
A. Shapememory alloys
This research concerns the combined experimental, analytical and
computational study of superelasticity and the shapememory effect
in metal alloys, especially NiTi and CuZnAl. The experimental portion of this
work is done in collaboration with
Professor R.O. Ritchie.
The following image shows the experimental setup for biaxial
(tensiontorsion) loading of thin NiTi tubes under displacement control,
slow loading rates and essentially isothermal conditions:
Related Publications:
 A. Sengupta, P. Papadopoulos, A. Kueck and A.R. Pelton.
``On Phase Transformation Models
for Thermomechanically Coupled Response of Nitinol''
,
Comp. Mech., 48, pp. 213227, (2011).
 A. Sengupta and P. Papadopoulos.
``Constitutive modeling and finite element approximation
of B2RB19' phase transformations in Nitinol polycrystals''
,
Comp. Meth. Appl. Mech. Engrg., 198, pp. 32143227, (2009).
 Y. Jung, P. Papadopoulos and R.O. Ritchie.
``Constitutive Modeling and Numerical Simulation of Multivariant Phase
Transformation in Superelastic Shapememory Alloys'',
Int. J. Num. Meth Engrg., 60, pp. 429460, (2004).
 J.M. McNaney, V. Imbeni, Y. Jung, P. Papadopoulos and R.O. Ritchie.
``An Experimental Study of the Superelastic Effect in a ShapeMemory Nitinol
Alloy Under Biaxial Loading'',
Mech. Mat., 35, pp. 969986, (2003).
Short course material:
P. Papadopoulos.
``Constitutive Modeling and Simulation of the Superelastic Effect in
ShapeMemory Alloys'' , CISM, Udine, July 2005.

B. Estimation of material properties using molecular dynamics
The purpose of this research is to estimate mechanical and thermal
properties of materials using methods of statistical mechanics, as implemented
computationally within the framework of molecular dynamics techniques.
Properties of particular interest include elasticities in metals and alloys,
as well as thermal conductivities in microscale systems.
The following snapshot shows an instance of a simple twodimensional
molecular dynamics calculation for Cu under constant temperature:
Related Publications:
 K.K. Mandadapu, R.E. Jones and P. Papadopoulos.
``A Homogeneous NonEquilibrium Molecular Dynamics Method
for Calculating the Heat Transport Coefficient of Mixtures and Alloys''
, J. Chem. Phys., 133, pp.
034122111, (2010).
 K.K. Mandadapu, R.E. Jones and P. Papadopoulos.
``Generalization of the Homogeneous NonEquilibrium Molecular Dynamics Method
for Calculating Thermal Conductivity to Multibody Potentials''
, Phys. Rev. E, 80, 04770214, (2009).
 K.K. Mandadapu, R.E. Jones and P. Papadopoulos.
``A Homogeneous NonEquilibrium Molecular Dynamics Method
for Calculating Thermal Conductivity with a ThreeBody Potential''
,
J. Chem. Phys., 130, 20410619, (2009).

C. Fabric materials
This research concerns the modeling and simulation of fabric materials
used in a wide array of applications ranging from lightweight
ballistic shields (e.g., body armor, aircraft fuselage barriers) to
highstrength flexible systems (e.g., parachutes) to everyday clothing
manufacture. Particular emphasis is given to specialpurpose materials such as
Kevlar and Zylon, which exhibit high strengthtoweight ratio.
The following image shows the numerical simulation of a pushtest on a
clamped fabric sheet made of Kevlar:
Related Publications:
 B. Nadler, P. Papadopoulos and D.J. Steigmann.
``Multiscale Constitutive Modeling and Numerical Simulation of Fabric
Material'',
Int. J. Solids Struct., 43, pp. 206221, (2006).
 B. Nadler, P. Papadopoulos and D.J. Steigmann.
``Convexity of the StrainEnergy Function in a TwoScale Model of Ideal
Fabrics'',
J. Elast., 84, pp. 223244, (2006).

D. Multiscale modeling of materials
This research focuses on the coupling of length and time scales using
atomistic and continuum methods. Emphasis is placed on both theoretical
and computational aspects with application to solids.
Related Publications:
 A. Sengupta, P. Papadopoulos and R.L. Taylor.
``A Multiscale Finiteelement Method for Modeling
FullyCoupled Thermomechanical Problems in Solids''
, to appear in
Int. J. Num. Meth. Engrg..
 K.K Mandadapu, A. Sengupta and P. Papadopoulos.
``A Homogenization Method for
Thermomechanical Continua using Extensive Physical Quantities''
,
Proc. Royal. Soc. London A., 468, pp. 16961715, (2012).
i>K.K Mandadapu, A. Sengupta and P. Papadopoulos.
``A Homogenization Method for
Thermomechanical Continua using Extensive Physical Quantities''
,
Proc. Royal. Soc. London A., 468, pp. 16961715, (2012).

E. Computational plasticity
This research focuses on the use of finite elementbased methods in the
analysis of problems of infinitesimal and finite plasticity within
the context of the strainspace formulation. Research in infinitesimal
plasticity concentrates on issues of stability and accuracy of the algorithms
used in the integration of the underlying differential/algebraic equations,
as well as solveability issues concerning nonassociative models.
Research in finite plasticity concerns the derivation and numerical
implementation of theoretically sound and physically plausible
models for analysis of the elasticplastic response of metallic bodies
that undergo finite deformations.
The following image shows the deformed shape and the equivalent plastic
strain of an initially curcular flange which is deepdrawn by pulling the
inner circular boundary inwards. Note the loss of axisymmetry, which is
due to the orthotropic yield condition:
Related Publications:
 A. Gupta, H.H. Bayraktar, J.C. Fox, T.M. Keaveny and P. Papadopoulos.
``Constitutive Modeling and Algorithmic Implementation of a Plasticitylike
Model for Trabecular Bone Structures'',
Comp. Mech., 40, pp. 6172, (2007).
 J. Lu and P. Papadopoulos.
``A Covariant Formulation of Anisotropic Finite Plasticity: Theoretical
Developments'',
Comp. Meth. Appl. Mech. Engrg., 193, pp. 53395358, (2004).
 P. Papadopoulos and J. Lu.
``On the Formulation and Numerical Solution of Problems
in Anisotropic Finite Plasticity'',
Comp. Meth. Appl. Mech. Engrg., 190, pp. 48894910, (2001).