The paper proves a rigidity structure theorem and computes an explicit kernel projection for maps of bounded deviatoric deformation in dimension n≥3, providing the main tools for relaxation and homogenization in BD_dev.
On the integral representation of variational functionals on $BD$
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abstract
Following the global method for relaxation we prove an integral representation result for a large class of variational functionals naturally defined on the space of functions with Bounded Deformation. Mild additional continuity assumptions are required on the functionals.
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Rigidity and functional properties of $\mathrm{BD}_{dev}(\Omega)$
The paper proves a rigidity structure theorem and computes an explicit kernel projection for maps of bounded deviatoric deformation in dimension n≥3, providing the main tools for relaxation and homogenization in BD_dev.