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We derive two consequences of the distributional form of the stress equilibrium condition while incorporating piecewise smooth stress and body force fields with singular concentrations on an interface. First, we obtain the local equilibrium conditions in the bulk and at the interface, the latter inclusive of interfacial stress and stress dipole fields. Second, we obtain the necessary and the sufficient conditions on the divergence-free non-smooth stress field for there to exist a stress function field such that the stress equilibrium is trivially satisfied. In doing so, we allow the domain to be non-contractible with mutually disjoint connected boundary components. Both derivations illustrate the utility of the theory of distributions in dealing with singular stress fields. [ABSTRACT FROM AUTHOR]

Anisotropic slipline theory, with non-uniform lattice rotation field, is used to discuss new slipline solutions for the plane strain problems of punch indentation and mode 1 stationary crack in a ductile single crystal with piecewise linear yield locus. The proposed solution allows for both linear dislocation arrays and sectors with bulk dislocation density. Such features provide considerable latitude in the number of allowable stress discontinuities, and their orientation, when compared to the solutions which assume uniform lattice rotation. [ABSTRACT FROM AUTHOR]