Non-physical finite element method: Multiple material discontinuities

•A novel finite element method for the modelling multiple shocks.•The establishment of non-physical duplicate fields to mirror physical counter parts.•The establishment of transport equations for non-physical fields.•The exact representation of multiple shocks within a classical finite element frame...

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Bibliographic Details
Published in:Computers & structures 2016-02, Vol.164, p.145-160
Main Authors: Darvizeh, R., Davey, K.
Format: Article
Language:English
Subjects:
Approximation
Computer simulation
Conservation laws
Discontinuity
Finite element
Finite element method
Impact engineering
Mathematical analysis
Mathematical models
Multiple material discontinuities
Transport
Transport equations
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Summary:•A novel finite element method for the modelling multiple shocks.•The establishment of non-physical duplicate fields to mirror physical counter parts.•The establishment of transport equations for non-physical fields.•The exact representation of multiple shocks within a classical finite element framework.•The testing and application of the non-physical approach to impact physics. The theory proposed in the paper provides a new approach for the modelling of multiple material discontinuities. The scope of this work is restricted to numerical methods and in particular an approach that utilises the benefits of traditional continuous finite element approximations but enhanced with an increased capacity for handling material discontinuities. The approach is founded on transport forms of the governing conservation laws describing discontinuous physics by means of bespoke moving control volumes and the non-physical field concept. The theory is demonstrated through its application to steady-state and transient flyer impact-plate problems for which analytical results are available.
ISSN:0045-7949
1879-2243
DOI:10.1016/j.compstruc.2015.11.010