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A highly-nonlinear theory is elaborated which describes elastic and inelastic
phenomena in media with complicated lattice structure consisting of two sublattices. In
the framework of this approach, the standard linear theory of acoustic and optic
oscillations of a complicated lattice is generalized, taking into account internal
translational symmetry of relative shear of the sublattices taken into account. As a
result, the interaction between the sublattices is characterized in terms of a
non-linear periodic force described, in particular, as sine of relative shear of two
atoms belonging to an elementary cell. The corresponding equations in the case of
solids without a central symmetry contain terms that describe the interatomic
interactions. We have the situation with quasistatic loading of solids. The dependence
of effective stresses on macroscopic strains is found which has a bifurcation point
responsible for a structural transformation of the twinning type. It is shown that the
transformation is related to a transformation of the interatomic interaction potential,
the namely occurrence of both an additional minimum of the potential and a new
structure (which has mirror symmetry relative to the initial structure.
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