Wave propagation in laminates using the nonhomogenized dynamic method of cells: An alternative to standard finite-difference hydrodynamic approaches

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The nonhomogenized dynamic method of cells (NHDMOC) uses a truncated expansion for the particle displacement field; the expansion parameter is the local cell position vector. In the NHDMOC, specifying the cell structure is similar to specifying the spatial grid used in a finite-difference hydrodynamic calculation. The expansion coefficients for the particle displacement field are determined by the equation of motion, any relevant constitutive relations, plus continuity of traction and displacement at all cell boundaries. The authors derive and numerically solve the NHDMOC equations for the first, second, and third-order expansions, appropriate for modeling a plate-impact experiment. The performance of the ... continued below

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42 p.

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Clements, B.E. & Johnson, J.N. September 1, 1997.

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The nonhomogenized dynamic method of cells (NHDMOC) uses a truncated expansion for the particle displacement field; the expansion parameter is the local cell position vector. In the NHDMOC, specifying the cell structure is similar to specifying the spatial grid used in a finite-difference hydrodynamic calculation. The expansion coefficients for the particle displacement field are determined by the equation of motion, any relevant constitutive relations, plus continuity of traction and displacement at all cell boundaries. The authors derive and numerically solve the NHDMOC equations for the first, second, and third-order expansions, appropriate for modeling a plate-impact experiment. The performance of the NHDMOC is tested, at each order, for its ability to resolve a shock-wave front as it propagates through homogeneous and laminated targets. They find for both cases that the displacement field expansion converges rapidly: given the same cell widths, the first-order theory gives only a qualitative description of the propagating stress wave; the second-order theory performs much better; and the third-order theory gives small refinements over the second-order theory. The performance of the third-order NHDMOC is then compared to that of a standard finite-difference hydrodynamic calculation. The two methods differ in that the former uses a finite-difference solution to update the time dependence of the equations, whereas the hydrodynamic calculation uses finite-difference solutions for both the temporal and spatial variables. Both theories are used to model shock-wave propagation in stainless steel arising from high-velocity planar impact. To achieve the same high-quality resolution of the stress and particle velocity profiles, the NHDMOC consistently requires less fine spatial and temporal grids, and substantially less artificial viscosity to control unphysical high-frequency oscillations in the numerical solutions. Finally, the third-order NHDMOC theory is used to calculate the particle velocity for a shock-wave experiment involving an epoxy-graphite laminate. Constitutive relations suitable for the various materials are used. This includes linear and nonlinear elasticity, and when appropriate, viscoelasticity. The results agree well with the corresponding plate-impact experiment, and are compared to the second-order theory of Clements, Johnson, and Hixson.

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42 p.

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OSTI as DE98001529

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  • International workshop on new models and numerical codes for shock wave processes in condensed media, Oxford (United Kingdom), 15-19 Sep 1997

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  • Other: DE98001529
  • Report No.: LA-UR--97-3735
  • Report No.: CONF-9709108--
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 658322
  • Archival Resource Key: ark:/67531/metadc703441

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  • September 1, 1997

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  • Sept. 12, 2015, 6:31 a.m.

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  • April 21, 2016, 10:11 p.m.

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Clements, B.E. & Johnson, J.N. Wave propagation in laminates using the nonhomogenized dynamic method of cells: An alternative to standard finite-difference hydrodynamic approaches, article, September 1, 1997; New Mexico. (digital.library.unt.edu/ark:/67531/metadc703441/: accessed December 10, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.