| Abstract: |
| In this talk, we discuss a linearization result for quasistatic fracture evolution in nonlinear elasticity.
As the stiffness of the material tends to infinity, we show that rescaled displacement fields and their
associated crack sets converge to a solution of quasistatic crack growth in linear elasticity without
any a priori assumptions on the geometry of the crack set. This result corresponds to the evolutionary
counterpart of the static linearization result by M. Friedrich, where a Griffith model for nonsimple brittle materials
has been considered featuring an elastic energy which also depends suitably on the second gradient of
the deformations. The proof relies on a careful study of unilateral global minimality, as determined by
the nonlinear evolutionary problem, and its linearization together with a variant of the jump transfer
lemma in GSBD proven by M. Friedrich and F. Solombrino.
This is a joint project with M. Friedrich (Linz, Austria) and K. Stinson (Salt Lake City, Utah). |
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