  To model the mechanically-driven phase transformations, e.g. martensitic
transformation, using the phase-field theory, suitable models are needed for
describing the mechanical fields of the individual non-vanishing phase-fields
in the interface regions in order to obtain the mechanical driving forces of
phase-field motion. Quantitative modeling requires satisfying the interfacial
static equilibrium and kinematic compatibility conditions which have already
been achieved in the literature for dual-phase-field materials by using the
rank-one relaxation (or convexification) of the energy density. A direct
generalization to the multi-phase-field case is not applicable without breaking
these conditions partially. To the best of our knowledge, no existing
multi-phase-field elasticity model has been able to satisfy the jump conditions
between all the locally-active phase-fields on their pairwise normals in triple
and higher-order junctions. In this work, we introduce a novel
multi-phase-field elasticity model based on the partial rank-one relaxation of
the elastic energy density defined on the pairwise interfaces...... (see PDF
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