Continuum Mechanics and Thermodynamics

, Volume 30, Issue 2, pp 421–455 | Cite as

Continuum modeling of twinning, amorphization, and fracture: theory and numerical simulations

  • J. D. Clayton
  • J. Knap
Original Article


A continuum mechanical theory is used to model physical mechanisms of twinning, solid-solid phase transformations, and failure by cavitation and shear fracture. Such a sequence of mechanisms has been observed in atomic simulations and/or experiments on the ceramic boron carbide. In the present modeling approach, geometric quantities such as the metric tensor and connection coefficients can depend on one or more director vectors, also called internal state vectors. After development of the general nonlinear theory, a first problem class considers simple shear deformation of a single crystal of this material. For homogeneous fields or stress-free states, algebraic systems or ordinary differential equations are obtained that can be solved by numerical iteration. Results are in general agreement with atomic simulation, without introduction of fitted parameters. The second class of problems addresses the more complex mechanics of heterogeneous deformation and stress states involved in deformation and failure of polycrystals. Finite element calculations, in which individual grains in a three-dimensional polycrystal are fully resolved, invoke a partially linearized version of the theory. Results provide new insight into effects of crystal morphology, activity or inactivity of different inelasticity mechanisms, and imposed deformation histories on strength and failure of the aggregate under compression and shear. The importance of incorporation of inelastic shear deformation in realistic models of amorphization of boron carbide is noted, as is a greater reduction in overall strength of polycrystals containing one or a few dominant flaws rather than many diffusely distributed microcracks.


Continuum mechanics Geometry Phase field Fracture Twinning Phase transformation Finsler space 


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Authors and Affiliations

  1. 1.Impact PhysicsUS ARLAberdeenUSA
  2. 2.A. James Clark School of EngineeringUniversity of MarylandCollege ParkUSA
  3. 3.Computational and Engineering SciencesUS ARLAberdeenUSA

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