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modern explosion science and engineering

Henry Tan's picture


Henry Tan's picture

An important fundamental problem is the study of detonation phenomena in solid explosives.

Experimental studies of chemical reactions and the structure of detonation and shock waves (including that at the micro- and mesoscale) face significant difficulties:

1) high intensity of detonation waves
2) the scales of detonation in time (nanoseconds) and space (from 10 to 100 angstrom).

Molecular-dynamics is an adequate research tool that allows one to resolve the fine spatial structure of wave phenomena in such systems and provides the most exhaustive information about them.

These data, if adequately averaged over mesoscale volumes in which local thermodynamic equilibrium is assumed, should yield continuum-approach parameters.

Henry Tan's picture

Carbon nanotubes (CNTs) have great potential applications in making ballistic-resistance materials.

The remarkable properties of CNTs makes them an ideal candidate for reinforcing polymers and other materials, and could lead to applications such as bullet-proof vests as light as a T-shirt, shields, and explosion-proof blankets.

For these applications, thinner, lighter, and flexible materials with superior dynamic mechanical properties are required.

Henry Tan's picture

Carbon nanotubes (CNT) display superior mechanical properties, and are an excellent candidate of reinforcements for nanocomposites. The CNT-reinforced composites, however, never reach their expected mechanical properties. This has triggered significant research efforts to understand this shortfall and to improve the mechanical properties of CNT-reinforced

Nanocomposites possess a large amount of interfaces due to the small (nanometer) size of reinforcements. The interface behavior can significantly affect the mechanical properties of nanocomposites. For example, carbon nanotubes in general do not bond well to polymers, and their interactions result mainly from the weak van der Waals forces. Consequently CNTs may slide inside the matrix and may not provide much reinforcing effect. It is, however, important to assess whether the poor interface behavior is indeed responsible for the short fall of CNT-reinforced composites in order to reach their expected properties.

The effect of van der Waals-based interface cohesive law on carbon
nanotube-reinforced composite materials

H. Tan, L. Y. Jiang, Y. Huang, B. Liu, and K. C. Hwang
Composite Science and Technology, 2007, accepted.

Henry Tan's picture

Review Article, 2007, NANO, accepted.

 Since the discovery of carbon nanotubes (CNTs) and the establishment of new effective methods to produce them, the properties of these novel materials and their potential technological applications have stimulated considerable interests in the research and engineering communities. Due to their perfect molecular structure, CNTs are found to possess superior mechanical properties, such as high elastic modulus (on the order of 1TPa), high tensile strength (~200 GPa) and high fracture strain (10-30%), and are therefore an ideal candidate for reinforcements in composite materials. One challenge in CNT-reinforced composites is the uniform dispersion and orientation alignment of CNTs in a matrix to avoid the agglomeration of CNTs into bundles. Significant efforts have been made to uniformly disperse and align CNTs in the matrix. For well-dispersed and aligned CNTs that are perfectly bonded to the matrix, the theoretical and computational models predict superior properties of CNT-reinforced composites. However, extensive experiments on CNT-reinforced composites show some improved properties, but many fall short to reach the theoretical predictions. The discrepancy between the theoretical models and experiments requires further investigations in order to fulfill the full potential of CNTs as reinforcement in composites.

Another challenge in CNT-reinforced composites is the load transfer efficiency across the CNT/matrix interface. Similar to the conventional fiber-reinforced composites, the interfacial load transfer between the CNTs and matrix is governed by three mechanisms.

(i) covalent bonding.
The covalent bonding between atoms from the CNT and matrix results from chemical reactions at the interface. The covalent bonding is strong. For example, Frankland et al. predicted that CNT/matrix shear strength can be enhanced by more than an order of magnitude with the formation of cross-links involving less than 1% of the carbon atoms on the CNT. The covalent bonding, however, requires the functionalization of CNT/matrix interfaces. This may increase the difficulty in processing, and also introduce defects to the CNT, which compromises the performance of composites. For example, the maximum compressive (buckling) force for ethyne functionalized nanotubes is reduced by 15% due to the functionalization.

