ABSTRACT of the Doctoral Thesis

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Elastoplastic Instabilities of Lamellar Structures

### by Benedikt Daum (2015)

The present work investigates local bucking in layered structures comprising a
thin elastic layer (lamella) embedded in a comparatively thick matrix under
in-layer-plane loading.
The matrix is considered to be in an elastoplastic state at the initiation of
the lamella buckling.
As an application, this setup can be thought to represent the microstructure of
certain alloys at the level of an individual metal-grain, although the
presented results are not limited to such a setup.
The presence of inelastic deformations in the matrix requires that stability of
the loading process is investigated rather then the stability of isolated
equilibrium states.
For irreversible deformations these two concepts of stability do not coincide.
A deformation process following an equilibrium path involving inelastic
deformations may become nonunique and can bifurcate even while the individual
states that comprise the path are in stable equilibrium when considered
isolated.
The theory that allows for the treatment of inelastic bifurcations is reviewed
from the literature and the present problem is formulated in its context.

The implications resulting from the theory of inelastic instabilities, with
particular regard for the post buckling behaviour, are demonstrated using a
simplified model that allows for analytical treatment of the problem.
Taking advantage of the homogeneous prebuckling stress distribution the
governing equations for plane strain J_{2}-plasticity are solved in a
simplified manner for more refined models, and approximate analytical results
for the bifurcation load where obtained.

Analytical considerations are complemented by numerical simulations to validate
the results.
For the simulations a suitable unit cell-model was developed and verified by
independent simulations.
Comparison of analytical predictions and numerical results are in good
accordance for the case of ideal plasticity in the matrix and provide some
insight in the underlying mechanisms for the case of a hardening matrix.
For both cases an analytical interpretation of the obtained buckling mode is
given.

revised 150823 (hjb)