On evolving deformation microstructures in non-convex partially damaged solids

Handle URI:
http://hdl.handle.net/10754/561784
Title:
On evolving deformation microstructures in non-convex partially damaged solids
Authors:
Gurses, Ercan; Miehe, Christian
Abstract:
The paper outlines a relaxation method based on a particular isotropic microstructure evolution and applies it to the model problem of rate independent, partially damaged solids. The method uses an incremental variational formulation for standard dissipative materials. In an incremental setting at finite time steps, the formulation defines a quasi-hyperelastic stress potential. The existence of this potential allows a typical incremental boundary value problem of damage mechanics to be expressed in terms of a principle of minimum incremental work. Mathematical existence theorems of minimizers then induce a definition of the material stability in terms of the sequential weak lower semicontinuity of the incremental functional. As a consequence, the incremental material stability of standard dissipative solids may be defined in terms of weak convexity notions of the stress potential. Furthermore, the variational setting opens up the possibility to analyze the development of deformation microstructures in the post-critical range of unstable inelastic materials based on energy relaxation methods. In partially damaged solids, accumulated damage may yield non-convex stress potentials which indicate instability and formation of fine-scale microstructures. These microstructures can be resolved by use of relaxation techniques associated with the construction of convex hulls. We propose a particular relaxation method for partially damaged solids and investigate it in one- and multi-dimensional settings. To this end, we introduce a new isotropic microstructure which provides a simple approximation of the multi-dimensional rank-one convex hull. The development of those isotropic microstructures is investigated for homogeneous and inhomogeneous numerical simulations. © 2011 Elsevier Ltd. All rights reserved.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Physical Sciences and Engineering (PSE) Division
Publisher:
Elsevier BV
Journal:
Journal of the Mechanics and Physics of Solids
Issue Date:
Jun-2011
DOI:
10.1016/j.jmps.2011.01.002
Type:
Article
ISSN:
00225096
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorGurses, Ercanen
dc.contributor.authorMiehe, Christianen
dc.date.accessioned2015-08-03T09:04:32Zen
dc.date.available2015-08-03T09:04:32Zen
dc.date.issued2011-06en
dc.identifier.issn00225096en
dc.identifier.doi10.1016/j.jmps.2011.01.002en
dc.identifier.urihttp://hdl.handle.net/10754/561784en
dc.description.abstractThe paper outlines a relaxation method based on a particular isotropic microstructure evolution and applies it to the model problem of rate independent, partially damaged solids. The method uses an incremental variational formulation for standard dissipative materials. In an incremental setting at finite time steps, the formulation defines a quasi-hyperelastic stress potential. The existence of this potential allows a typical incremental boundary value problem of damage mechanics to be expressed in terms of a principle of minimum incremental work. Mathematical existence theorems of minimizers then induce a definition of the material stability in terms of the sequential weak lower semicontinuity of the incremental functional. As a consequence, the incremental material stability of standard dissipative solids may be defined in terms of weak convexity notions of the stress potential. Furthermore, the variational setting opens up the possibility to analyze the development of deformation microstructures in the post-critical range of unstable inelastic materials based on energy relaxation methods. In partially damaged solids, accumulated damage may yield non-convex stress potentials which indicate instability and formation of fine-scale microstructures. These microstructures can be resolved by use of relaxation techniques associated with the construction of convex hulls. We propose a particular relaxation method for partially damaged solids and investigate it in one- and multi-dimensional settings. To this end, we introduce a new isotropic microstructure which provides a simple approximation of the multi-dimensional rank-one convex hull. The development of those isotropic microstructures is investigated for homogeneous and inhomogeneous numerical simulations. © 2011 Elsevier Ltd. All rights reserved.en
dc.publisherElsevier BVen
dc.subjectDamage mechanicsen
dc.subjectEnergy relaxationen
dc.subjectMaterial instabilitiesen
dc.subjectMicrostructuresen
dc.subjectNon-convex variational problemsen
dc.titleOn evolving deformation microstructures in non-convex partially damaged solidsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalJournal of the Mechanics and Physics of Solidsen
dc.contributor.institutionInstitute of Applied Mechanics, University of Stuttgart, Pfaffenwaldring 7, 70550 Stuttgart, Germanyen
kaust.authorGurses, Ercanen
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