(ii) mechanical interlocking.
The mechanical interlocking usually results from defects around the interfaces in conventional composites. But this mechanism hardly occurs in CNTs because their (nearly) defect-free atomic structure.

(iii) van der Waals force.
The van der Waals (vdW) force between CNTs and matrix is the most common mechanism for interfacial load transfer efficiency since it always exists and does not require any functionalization. The vdW force, however, is weak such that the CNTs do not bond well to the polymer matrix, which gives relatively low load transfer efficiency.

There are extensive experimental and atomistic studies on the vdW force at the CNT/matrix interfaces.29-31,45-48 These studies provide insights into the fundamental understanding of CNT-matrix interactions, but not the direct relation between the vdW force and the macroscopic properties and behavior of CNT-reinforced composites. Furthermore, the atomistic studies widely used in studying the individual CNTs have limitations on both length scale (10-9-10-6 m) and time scale (10-12-10-9 s), and are not suitable to study macroscopic properties and behavior of CNT-reinforced composites, which involve large numbers of CNTs in the matrix.

Continuum models have been developed to study the mechanical properties of individual CNTs and also the CNT-reinforced composites. As compared to atomistic simulations such as molecular dynamics, the above continuum models for CNT reinforced composites are not constrained on the length and time scales, but they have not accounted for the important vdW force at the CNT/matrix interfaces. Since nanocomposites in general have high specific
surface aspect ratio (i.e., high interface area per unit volume of the composite), the behavior of the CNT/matrix interfaces may significantly influence the macroscopic behavior of composites. The interface debonding and sliding in conventional composites has been studied via cohesive zone models in the continuum analysis. A cohesive zone model assumes a relation between the normal (and shear) traction(s) and the opening (and sliding)
displacement(s). When implemented in the finite element method, the cohesive zone model is capable of simulating interface debonding and sliding. The existing cohesive models, however, are all phenomenological because it is difficult to measure directly the cohesive laws for interfaces in experiments. There are some recent experimental studies of microscale cohesive laws, but none on nanoscale cohesive laws such as for the CNT/polymer interfaces. Recently, Jiang et al. developed a cohesive law for CNT/polymer interfaces based on the vdW force. Such an approach avoids any assumed phenomenological cohesive laws, and accurately accounts for the vdW foces in the continuum model. Lu et al. extended such an approach to the cohesive law for multi-wall CNTs, and Tan et al. used this vdW-based cohesive law to study the effect of interface debonding on the macroscopic behavior of CNT-reinforced composites.

Bin Liu's picture

We have studied the following woven nano-structure of carbon nanotubes as one of potential designs for ballistic-resistance materials via the atomic-scale finite element method (AFEM). Our study shows that this structure is insensitive to structure defects. More details can be found in our paper.Liu B, Jiang H, Huang Y, Qu S, Yu M-F, and Hwang KC, (2005), Atomic-scale finite element method in multiscale computation with applications to carbon nanotubes. PHYSICAL REVIEW B 72(3): Art. No. 035435.

Henry Tan's picture

How about embedding the woven nanotubes into a matrix material?

Babichev's picture

Dear Bin Liu, your paper is a very interesting to me! I am engaged in buckling of nanotubes and we have the FE code for the solution of such problems. It would be very interesting to simulate your model (woven nanotubes) on our software. Whether you can send me model? Many thanks


Bin Liu's picture

Hi, Babichev,


Thanks for your interest. Please give me your email address, and I will send it to you. My email address is

Henry Tan's picture


Nice work and great point! I believe that this woven nanostructure can be developed into energy-absorbing material systems that will protect the future soldiers against ballistic impact and blast waves.

The effort may begin at the molecular level that provide the mechanical resistance to withstand blast waves and ballistic fragments and yet are still lightweight and flexible enough to maintain soldier mobility.

Henry Tan's picture

Henry Tan's picture

The Physics of Bubbles and Antibubbles
Bubbles are a familiar phenomenon so common in our everyday lives that hardly ever do we stop to consider physical properties of these strange objects. From the quantum foam of the microcosm or the tingle in our mouths with the ingestion of a carbonated beverage, to perhaps even the large scale structure of space-time itself, bubbles play important roles in everyday phenomena.


