Titlebook: Introduction to Geometrically Nonlinear Continuum Dislocation Theory; FE Implementation an Christian B. Silbermann,Matthias Baitsch,Jörn Ih

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Numerical Solution with the Finite Element Method,islocation theory by means of the finite element method. For the special case of a continuously dislocated, plane, cubic primitive single crystal with two active slip systems, the discretized integral equations for one finite element are transformed to matrix notation.

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Outlook, outlined. On the one hand, this concerns possible theoretical extensions of the model and the numerical studies. On the other hand, proper experiments are suggested for the validation of the numerical results. Thereby, the focus is on cubic minerals.

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Christian B. Silbermann,Matthias Baitsch,Jörn IhleComprehensive introduction to single crystal plasticity with continuously distributed dislocations.Provides a straightforward preparation for the implementation into FEM codes.Presents simulations int

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Nonlinear Kinematics of a Continuously Dislocated Crystal,he deformation and the slip-system-based decomposition of the velocity gradient. Eventually, appropriate measures for the crystal’s strain and geometrically necessary dislocation densities are derived.

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Special Cases Included in the Theory, cases, which are briefly described in this chapter. This also involves a rigorous treatment of the important case of single slip, and the geometrical linearization. Thereby, some subtle but significant differences to geometrically . continuum dislocation theory are discovered.

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Variational Formulation of the Theory,ower [.]. Inserting special virtual motions, the balance equations of linear and angular momentum are derived. For the case of a continuously dislocated, plane, cubic primitive single crystal with two active slip systems, the governing integral equations are transformed to matrix notation.

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Numerical Solution with the Finite Element Method,islocation theory by means of the finite element method. For the special case of a continuously dislocated, plane, cubic primitive single crystal with two active slip systems, the discretized integral equations for one finite element are transformed to matrix notation.