Acta Mech. 227, 2843-2859, 2016
B. Daum, F.G. Rammerstorfer
Institute of Lightweight Design and Structural Biomechanics,
TU Wien, Vienna, Austria
The present work considers lamellar (micro) structures of thin, elastic
lamellae embedded in a yielding matrix as a stability problem in the context of
the theory of stability and uniqueness of path-dependent systems.
The volume ratio of the stiff lamellae to the relatively soft matrix is assumed
low enough to initiate a symmetric buckling mode, which is investigated by
analytical and numerical means.
Using a highly abstracted, incompatible model, a first approach is made, and
the principal features of the problem are highlighted.
Assuming plane strain deformation, an analytic expression for the bifurcation
load of a refined, compatible model is derived for the special case of ideal
plasticity and verified by numerical results.
The effect of lamella spacing and matrix hardening on the bifurcation load is
studied by a finite element unit cell model.
Some of the findings for the ideal plastic matrix are shown to also apply for a
mildly hardening matrix material.
Furthermore, the postbuckling behaviour and the limit load are investigated by
simulating a bulk lamella array.