## UC Berkeley / Lawrence Berkeley Laboratory

#### Computational Structures and Materials Characterization with Branch-Following and Bifurcation Techniques

**Ryan Elliott, University of Minnesota**

##### October 18th, 2017 at 4:00PM–5:00PM in 891 Evans Hall [Map]

Historically, engineers have tried to avoid working with materials and
structures under conditions where instabilities are likely to occur. Classical
stability analyses have focused on predicting the onset of instability for use
as an upper bound on allowable loads or as a design constraint. More recently
it is becoming common to take advantage of these instabilities in order to
design materials and structures with new and improved properties. Examples
include, the remarkable properties and applications of shape memory alloys,
phase transforming materials for solid state computer memory, and flexible high
aspect-ratio airplane wings (providing improved manoeuvrability) designed to
operate under flutter conditions and actively controlled against dynamic
instability. Physical models (of materials, structures, aircraft, etc.)
capable of predicting such instabilities are highly nonlinear. Thus, it is
often extremely difficult to explore and understand all of the behavior
predicted by a model. This presentation will review the theory and numerical
implementation of Branch-Following and Bifurcation (BFB) techniques for
exploring and understanding instabilities in physical systems. These
techniques provide a systematic approach to the identification and
interpretation of a model's behavior. The application of these techniques will
be illustrated through examples: (i) atomistic modeling of shape memory alloys;
(ii) finite element modeling of periodic structural materials such as
honeycombs; and (iii) atomistic modeling of nano-structures such as
nano-pillars.