Research Activity & Interests
- Field theory of dislocation mechanics
The study of the solid mechanics of crystalline
bodies of structural dimensions in the 1µm – 10nm range requires the
consideration of crystal lattice defects, the most common of which is the
crystal dislocation. Some technologically interesting examples of such structures
are semiconductor thin films used in electronic devices (LEDs, transistors),
metallic interconnects in Integrated circuitry and actuators in MEMS devices.
It is well known that deformation microstructures in structural metals critically
affect their response to loads – such microstructures are also the result
of plasticity in the length-scale range mentioned above.
The goal of this research is to understand the phenomena
mentioned above within the context of a nonlinear field theory of dislocation
mechanics and crystal plasticity (Acharya, 2000). The constitutive inputs
of the theory relate explicitly to dislocation velocity and nucleation and
crystal elasticity; its predictions relate to stress-state (both residual
and those induced by loads), permanent deformation and strain-hardening in
single crystals. The work is intended to be of use in the prediction of time-dependent
mechanical response of bodies containing a single, a few, or a distribution
of dislocations.
We pursue theoretical as well as numerical (FEM)
modeling approaches in our effort to rigorously understand dislocation mechanics
in nanoscale structures. A distant, grand and glorious aim is to use an appropriate
averaging procedure (not necessarily spatial) to determine the form of a
crystal plasticity theory with resolution in the mesoscale.
- Continuum thermomechanics
- Metal plasticity theory with meso-microscale
resolution: We seek to understand the thermomechanics
of length-scale dependent response of metallic materials within the context
of the continuum theory of crystal plasticity based on the notion of slip
and mesoscale lattice incompatibility (Acharya & Shawki, 1995; Acharya
& Bassani, 2000; Acharya & Beaudoin, 2000; Beaudoin et al., 2000).
The applications of the theory relate to the polycrystal size-effect, nano-indentation,
shear localization in single and polycrystalline structural materials, to
mention a few examples. The work involves both theoretical and large scale
finite element computations.
- Computational modeling of polymer response: The goal here is to understand and numerically model
the thermomechanical behavior of polymers (implementation of nonlinear viscoelastic
material model in the general-purpose nonlinear FE code ABAQUS; ABAQUS keyword
*Hysteresis). Applications of interest are solid propellants, filled/unfilled
rubbers for tires.
- Finite element analysis of nonlinear
and/or strongly coupled thermomechanical phenomena with emphasis on systems
with moving interfaces
Well-posedness and finite-element modeling of theories
of inelastic deformation which admit solutions with strong discontinuities
or sharp gradients. Applications of interest are dynamic deformations of elastic-plastic
and elastic-viscoplastic materials, dynamic phase transitions and solid-gas
interaction in solid propellant booster rockets (Parsons et al. 2000).
- Structural mechanics; nonlinear
shell theory
- Kinematics on manifolds with applications to
geometrically exact treatment of shells (Acharya, 2000).
- Finite-element implementation of geometrically
exact theories of shells, rods and oriented bodies (development of ABAQUS
shell element S4).
- General methods for defining constitutive theories
for ‘lower-dimensional’ bodies (shells, rods) from corresponding theory for
the actual three-dimensional body.
Applications of research relate to the understanding
of the structural response and failure of aircraft/space structures, pressure
vessels, autoframes, reinforced tires.
- Analysis of discontinuous mechanical
processes using the discrete element method
- Analysis of grinding, mixing, size segregation
and material handling in industrial processes. Related applications: ball-milling
(Acharya, 2000), ultra-fine grinding, material transport, material deposition
- Understanding and direct numerical simulation,
using the (DEM), of slow deformations of granular materials dominated by
contact and friction to understand the evolution of the contact orientation
distribution (fabric) and its effect on macroscopic constitutive response.
Application: quasi-static material response of dense granular assemblies.
- Understanding of the ‘wet’ behavior of granular
assemblies through numerical studies with coupled finite-element and distinct-element
technology. Applications: slope stability, flow through porous media