## Smart Active Materials

In recent years, there has been an increased effort by scientists to obtain new composite materials with extreme properties. Inspired by natural and biological processes, scientists have proposed the use of hierarchical architectures (i.e., assembly of structural components) spanning several length scales from nanometer to centimeter sizes. Depending each time on the desired properties of the composite material, optimization with respect to its stiffness, weight, density, toughness and other properties is carried out. In the present subject, the interest is in magneto-mechanical coupling and tailored instabilities. Hierarchical materials, such as magnetorheological elastomers (MREs) which combine magnetic particles (at the scale of nanometers and micrometers) embedded in a soft polymeric non-magnetic matrix, give rise to a coupled magneto-mechanical response at the macroscopic (order of millimeters and centimeters) scale when they are subjected to combined magneto-mechanical external stimuli. These composite materials can deform at very large strains due to the presence of the soft polymeric matrix without fracturing. From an unconventional point of view, a remarkable property of these materials is that while they can become unstable by combined magneto-mechanical loading, their response is well controlled in the post-instability regime. This, in turn, allows us to try to operate these materials in this critically stable region, similar to most biological systems. These instabilities can lead to extreme responses such as wrinkles (for haptic applications), actively controlled stiffness (for cell-growth) and acoustic properties with only marginal changes in the externally applied magnetic fields. Unlike the current modeling of hierarchical composites, MREs require the development of novel experimental techniques and advanced coupled nonlinear magneto-mechanical models in order to tailor the desired macroscopic instability response at finite strains.

## Nonlinear Homogenization and Damage

Due to their critical technological importance, high strength steels
have been the focus of continued attention over the last twenty
years. Due to fabrication reasons, however, these materials
consist, in general, of two phases;
the standard metallic matrix phase and second phase particles (e.g.,
other ingredients or impurities). These two phases have different
material properties (e.g., Young modulus, yield stress, hardening
exponent etc.) and hence such a material system constitutes a
two-phase composite material, with the particles usually being
stiffer than the matrix itself. The mechanisms for material failure
in such solids is the nucleation, growth and eventual coalesce of
voids and micro-cracks as a result of the applied loading
conditions, either by particle rupture or near the matrix-particle
interface.
This research project deals with rate-(in)dependent constitutive
models for porous materials with a matrix phase described by either
J2-flow theory or crystal plasticity with arbitrary number of slip
systems and orientations. The material comprises ellipsoidal voids
at arbitrary orientations and is subjected to general
three-dimensional loadings. The proposed modified variational models
(MVAR), are based on the nonlinear variational homogenization
method, which makes use of a linear comparison porous material to
estimate the response of the nonlinear porous material. The MVAR
models are validated by periodic finite element simulations (left movie) for a
large number of parameters including general void shapes and
orientations, various creep exponents (i.e., nonlinearity) and
general loading conditions. The MVAR model with the isotropic matrix
is implemented in a UMAT and used to simulate 3D geometries of real
experimental setups (right movie). Strain localization and damage as
this is measured by the evolution of the underlying porosity and
void shapes is also studied. The models are also used to probe
experiments. A recent effort to develop high-end experiments of thin
specimens under an SEM (scanning electron microscope) is underway.

## Discrete Dislocation and Strain Gradient Plasticity

In this research project, we employ two-dimensional discrete
dislocation models and strain-gradient plasticity theories to
investigate size effects in plasticity at
micron scales. The project is be divided into two main sections.
In the first section, we investigate the role of interfaces in the elastic-plastic
response of a sheared single crystal making use of discrete dislocation dynamics and
strain gradient crystal plasticity theories. More specifically, the upper and lower faces of a
single crystal are bonded to rigid adherends via interfaces of finite thickness. The sandwich
system is subjected to simple shear, and the effect of the compliance of crystal layer and of
interfaces upon the overall response are explored. In the second section, we implement
the tensorial strain gradient plasticity theory of Gudmundson (2004) and Fleck and Willis
(2009b) in a mixed finite element framework in order to predict indentation hardness. Three
length scale parameters are introduced and a fairly general investigation of the role of these
parameters on the indentation hardness is carried out. The resulting hardness trends are also
explored in the context of hardening materials. Moreover, following Johnson (1970), we find
that by proper normalization of the material constants and the geometrical properties of the
indenter, material hardness becomes independent of the shape of the indenter. Finally, other
models proposed in the literature (such as spherical void expansion and Nix-Gao model) are
evaluated by making use of the current strain gradient formulation.