Research Interests
Shock Initiation of High Energetic Materials
In collaboration with
Dr. Julian Rimoli and
Prof. 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 defect-free energetic single crystals is comparatively less well-understood,
but dislocation-mediated plastic deformation suggests itself as an explanation for the observed orientation dependencies. It is well-known that
dislocation-mediated plastic deformation is almost universally inhomogenous at the sub-grain 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 hot-spots for initiation in void-free
energetic polycrystals.
We develop a multiscale model for the shock ignition in defect-free 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 sub-grain 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 defect-free energetic polycrystalline PETN. Strong localization
of temperature in the hot spots causes molecular decomposition which was modeled by an
Arrhenius type depletion law. The sub-grain microstructure construction is integrated into a
finite element framework and the proposed model is used to simulate the response of
PETN in a plate-impact configuration. The pop-plot data generated
from numerical simulations yields a linear relation in a log-log plot as observed in experiments.
Related publications:
Rimoli, J., Gürses, E. and Ortiz, M.
Shock-Induced Subgrain Microstructures as Possible Homogenous sources of Hot Spots and Initiation Sites in Energetic Polycrystals, in preparation.
Multiscale Modeling of Subgrain Dislocation Structures in Crystal Plasticity
In collaboration with
Prof. Michael Ortiz
The plastic deformation of crystalline materials is a direct consequence of
dislocations running on well-characterized crystallographic slip planes.
As a result of plastic deformations, crystals start to develop variety of
dislocations structures which are observed in single and polycrystals under
both monotonic and cyclic loading conditions. It is often observed that the activity of slip systems in neighboring cells
or lamellae which are separated by dislocation boundaries or walls are different. This variation in the slip system activity
is related with the latent hardening property of single crystals. The strong latent hardening observed
in ductile single crystals often prevents the simultaneous activation of more than one slip system over the same region of the crystal. As a
consequence, the slip activity is expected to be divided into regions in which single slip system is operative.
It has been shown by Ortiz and Repetto [1999] that the crystal plasticity models with strong latent hardening results in non-convex
incremental variational problems which often suffer from the lack of solutions and exhibit fine scale oscillations.
We study a non-local extension of the model based on analytical relaxation results of
Conti and Ortiz [2005]. The original relaxed model is the ideal multislip plasticity and has no intrinsic length scale. In the new
constitutive model, we make use of the optimal microstructure construction given in Conti and Ortiz [2005] and consider the
contribution of the dislocation walls into the plastic energy. This additional energy contribution provides the hardening behavior and renders
the model to be size-dependent. As a result, we obtain a fast multiscale crystal plasticity model which has a length scale and exhibits
a micromechanically motivated hardening response.
Related publications:
Gürses, E. and Ortiz, M.
Fast Multiscale Models of Subgrain Dislocation Structures in Crystal Plasticity, in preparation.
Conti, S. and Ortiz, M.
Dislocation Microstructures and the Effective Behavior of Single Crystals
Archive for Rational Mechanics and Analysis, vol. 176, 2005, pp.103-147.
Otriz, M. and Repetto E. A.
Nonconvex Energy Minimization and Dislocation Structures in Ductile Single Crystals
Journal of the Mechanics and Physics of Solids, vol.47, 1999, pp.397-462.
Configurational-Force-Driven Crack Propagation based on Incremental Energy Minimization
In collaboration with
Prof. Christian Miehe
We consider a variational formulation of quasi-static brittle fracture and develop a new finite-element based
computational framework for propagation of cracks in three-dimensional 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 Clausius-Planck 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 space-discretized finite element context is naturally related to discrete nodes of a typical
finite element mesh. In a consistent way with the node-based 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 r-adaptive crack-facet reorientation
procedure based on configurational-force-based 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:
Gürses, E. and Miehe, C.
A Computational Framework of Three Dimensional Configurational Force Driven Brittle Crack Propagation,
Computer Methods in Applied Mechanics and Engineering, vol.198, 2009, pp.1413-1428.
Miehe, C., Gürses, E. and Birkle, M.
A Computational Framework of Configurational-Force-Driven Brittle Fracture Based on Incremental Energy Minimization.
International Journal of Fracture, vol.145, 2007, pp.245-259.
Miehe, C. and Gürses, E.
A Robust Algorithm for Configurational-Force-Driven Brittle Crack Propagation with R-Adaptive Mesh Alignment.
International Journal for Numerical Methods in Engineering, vol.72, 2007, pp.127-155.
Gürses, E.
Aspects of Energy Minimization in Solid Mechanics: Evolution of Inelastic Microstructures and Crack Propagation,
PhD Thesis, University of Stuttgart, 2007. (pdf)
Non-Convex Variational Problems, Relaxation Theory and Application to Damage Mechanics and Crystal Plasticity
In collaboration with
Prof. 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 by non-convex variational
problems. Furthermore, it has been shown that non-existence 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. Non-convex 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 non-quasiconvex 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 rank-one 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 non-convex potentials arise and develop numerical
relaxation schemes based on rank-one convexification. The performance of the relaxation methods is shown by the
well-behaved objective global response of the finite element solutions.
Related publications:
Miehe, C., Lambrecht, M. and Gürses, E.
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, 2004, pp.2725-2769.
Gürses, E. and Miehe, C.
On Evolving Deformation Microstructures in Non-Convex Partially Damaged
Solids,
submitted to Journal of the Mechanics and Physics of Solids.
Gürses, E., Mainik, A., Miehe, C. and Mielke, A.
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: 443-481. Springer, 2006.
Aspects of Energy Minimization in Solid Mechanics: Evolution of Inelastic Microstructures and Crack Propagation,
PhD Thesis, University of Stuttgart, 2007. (pdf)
