Lagrangian Formulation

  • John D. Clayton
Part of the Shock Wave and High Pressure Phenomena book series (SHOCKWAVE)


The standard nonlinear thermoelastic model most often used for modeling wave mechanics in single crystals and polycrystals, either anisotropic or isotropic, is described. The theoretical formulation is based on a Lagrangian finite strain tensor. General kinematics and thermodynamics are developed, followed by application to planar shock loading along a pure mode direction. An explicit analytical solution is reported for planar shock compression of a solid characterized by an internal energy potential of order four in strain but truncated at first order in entropy. Particular forms of material coefficients are presented for cubic crystals and isotropic materials.


Shock compression Nonlinear elasticity Lagrangian elasticity Crystal Anisotropy 


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Copyright information

© This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2019

Authors and Affiliations

  • John D. Clayton
    • 1
    • 2
  1. 1.Impact Physics CCRL-WMP-CUnited States Army Research LaboratoryAberdeenUSA
  2. 2.University of MarylandCollege ParkUSA

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