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Generalized Continua and Phase-Field Models: Application to Crystal Plasticity

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Mesoscale Models

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 587))

Abstract

Three continuum field theories are presented that account for the size-dependent behaviour of materials. The micromorphic medium is endowed with microdeformation degrees of freedom that describe the rotation and distortion of a triad of microstructural directions, like crystallographic lattice directions. It is a very general framework that can be specialized to strain gradient plasticity theory dedicated to the modelling of plastic events in metals and alloys. Both frameworks are developed here in the special case of crystal plasticity as a complete example of transition from micro-physical phenomena to continuum macro-modelling. Finally the phase field method is introduced in this landscape as a continuum modelling approach to the motion of phase boundaries and interfaces driven by thermodynamics and mechanics.

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Notes

  1. 1.

    and in fact of small gradient of elastic strain.

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Authors and Affiliations

  1. Centre des Matériaux, Mines ParisTech CNRS, Paris, France

    Samuel Forest, Kais Ammar & Victor de Rancourt

  2. Institut Jean Lamour, University of Lorraine, Nancy, France

    Benoit Appolaire

  3. Institute of Applied Mechanics, RWTH Aachen University, Aachen, Germany

    Stephan Wulfinghoff

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  1. Samuel Forest
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  2. Kais Ammar
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  3. Benoit Appolaire
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  4. Victor de Rancourt
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  5. Stephan Wulfinghoff
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Correspondence to Samuel Forest .

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Editors and Affiliations

  1. Department of Mechanical and Materials Engineering, Washington State University, Pullman, WA, USA

    Sinisa Mesarovic

  2. Centre des Matériaux, Mines ParisTech, Evry, France

    Samuel Forest

  3. Department of Mechanical and Materials Engineering, Washington State University, Pullman, WA, USA

    Hussein Zbib

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Forest, S., Ammar, K., Appolaire, B., Rancourt, V.d., Wulfinghoff, S. (2019). Generalized Continua and Phase-Field Models: Application to Crystal Plasticity. In: Mesarovic, S., Forest, S., Zbib, H. (eds) Mesoscale Models. CISM International Centre for Mechanical Sciences, vol 587. Springer, Cham. https://doi.org/10.1007/978-3-319-94186-8_6

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