
Dr. Ercan Gürses
Associate Professor
Department of Aerospace Engineering
Middle East Technical University
Ankara, Turkey 06800
Office: 202
Tel: +90312210 4257
Fax: +90312338 4250
Email: gurses@metu.edu.tr 

[Nanocrystalline Materials  Explosives  Fracture Mechanics  Semicrystalline Polymers  Nonconvex Problems and Microstructures]
In collaboration with Dr. Tamer El Sayed
Nanocrystalline (nc) materials are known to posses several distinct features when compared to coarse grained polycrystals. These include high strength and fatigue resistance, low ductility, pronounced rate dependence, tensioncompression asymmetry and susceptibility to plastic instability. We develop a variational multiscale constitutive models in the finite deformation regime capable of capturing the mechanical behavior of nanocrystalline (nc) fcc metals. The ncmaterial is modeled as a twophase material consisting of a grain interior phase and a grain boundary effected zone (GBAZ). A rateindependent isotropic porous plasticity model is employed to describe the GBAZ, whereas a crystalplasticity model which accounts for the transition from partial dislocation to full dislocation mediated plasticity is employed for the grain interior. The constitutive models of both phases are formulated in a small strain framework and extended to finite deformation by use of logarithmic and exponential mappings. Assuming the rule of mixtures, the overall behavior of a given grain is obtained via volume averaging. The scale transition from a single grain to a polycrystal is achieved by Taylortype homogenization where a lognormal grain size distribution is assumed. It is shown that the proposed model is able to capture the enhanced rate sensitivity and the inverse HallPetch effect, i.e., loss of strength with grain size refinement.
Related publications:
E. Gürses, T. El Sayed, A Constitutive Model of Nanocrystalline Metals Based on Competing Grain Boundary and Grain Interior Deformation Mechanisms, Submitted to Materials Letters, 2011.
E. Gürses, T. El Sayed, Constitutive Modeling of Strain Rate Effects in Nanocrystalline and Ultrafine Grained Polycrystals, International Journal of Solids and Structures, vol. 48, pp. 16101616, 2011.
E. Gürses, T. El Sayed, A Variational Multiscale Constitutive Model for Nanocrystalline Materials, Journal of the Mechanics and Physics of Solids, vol. 59, pp. 732749, 2011.
E. Gürses, T. El Sayed, On TensionCompression Asymmetry in UltrafineGrained and Nanocrystalline Metals, Computational Materials Science, vol. 50, pp. 639644, 2010.
In collaboration with
Dr. Julian Rimoli
and Dr. Michael Ortiz
Microscopic defects such as voids are thought to be a prime source of hot spots in crystalline energetic materials.
For instance, the formation of jets during the collapse of voids may result in temperatures and pressures that greatly exceed values in the
bulk, thereby promoting molecular decomposition. The impact sensitivity of defectfree energetic single crystals is comparatively less
wellunderstood, but dislocationmediated plastic deformation suggests itself as an explanation for the observed orientation dependencies. It is wellknown
that dislocationmediated plastic deformation is almost universally inhomogenous at the subgrain level and exhibits microstructural
patterns that include localization of deformation and temperature to slip lines. We investigate the role of such slip lines as possible hotspots for
initiation in voidfree energetic polycrystals.
We develop a multiscale model for the shock ignition in defectfree polycrystalline high energetic materials. The model consists of three levels: (i) a
polycrystalline structure at macroscale, (ii) a single crystal plasticity at mesoscale and (iii)
subgrain microstructures at microscale. The development of subgrain level microstructures is
taken into account by an energetically optimal explicit construction of sequential lamination. The explicit
construction exhibits microstructural patterns that include localization of deformation
and temperature to slip lines. We investigated the role of such slip lines as possible
hot spots for initiation in a defectfree energetic polycrystalline PETN. Strong localization
of temperature in the hot spots causes molecular decomposition which was modeled by an
Arrhenius type depletion law. The subgrain microstructure construction is integrated into a
finite element framework and the proposed model is used to simulate the response of
PETN in a plateimpact configuration. The popplot data generated from numerical simulations yields a linear relation in a loglog
plot as observed in experiments.
Related publications:
J. Rimoli, E. Gürses, M. Ortiz ShockInduced Subgrain Microstructures as Possible Homogenous sources of Hot Spots and Initiation Sites in Energetic Polycrystals, Physical Review B, vol. 81, p. 014112, 2010.
