Analysis of material instabilities in inelastic solids by incremental energy minimization and relaxation methods: evolving deformation microstructures in finite plasticity

Date

2004-12-01

Author

MIEHE, CHRISTIAN
LAMBRECHT, MATTHIAS
Gürses, Ercan

Metadata

Show full item record

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

Item Usage Stats

153
views

0
downloads

We propose an approach to the definition and analysis of material instabilities in rate-independent standard dissipative solids at finite strains based on finite-step-sized incremental energy minimization principles. The point of departure is a recently developed constitutive minimization principle for standard dissipative materials that optimizes a generalized incremental work function with respect to the internal variables. In an incremental setting at finite time steps this variational problem defines a quasi-hyperelastic stress potential. The existence of this potential allows to be recast a typical incremental boundary-value problem of quasi-static inelasticity into a principle of minimum incremental energy for standard dissipative solids. Mathematical existence theorems for sufficiently regular minimizers then induce a definition of the material stability of the inelastic material response in terms of the sequentially weakly lower semicontinuity of the incremental variational functional. As a consequence, the incremental material stability of standard dissipative solids may be defined in terms of the quasi-convexity or the rank-one convexity of the incremental stress potential. This global definition includes the classical local Hadamard condition but is more general. Furthermore, the variational setting opens up the possibility to analyze the post-critical development of deformation microstructures in non-stable inelastic materials based on energy relaxation methods. We outline minimization principles of quasi- and rank-one convexifications of incremental non-convex stress potentials for standard dissipative solids. The general concepts are applied to the analysis of evolving deformation microstructures in single-slip plasticity. For this canonical model problem, we outline details of the constitutive variational formulation and develop numerical and semi-analytical solution methods for a first-level rank-one convexification. A set of representative numerical investigations analyze the development of deformation microstructures in the form of rank-one laminates in single slip plasticity for homogeneous macro-deformation modes as well as inhomogeneous macroscopic boundary-value problems. The well-posedness of the relaxed variational formulation is indicated by an independence of typical finite element solutions on the mesh-size.

Subject Keywords

Mechanical Engineering, Mechanics of Materials, Condensed Matter Physics

URI

https://hdl.handle.net/11511/48790

Journal

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS

DOI

https://doi.org/10.1016/j.jmps.2004.05.011

Collections

Department of Aerospace Engineering, Article

Suggestions

OpenMETU
Core

Modeling of the atomic ordering processes in Fe3Al intermetallics by the Monte Carlo simulation method combined with electronic theory of alloys Mehrabov, Amdulla; Akdeniz, Mahmut Vedat (Springer Science and Business Media LLC, 2003-12-01) The evolution of atomic ordering processes in Fe3Al has been modeled by the Monte Carlo (MC) simulation method combined with the electronic theory of alloys in pseudopotential approximation. The magnitude of atomic ordering energies of atomic pairs in the Fe3Al system has been calculated by means of electronic theory in pseudopotential approximation up to sixth coordination spheres and subsequently used as input data for MC simulation for more detailed analysis for the first time. The Bragg–Williams long-ra...
Preconditioning Techniques for Nonsymmetric Linear Systems in the Computation of Incompressible Flows Manguoğlu, Murat; Saied, Faisal; Tezduyar, Tayfun E.; Sathe, Sunil (ASME International, 2009-03-01) In this paper we present effective preconditioning techniques for solving the nonsymmetric systems that arise from the discretization of the Navier-Stokes equations. These linear systems are solved using either Krylov subspace methods or the Richardson scheme. We demonstrate the effectiveness of our techniques in handling time-accurate as well as steady-state solutions. We also compare our solvers with those published previously. [DOI: 10.1115/1.3059576]
A micro macro approach to rubber like materials Part II The micro sphere model of finite rubber viscoelasticity Christian, Miehe; Göktepe, Serdar (Elsevier BV, 2005-10-01) A micromechanically based non-affine network model for finite rubber elasticity incorporating topological constraints was discussed in Part 1 (2004. J. Mech. Phys. Solids 52, 2617-2660) of this work. In this follow-up contribution we extend the non-affine microsphere model towards the description of time-dependent viscoelastic effects. The viscoelastic network model is constructed by an additive split of the overall response into elastic equilibrium-stress and viscoelastic overstress contributions. The equi...
Multi-scale characterization of particle clustering in discontinuously reinforced composites CETIN, Arda; Kalkanlı, Ali (Elsevier BV, 2009-06-01) The applicability of a quantitative characterization scheme for cluster detection in particle reinforced composites is discussed. The method considers the pattern from the perspective of individual particles, so that even in a pattern that globally conforms to a random distribution, micro-scale heterogeneities can be detected. The detected clusters are visualized by kernel surfaces. Results indicate that the presented methodology is an effective discriminator of clusters and can successfully be used for qua...
A variational multiscale constitutive model for nanocrystalline materials Gürses, Ercan (Elsevier BV, 2011-03-01) This paper presents a variational multi-scale constitutive model in the finite deformation regime capable of capturing the mechanical behavior of nanocrystalline (nc) fcc metals. The nc-material is modeled as a two-phase material consisting of a grain interior phase and a grain boundary effected zone (GBAZ). A rate-independent isotropic porous plasticity model is employed to describe the GBAZ, whereas a crystal-plasticity model which accounts for the transition from partial dislocation to full dislocation m...

Citation Formats

C. MIEHE, M. LAMBRECHT, and 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, pp. 2725–2769, 2004, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48790.