Laplace's Law for bubbles
Pressure is transmitted undiminished in an enclosed static fluid.

Continuous Chain of bubbles in concentrated Polymeric solutions
Physics of Fluids, Vol 14, number 10; October 2002
In concentrated polymer solutions bubbles may form a very stable, continuous, slowly rising, connected long chain similar to beads, or bubble “sausage”.

Path and Wake of a Rising bubble
The dynamics of a single rising bubble in pure quiescent water. The main problems involved are the bubble production and release, the shape of the bubble, the path instability, the wake configuration and dynamics, the purity of the water and the interactions with boundaries.

Bubble Puzzles
Bubbles are familiar from daily life and occupy an important role in physics, chemistry, medicine, and technology. Nevertheless, their behavior is often surprising and unexpected--and, in many cases, still not understood

The Air Film of an Antibubble
A regular bubble is a pocket of air or gas within a film or layer of liquid, the whole thing surrounded by gas. An antibubble is a pocket of liquid enclosed within a layer of gas, the whole thing surrounded by liquid.

The life and death of antibubbles
Using a high-speed video camera, physicists in Belgium have watched “antibubbles” form, move and then burst in a liquid for the first time.

Henry Tan's picture

CartaBlanca (
), developed by the Los Alamos National Laboratory, is a Java-based simulation software package, can be used to simulate explosions. CartaBlanca aims to simplify modeling and visualizing complex physics, materials science, and computational fluid dynamics equations and experiments.

Luming Shen's picture


Have you ever used this software? How good is it? If I am going to implement new constitutive models into CartaBlanca, do I need to know Java?



Henry Tan's picture


Simulating explosion is not an easy job. I used some software packages developed for these purposes. But seems none of them are mature enough, either in simulation methods, or in software design.

Regarding your question, actually I never programmed with Java, although I spent a lot of time on C++.

Henry Tan's picture

We develop a method to determine the cohesive law for interfaces between energetic crystals and the polymeric binder in the high explosive PBX 9501. This method has fundamental importance in understanding and designing plastic bonded explosives.

  • We use the digital image correlation technique to obtain the stress and displacement around a macroscopic crack tip in the modified compact tension experiment of PBX 9501.
  • We use the extended Mori–Tanaka method (which accounts for the effect of interface debonding) and the equivalence of cohesive energy on the macroscale and microscale to link the macroscale compact tension experiment to the microscale cohesive law for particle/matrix interfaces.

Such an approach enables us to quantitatively determine key parameters in the microscale cohesive law, namely the linear modulus, cohesive strength, and softening modulus of particle/matrix interfaces in the high explosive PBX 9501.

Title: The cohesive law for the particle/matrix interfaces in high explosives
Author(s): Tan H, Liu C, Huang Y, Geubelle PH

Henry Tan's picture

Energetic materials, such as solid propellants and plastic bonded explosives, can be considered as composite materials with energetic particles embedded in polymeric binder matrix.

These energetic materials display strong particle size effects. For example, large particles debond earlier than small ones in high explosives. A mix of large and small particles gives much higher explosiveness than small particles only, at a fixed volume fraction of energetic particles.

Title: Effect of nonlinear interface debonding on the constitutive model of composite materials
Author(s): Tan H, Huang Y, Liu C, Geubelle PH

Henry Tan's picture

Dewetting of energetic crystals from the polymeric binder can significantly affect the macroscopic behavior of solid propellants and high explosives.

Large particles in PBX 9501 may lead to catastrophic debonding (i.e., sudden debonding even under static load) that may trigger the reaction or detonation of high explosives.

Hotspot may form from the localized sudden interface debonding, thus trigger detonation of high explosives under low-level loading.

Title: The Mori-Tanaka method for composite materials with nonlinear interface debonding
Author(s): Tan H, Huang Y, Liu C, Geubelle PH
Source: INTERNATIONAL JOURNAL OF PLASTICITY 21 (10): 1890-1918 2005

Henry Tan's picture

Debonding of energetic crystals (e.g. HMX) from the polymeric binder can significantly affect the macroscopic behavior of the energetic composite.

