Analytical and numerical methods for finite-strain elastoplasticity

Date

2006-11-27

Author

Gürses, Ercan
Miehe, Christian
Mielke, Alexander

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

109
views

0
downloads

An important class of finite-strain elastoplasticity is based on the multiplicative decomposition of the strain tensor F = Fel Fpl and hence leads to complex geometric nonlinearities. This survey describes recent advances in the analytical treatment of time-incremental minimization problems with or without regularizing terms involving strain gradients. For a regularization controlling all of ∇ Fpl we provide an existence theory for the time-continuous rate-independent evolution problem, which is based on a recently developed energetic formulation for rateindependent systems in abstract topological spaces. In systems without gradient regularization one encounters the formation of microstructures, which can be described by sequential laminates or more general gradient Young measures. We provide a mathematical framework for the evo lution of such microstructures and discuss algorithms for solving the associated spacetime discretizations. In a finite-step-sized incremental setting of standard dissipative materials (also called generalized standard materials) we outline also details of relaxation-induced microstructure developments for strain softening von Mises plasticity and single-slip crystal plasticity. The numerical implementations are based on simplified assumptions concerning the complexity of the microstructures. © Springer-Verlag Berlin Heidelberg 2006.

URI

https://hdl.handle.net/11511/56945

Journal

Lecture Notes in Applied and Computational Mechanics

DOI

https://doi.org/10.1007/978-3-540-34961-7_15

Collections

Department of Aerospace Engineering, Article

Suggestions

OpenMETU
Core

Analytical Solutions to the Klein-Gordon Equation with Position-Dependent Mass for q-Parameter Poschl-Teller Potential Arda, Altug; Sever, Ramazan; TEZCAN, CEVDET (IOP Publishing, 2010-01-01) The energy eigenvalues and the corresponding eigenfunctions of the one-dimensional Klein-Gordon equation with q-parameter Poschl-Teller potential are analytically obtained within the position-dependent mass formalism. The parametric generalization of the Nikiforov-Uvarov method is used in the calculations by choosing a mass distribution.
Analytical solution of the Schrodinger equation for Makarov potential with any l angular momentum Bayrak, O.; Karakoc, M.; Boztosun, I.; Sever, Ramazan (Springer Science and Business Media LLC, 2008-11-01) We present the analytical solution of the Schrodinger Equation for the Makarov potential within the framework of the asymptotic iteration method for any n and l quantum numbers. Energy eigenvalues and the corresponding wave functions are calculated. We also obtain the same results for the ring shaped Hartmann potential which is the special form of the non-central Makarov potential.
Exact Pseudospin Symmetric Solution of the Dirac Equation for Pseudoharmonic Potential in the Presence of Tensor Potential AYDOĞDU, OKTAY; Sever, Ramazan (Springer Science and Business Media LLC, 2010-04-01) Under the pseudospin symmetry, we obtain exact solution of the Dirac equation for the pseudoharmonic potential in the presence of the tensor potential with arbitrary spin-orbit coupling quantum number kappa. The energy eigenvalue equation of the Dirac particles is found and the corresponding radial wave functions are presented in terms of confluent hypergeometric functions. We investigate the tensor potential dependence of the energy of the each state in the pseudospin doublet. It is shown that degeneracy b...
EXACT SPIN AND PSEUDO-SPIN SYMMETRIC SOLUTIONS OF THE DIRAC-KRATZER PROBLEM WITH A TENSOR POTENTIAL VIA LAPLACE TRANSFORM APPROACH Arda, Altug; Sever, Ramazan (2012-09-28) Exact bound state solutions of the Dirac equation for the Kratzer potential in the presence of a tensor potential are studied by using the Laplace transform approach for the cases of spin- and pseudo-spin symmetry. The energy spectrum is obtained in the closed form for the relativistic as well as non-relativistic cases including the Coulomb potential. It is seen that our analytical results are in agreement with the ones given in the literature. The numerical results are also given in a table for different p...
MUTUAL COUPLING EFFECTS OF FINITE RECTANGULAR PHASED-ARRAYS YAVUZ, H; BUYUKDURA, OM (1994-04-14) A rigorous integral equation formulation for the analysis of a phased array of flangemounted waveguide apertures is given for a finite number of elements and nonuniform spacings. The resulting set of ihtegrd equations is reduced to a matrix equation called the coupling matrix which relates the coefficients of all the modes in all the waveguides to one another. The solution then yields the dominant mode reflection coefficient, coefficients of scattered modes and hence the field in each waveguide. The blockTo...

Citation Formats

E. Gürses, C. Miehe, and A. Mielke, “Analytical and numerical methods for finite-strain elastoplasticity,” Lecture Notes in Applied and Computational Mechanics, pp. 491–529, 2006, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/56945.