We consider the key systems describing steady state of a locally inhomogeneous electroconductive non-ferromagnetic solid within framework of the local gradient approach in thermomechanics. An arbitrarily chosen subdomain of the solid is regarded as a thermodynamically open system that can exchange by mass with environment. It is assumed that this exchange occurs suddenly at the initial time when the body structure is instantly set. The mass sources are introduced into the model to conform the actual and reference body states. The sources are associated with method of body surface forming.

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