Wave propagation in laminates: A study of the nonhomogenized dynamic method of cells

• Published in: Wave motion Vol. 27; no. 3; pp. 193 - 209
• Main Authors: Clements, B.E., Johnson, J.N., Addessio, F.L.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.04.1998
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/S0165-2125(97)00051-6

The nonhomogenized dynamic method of cells (NHDMOC) method uses a truncated expansion for the particle displacement field; the expansion parameter is the local cell position vector. We derive and numerically solve the NHDMOC equations for the first-, second-, and third-order expansions, appropriate for modeling a plate-impact experiment. All materials are linear elastic. The performance of the NHDMOC is tested at each order for its ability to resolve the shock wave front as it propagates through a homogeneous target. The same performance is again tested for a shock propagating through a bilaminate target. We 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. In the third-order theory the stress is nearly always continuous across material boundaries, whereas in first-order, one commonly encounters substantial stress discontinuities. The first-order theory requires a considerable finer computational grid to achieve the same satisfactory representation of the wave profile as the third-order theory. Thus very little computational time is saved by using it. The numerical (unphysical) oscillations inherent in these calculations are largely reduced in the third-order theory, again indicating the rapid convergence of the displacement series.