unfortunately, our library doesn't have this book "Introduction to Detonation Theory". Anyway, I will manage to get a copy of that.



Henry Tan's picture

The author, Wildon Fickett, had another book, Detonation: Theory and Experiment.

HELLO I am the first knowledge of LS-DYNA and I wanted to ask if anyone knows how fuzion and its various applications in simulation of an explosion of a mine of keyword * load_blast ls-dyna?



A part of my project along with underwater explosion simulation software is Abaqus. I seriously need a video file that performing this simulation explain.

Please help in this regard.

Thank you

Several people have asked me about the raw data for various tempers of 4340 steel.  I've attached a file containing some of the processed data that I used for my paper on 4340 steel.  I think the raw data are also around somewhere and I'll add those data when I locate them.


-- Biswajit

I've dug up some more stress-strain data for 4340 steel and attached them to this post.  Don't get confused by the .txt extension.  The files are in zip format and you may have to rename them before unzipping.

-- Biswajit 

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