Continuum Mechanics and Thermodynamics

, Volume 30, Issue 4, pp 825–860 | Cite as

An anisotropic elastoplastic constitutive formulation generalised for orthotropic materials

  • M. K. Mohd Nor
  • N. Ma’at
  • C. S. Ho
Original Article


This paper presents a finite strain constitutive model to predict a complex elastoplastic deformation behaviour that involves very high pressures and shockwaves in orthotropic materials using an anisotropic Hill’s yield criterion by means of the evolving structural tensors. The yield surface of this hyperelastic–plastic constitutive model is aligned uniquely within the principal stress space due to the combination of Mandel stress tensor and a new generalised orthotropic pressure. The formulation is developed in the isoclinic configuration and allows for a unique treatment for elastic and plastic orthotropy. An isotropic hardening is adopted to define the evolution of plastic orthotropy. The important feature of the proposed hyperelastic–plastic constitutive model is the introduction of anisotropic effect in the Mie–Gruneisen equation of state (EOS). The formulation is further combined with Grady spall failure model to predict spall failure in the materials. The proposed constitutive model is implemented as a new material model in the Lawrence Livermore National Laboratory (LLNL)-DYNA3D code of UTHM’s version, named Material Type 92 (Mat92). The combination of the proposed stress tensor decomposition and the Mie–Gruneisen EOS requires some modifications in the code to reflect the formulation of the generalised orthotropic pressure. The validation approach is also presented in this paper for guidance purpose. The \({\varvec{\psi }}\) tensor used to define the alignment of the adopted yield surface is first validated. This is continued with an internal validation related to elastic isotropic, elastic orthotropic and elastic–plastic orthotropic of the proposed formulation before a comparison against range of plate impact test data at 234, 450 and \({\mathrm {895\,ms}}^{\mathrm {-1}}\) impact velocities is performed. A good agreement is obtained in each test.


Elastoplastic deformation Shockwave propagation Spall failure Orthotropic materials 


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Crashworthiness and Collisions Research Group, Mechanical Failure Prevention and Reliability Research Center, Faculty of Mechanical and Manufacturing EngineeringUniversiti Tun Hussein Onn MalaysiaParit RajaMalaysia

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