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The incompatibility of linearized piecewise smooth strain field, arising outof volumetric and surface densities of topological defects and metricanomalies, is investigated. First, general forms of compatibility equations arederived for a piecewise smooth strain field, defined over a simply connecteddomain, with either a perfectly bonded or an imperfectly bonded interface.Several special cases are considered and discussed in the context of existingresults in the literature. Next, defects, representing dislocations anddisclinations, and metric anomalies, representing extra matter, interstitials,thermal, and growth strains, etc., are introduced in a unified framework whichallows for incorporation of their bulk and surface densities, as well as forsurface densities of defect dipoles. Finally, strain incompatibility relationsare derived both on the singular interface, and away from it, with sources interms of defect and metric anomaly densities. With appropriate choice ofconstitutive equations, the incompatibility relations can be used to determinethe state of internal stress within a body in response to the givenprescription of defects and metric anomalies.

Topological defects and metric anomalies as sources of incompatibility for piecewise smooth strain fields