In collaboration with Dr. Christian Miehe
We consider a variational formulation of quasistatic brittle fracture and develop a new finiteelement based
computational framework for propagation of cracks in threedimensional bodies. We outline a consistent
thermodynamical framework for crack propagation in elastic solids and show that both the elastic
equilibrium response as well as the local crack evolution follow in a natural format by exploitation of a
global ClausiusPlanck inequality in the sense of Coleman's method. Consequently, the crack propagation
direction associated with the classical Griffith criterion is identified by the material configurational force
which maximizes the local dissipation at the crack front. The variational formulation is realized numerically
by a standard spatial discretization with finite elements which yields a discrete formulation of the
global dissipation in terms configurational nodal forces. Therefore, the constitutive setting of crack propagation
in the spacediscretized finite element context is naturally related to discrete nodes of a typical
finite element mesh. In a consistent way with the nodebased setting, the discretization of the evolving
crack discontinuity is performed by the doubling of critical nodes and interface facets of the mesh. The
crucial step for the success of this procedure is its embedding into an radaptive crackfacet reorientation
procedure based on configurationalforcebased indicators in conjunction with crack front constraints.
We propose a staggered solution procedure that results in a sequence of positive definite discrete subproblems
with successively decreasing overall stiffness, providing a robust algorithmic setting in the
postcritical range. The predictive capabilitiy of the proposed formulation is demonstrated by means of
representative numerical simulations.
Related publications:
E. Gürses, C. Miehe, A Computational Framework of Three Dimensional Configurational Force Driven Brittle Crack Propagation, Computer Methods in Applied Mechanics and Engineering, vol. 198, pp. 14131428, 2009.
C. Miehe, E. Gürses, M. Birkle, A Computational Framework of ConfigurationalForceDriven Brittle Fracture Based on Incremental Energy Minimization, International Journal of Fracture, vol. 145, pp. 245259, 2007.
C. Miehe, E. Gürses, A Robust Algorithm for ConfigurationalForceDriven Brittle Crack Propagation with RAdaptive Mesh Alignment, International Journal for Numerical Methods in Engineering, vol. 72, pp. 127155, 2007.
E. Gürses, Aspects of Energy Minimization in Solid Mechanics: Evolution of Inelastic Microstructures and Crack Propagation, PhD Thesis, University of Stuttgart, 2007.
(pdf) .
In collaboration with Dr. Serdar Göktepe
In collaboration with Dr.
Christian Miehe
Microstructures that are observed in nature often show complex patterns with length scales
much smaller than characteristic macroscopic dimensions of the problem considered. It
is possible mathematically to describe these microstructures bynonconvex variational
problems. Furthermore, it has been shown that nonexistence of minimizers in these variational
problems are closely related to fine scale oscillatory infimizing sequences which
are interpreted as microstructures. In particular, there is a strong parallelism between
the microstructures that develop in martensitic phase transformations and fine scale oscillatory
infimizing sequences of energy functionals describing phase transforming elastic crystals.
The existence of solutions for the boundary value problems of nonlinear elasticity demands the sequential weak
lower semicontinuity of the energy functional which is ensured provided that the energy storage function
possesses particular weak convexity and growth conditions. For vector valued variational problems the
crucial weak convexity notion is the quasiconvexity. Nonconvex variational problems which often suffer from the
lack of solutions in the classical sense can be treated by the relaxation theory which is the replacement of
the nonquasiconvex storage function by its quasiconvex envelope. However, quasiconvexity is a global integral
condition which is hard to verify in practice. More manageable condition is the slightly weaker rankone convexity
notion that is considered to be a close approximation of quasiconvexity. We investigate two model problems, namely
single crystal plasticity and the damage mechanics, where nonconvex potentials arise and develop numerical
relaxation schemes based on rankone convexification. The performance of the relaxation methods is shown by the
wellbehaved objective global response of the finite element solutions.
Related publications:
E. Gürses, C. Miehe,
On Evolving Deformation Microstructures in NonConvex Partially Damaged Solids,
Journal of the Mechanics and Physics of Solids, vol. 59, pp. 12681290, 2011.
C. Miehe, M. Lambrecht, E. Gürses,
Analysis of Material Instabilities in Inelastic Solids by Incremental Energy Minimization and Relaxation Methods: Evolving Deformation Microstructures in Finite Plasticity,
Journal of the Mechanics and Physics of Solids, vol. 52, pp. 27252769, 2004.
E. Gürses, A. Mainik, C. Miehe, A. Mielke, Analytical and Numerical Methods for Finite Strain Elastoplasticity,
In R. Helmig, A. Mielke, B. Wohlmuth, editors, Multifield Problems in Fluid and Solid Mechanics. Series Lecture Notes in Applied and Computational Mechanics, 28:443481. Springer, 2006.
E. Gürses, Aspects of Energy Minimization in Solid Mechanics: Evolution of Inelastic Microstructures and Crack Propagation, PhD Thesis, University of Stuttgart, 2007.
(pdf) .
   