Interaction and multiscale mechanics

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Interaction fields based on incompatibility tensor in field theory of plasticity-Part I: Theory-

  • Received : 2008.03.23
  • Accepted : 2008.08.15
  • Published : 2009.03.25
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Abstract

This paper proposes an interaction field concept based on the field theory of plasticity. Relative deformation between two arbitrary scales, e.g., macro and micro fields, is defined which can be implemented in the crystal plasticity-based constitutive framework. Differential geometrical quantities responsible for describing dislocations and defects in the interaction field are obtained, based on which dislocation density and incompatibility tensors are further derived. It is shown that the explicit interaction exists in the curvature or incompatibility tensor field, whereas no interaction in the torsion or dislocation density tensor field. General expressions of the interaction fields over multiple scales with more than three scale levels are derived and implemented into the present constitutive equation.

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References

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  2. On Finsler Geometry and Applications in Mechanics: Review and New Perspectives vol.2015, 2015, https://doi.org/10.1155/2015/828475
  3. FTMP-BASED SIMULATION OF TWIN NUCLEATION AND SUBSTRUCTURE EVOLUTION UNDER HYPERVELOCITY IMPACT vol.02, pp.03n04, 2013, https://doi.org/10.1142/S2047684113500218
  4. Modeling and Simulations of Experimentally-Observed Dislocation Substructures Based on Field Theory of Multiscale Plasticity (FTMP) Combined with TEM and EBSD-Wilkinson Method for FCC and BCC Poly/Single Crystals vol.55, pp.5, 2014, https://doi.org/10.2320/matertrans.M2013226
  5. Interaction fields based on incompatibility tensor in field theory of plasticity-Part II: Application- vol.2, pp.1, 2009, https://doi.org/10.12989/imm.2009.2.1.015