The non‐linear theory of elastic shells undergoing phase transitions was proposed by two first authors in J. Elast. 79, 67–86 (2004). In the present paper the theory is extended by taking into account also the elastic strain energy density of the curvilinear phase interface as well as the resultant forces and couples acting along the interface surface curve itself. All shell relations are found from the variational principle of stationary total potential energy. In particular, we derive the extended natural continuity conditions at coherent and/or incoherent surface curves modelling the phase interface. The continuity conditions allow one to establish the final position of the interface surface curve after the phase transition. The results are illustrated by an example of a phase transition in an infinite plate with a central hole.
We formulate the exact, resultant equilibrium conditions for the non-linear theory of branching and self-intersecting shells. The conditions are derived by performing direct through-the-thickness integration in the global equilibrium conditions of continuum mechanics. At each regular internal and boundary point of the base surface our exact, local equilibrium equations and dynamic boundary conditions are equivalent, as expected, to the ones known in the literature. As the new equilibrium relations we derive the exact, resultant dynamic continuity conditions along the singular surface curve modelling the branching and self-intersection as well as the dynamic conditions at singular points of the surface boundary. All the results do not depend on the size of shell thicknesses, internal through-the-thickness shell structure, material properties, and are valid for an arbitrary deformation of the shell material elements.
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