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Wave Propagation Prediction in Homogeneous Materials Using Hybrid

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Wave Propagation Prediction in Homogeneous Materials Using Hybrid Powered By Docstoc
					      Wave Propagation Prediction in
       Homogeneous Materials Using
      Hybrid Lattice Particle Modeling
            Investigators: Ge Wang, Ahmed. Al-Ostaz,
        Alexander H.-D. Cheng and P. Raju Mantena
                     Civil Engineering Department
                       University of Mississippi

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                  Research Background
      Dynamic deformation often
       involves wave propagation,
       i.e., stress has to travel                                                       Hopkinson Bar Test
                                                                                        (by M.A. Kaiser, 1998)
       through the material body.



      Dynamic        fracture     and
       fragmentation under high
       strain rate loads (impact,
       blasting, crush, collapse, high
       speed puncture/penetration,
       comminution, .etc.) has broad     Spallation as a result of impact without   Shock on a sharp-nosed
       civilian/military applications.     penetration of the impacting object         supersonic body

                                                    (http://en.wikipedia.org/wiki)
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                        Outline

           Brief review of major macroscopic
            dynamic fracture approaches
           Hybrid lattice particle modeling (HLPM)
           HLPM of wave propagation and
            applications
           Conclusions

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                        Outline

           Brief review of major dynamic fracture
            approaches
           Hybrid lattice particle modeling (HLPM)
           HLPM of wave propagation and
            applications
           Conclusions

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       1. Brief review of major dynamic
               fracture approaches
      Continuum Mechanics Based Approaches
       (CMBA):
           FEM
      Discrete Element Based Approaches (DEBA):
           PFC, SPH, PM, etc.
      Combinations of CMBA-DEBA:
           PFEM, MPM (material point method), etc.


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Simulations with meshing techniques




            Lagrange           Euler              ALE                  Meshless (SPH)
                                          (Arbitrary Lagrange Euler)




                               FEM

                       (AUTODYN course materials)
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                        Outline

           Brief review of major dynamic fracture
            approaches
           Hybrid      lattice particle modeling
            (HLPM)
           HLPM of wave propagation and
            applications
           Conclusions
3/25/2011                                        7
              Hybrid Lattice Particle Modeling (HLPM) of Dynamic Fragmentation of Solids
                            Ge Wang, Ahmed Al-Ostaz, Alexander H.-D. Cheng and P. Raju Mantena
               Department of Civil Engineering, the University of Mississippi, MS 38655, http://www.olemiss.edu/~gewang


             Motivations                              Interactions of HLPM                                       Thermally induced fracture:
                                                                                                                    Mixture of calcite and pyrite subject to a microwave
Mechanical behavior of a solid material is
controlled by its microstructure. Complex      Linear:
macroscopic behaviors, such as fracture
and failure, arise from microstructure                                          
                                               Non-linear:                            Meshing structures
interactions. Thus, if the microstructure                                                                           (a) Temperature                   (b) Fracture
and the microstructural interactions within                                                                           Blasting:
a numerical model could be correctly and
accurately replicated, then that model
should      precisely    reproduce      the           (a) Polynomial                (b) Lennard–Jones
macroscopic behaviors. However, current
computing power limits the size of the                 Validations of HLPM
atomic ensemble to numbers of atoms that                                                                              Crack propagation:
are too small to be useful for most
engineering-scale systems. Hybrid Lattice
Particle Modeling (HLPM) is developed to
directly mimic microstructural features and                                                                      Spallation of plate impact:
can be executed in reasonable times on
standard computers.

       Model Introduction                         (a) Epoxy in tension (b) Indentation of polymeric materials


HLPM is a dynamic simulation that uses                                                                                Wave propagation:
                                                      Applications of HLPM
small discrete solid physical particle (or
quasi-molecular     particles)    as     a        High strain rate loading:
representation of a given fluid or solid.
Different particle interaction schemes                                                                                3-D puncture/penetration:
and mesh structures can be adopted. It
combines the knowledge of both lattice
     3/25/2011                                                                                                                                                             8
modeling and particle modeling.
        Numerical discretization scheme in PFC (particle
       flow code), PFEM (particle finite element method)
                          and HLPM
          PFC                        PFEM                                 HLPM
                                                                             Fi , k
                                                                   , k 
                                                                   ri
                                                                             mi
                                                                                        (t )
                                                                   ri ,1/ 2  ri ,0 
                                                                                            ,0
                                                                                              ri
                                                                                         2
                                                                   ri ,k 1/ 2  ri ,k 1/ 2  ( t ),k
                                                                                                   ri

                                                                   ri , k 1  ri , k  ( t ) ri , k 1/ 2
                                                                                               

    critical time increment:      critical time increment:         critical time increment:



          k : the stiffness           k : the stiffness                  k : the stiffness
          m: a point mass             m: a point mass                    m: a point mass
          x: displacement             u: displacement                    r: displacement

    3/25/2011                                                                                                 9
                        Outline

           Brief review of major dynamic fracture
            approaches
           Hybrid lattice particle modeling (HLPM)
           HLPM of wave propagation and
            applications
           Conclusions

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       HLPM simulations of Wave Propagation
        Prediction in Homogeneous Materials
      Problem descriptions:
           Material properties:   1140 kg / m3 , E  3GPa ,   0.33 .
           Theoretical wave propagation speeds:
                1-D:   C p  E /   1622 m / s

                2-D:   C p  ( K  4G / 3) /   1986 m / s




                                                                             2
                1-D: L=12.7 cm                           2-D: A=12.7x1.21 cm
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(cont.) Using dynamic BC
      Dynamics BC: P  CV  6.78 MPa . Duration= 1. 107 s




                                    Horizontal amplitude

            Wave propagation speed: (i) 1D: 2000.0 m/s; (ii) 2D: 2133.0 m/s
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(cont.) Using dynamic BC




             Vertical amplitude
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(cont.) Using Kinematic BC
      Kinematic BC:      constantly P  CV  10.0 MPa




                           Horizontal amplitude

                  Wave propagation speed: 2133.0 m/s
3/25/2011                                                 14
(cont.) Using Kinematic BC




              Vertical amplitude
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                        Applications
                      Spall Crack Formation




            (a) HLPM simulations       (b) MD simulations
                                         (A. M. Krivtsov, 2004)
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(cont.)




            (a) weak interface interaction   (b) strong interface interaction


                                   HLPM simulations
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(cont.)
            Cavity Blasting




               HLPM simulations
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                        Outline

           Brief review of major dynamic fracture
            approaches
           Hybrid lattice particle modeling (HLPM)
           HLPM of wave propagation and
            applications
           Conclusions

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                      Conclusions
      Hybrid lattice particle modeling (HLPM) can be an
       alternative tool to explore wave propagation in
       materials.

      HLPM is being developed ultimately              for
       investigating shock wave related problems.


      Validations are required in the coming stage.

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                 Grant Acknowledgement
       Department of Homeland Security-through Southeast Region Research
       Initiative (SERRI), USA.
       ONR, Office of Naval Research, Solid Mechanics Program, USA.




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