We have used a nonlinear cohesive law for particle/matrix interfaces to study interface debonding and its effect on particulate composite materials subject to uniaxial tension.

The solution shows that, at a fixed particle volume fraction, small particles lead to hardening behavior of the composite while large particles yield softening behavior.

Interface debonding of large particles is unstable since the interface opening (and sliding) displacement(s) may have a sudden jump as the applied strain increases, which is called the catastrophic debonding.

A simple estimate is given for the critical particle radius that separates the hardening and softening behavior of the composite.

Title: The uniaxial tension of particulate composite materials with nonlinear interface debonding
Author(s): Tan H, Huang Y, Liu C, Ravichandran G, Inglis HM, Geubelle PH

Henry Tan's picture

The effect of damage due to particle debonding on the constitutive response of highly filled composites is investigated using two multiscale homogenization schemes:

one based on a closed-form micromechanics solution,

and the other on the finite element implementation of the mathematical theory of homogenization.

Title: Cohesive modeling of dewetting in particulate composites: micromechanics vs. multiscale finite element analysis
Author(s): Inglis HM, Geubelle PH, Matous K, Tan H, Huang Y
Source: MECHANICS OF MATERIALS 39 (6): 580-595 JUN 2007

Henry Tan's picture

We developed a micromechanics model to study the effect of nonlinear interface debonding on the constitutive behavior of composite materials.

While implementing this micromechanics model into a large simulation code on solid rockets, we are challenged by problems such as tension/shear coupling and the nonuniform distribution of displacement jump at the particle/matrix interfaces. We therefore propose an energy approach to solve these problems.

An Energy Approach to a Micromechanics Model Accounting for Nonlinear Interface Debonding

H. Tan, Y. Huang, and P. Geubelle
University of Illinois at Urbana-Champaign, Urbana, IL

C. Liu, Los Alamos National Laboratory, Los Alamos, NM

M. Breitenfeld, University of Illinois at Urbana - Champaign, Urbana, IL

Henry Tan's picture

High-Speed Combustion in Gaseous and Condensed-Phase Energetic Materials

D. Scott Stewart
University of Illinois-Urbana Champaign

Ashwani K. Kapila
Rensselaer Polytechnic Institute

High-speed combustion of gaseous reactants displays a variety of phenomena, including flame acceleration, deflagration-to-detonation transition (DDT), detonation instability, and quenching. The equations of reactive gasdynamics provide a reasonable model for a study of these phenomena. The state of affairs is far from satisfactory for condensed-phase explosives, however. The range of observed behavior is substantially broader for this class of materials, especially when these are in a granular or porous form. Deflagrations can travel at elevated speeds, the materials are more sensitive to applied stimuli, and there is an increased propensity for DDT. The mechanical response of the material is richer, and it couples strongly with the confinement, the chemistry, and the energetics to determine the course of combustion.

The recognition that porosity may appear unintentionally (through degradation over time or through accidental damage), and lead to unexpected behavior, has lent some urgency to the need for improved quantitative understanding of the manner in which energetic materials combust. Considerations of safety demand, in particular, the capacity to identify the mechanical or thermal loadings that will, or will not, lead to a detonation.

When a detonation IS the desired goal, there is the need to determine, precisely and economically, the locus of the detonation front, especially as it negotiates corners and obstacles, or propagates through ducts of varying cross section.  

IMA Tutorial: High-Speed Combustion

Henry Tan's picture

A guide to detonation stability

Mark Short
University of Illinois

Henry Tan's picture

Elements of detonation theory (high-speed combustion)

A. Kapila
Rensselaer Polytechnic Institute

Henry Tan's picture

Vilem Petr
Research Assistant Professor of Mining Engineering Department
Colorado School of Mines

Handbook for explosives engineering students 
Explosive Engineering
Rock Fragmentation 

Henry Tan's picture

I am thinking about writing a research proposal: applying nanotechnology to explosion mitigation and protection. One focus is on developing advanced energy-absorbing materials using nanotechnology, the other is on the sensitivity and safety of energetic materials.
I am grateful for your comments.

Hi Mr. Tan.


I 've tried to read  your Lecture notes in Physics of Explosion, but i can't access: the links don't work.




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