We consider linear elliptic systems which arise
in coupled elastic continuum mechanical models. In these systems, the strain
tensor εP := sym (P-1∇u) is redefined to include a
matrix valued inhomogeneity P(x) which cannot be described by a space
dependent fourth order elasticity tensor. Such systems arise naturally in
geometrically exact plasticity or in problems with eigenstresses.
The tensor field P induces a structural change of the elasticity equations. For
such a model the FETI-DP method is formulated and a convergence estimate
is provided for the special case that P-T = ∇ψ is a gradient.
It is shown that the condition number depends only quadratic-logarithmically
on the number of unknowns of each subdomain. The
dependence of the constants of the bound on P is highlighted. Numerical
examples confirm our theoretical findings. Promising results are also obtained
for settings which are not covered by our theoretical estimates.