Numerical Study on Crack Dilatancy Part I: Models and Stability Analysis

Feenstra, P.H.; Borst, René de; Rots, J.G.

doi:10.1061/(asce)0733-9399(1991)117:4(733)

Cited by 34 publications

(10 citation statements)

References 6 publications

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“…The strain components, assembled in the vector Ε = (ε xx , ε yy , ε ZZ , ε xy ) are related to the displacement vector u = (u x , u y ) by the matrix L as indicated in (17). The total strain rate is additively decomposed into an elastic part e and a plastic part p .…”

Section: The Non-local Conceptmentioning

confidence: 99%

“…Restricting attention to flow theories of plasticity and small deformation gradients, and neglecting body forces the elasto-plastic rate problem is completely defined by the equilibrium condition: (16) the kinematic relation: (17) and a set of constitutive equations: (18) (19) (20) subject to the constraints: (21) In (16)- (21) σ is a vector that contains the stress components, e.g. σ = (σ xx , σ yy , σ zz , σ xy ) for a two-dimensional configuration and L is a differential operator matrix, which, for the two-dimensional case, is conveniently defined as:…”

Section: The Non-local Conceptmentioning

confidence: 99%

“…A discrete mechanical system then attains the limiting case of a neutrally stable equilibrium (loss of positive-definiteness of K) if 6,17 :…”

Section: Mathematical Implicationsmentioning

confidence: 99%

See 2 more Smart Citations

Fundamental Issues in Finite Element Analyses of Localization of Deformation

Borst

Sluys

Mühlhaus

et al. 1993

Engineering Computations

573

303

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Classical continuum models, i.e. continuum models that do not incorporate an internal length scale, suffer from excessive mesh dependence when strain-softening models are used in numerical analyses and cannot reproduce the size effect commonly observed in quasi-brittle failure. In this contribution three different approaches will be scrutinized which may be used to remedy these two intimately related deficiencies of the classical theory, namely (i) the addition of higher-order deformation gradients, (ii) the use of micropolar continuum models, and (iii) the addition of rate dependence. By means of a number of numerical simulations it will be investigated under which conditions these enriched continuum theories permit localization of deformation without losing ellipticity for static problems and hyperbolicity for dynamic problems. For the latter class of problems the crucial role of dispersion in wave propagation in strain-softening media will also be highlighted.

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Section: The Non-local Conceptmentioning

confidence: 99%

Section: The Non-local Conceptmentioning

confidence: 99%

See 1 more Smart Citation

Fundamental Issues in Finite Element Analyses of Localization of Deformation

Borst

Sluys

Mühlhaus

et al. 1993

Engineering Computations

573

303

View full text Add to dashboard Cite

show abstract

“…No separate stability study has been undertaken for the present model, in the sense of that undertaken by Feenstra et al [9,10], but as with any model that involves the simulation of softening behaviour, the tangent constitutive matrix of the present model can become non-positive definite. In such cases it can be advantageous, when the model is applied in a finite element code, to use an approximate tangent matrix, which maintains positive definiteness.…”

Section: Comments Thermodynamic Validity and Stabilitymentioning

confidence: 96%

Constitutive modelling of aggregate interlock in concrete

Jefferson

2002

Num Anal Meth Geomechanics

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SUMMARYA model for formed cracks in concrete is presented. The model can be used in isolation for existing cracks or linked with other damage or plasticity models and applied once a crack has fully formed. It can be applied directly to interface finite elements or used to control the behaviour of crack planes in more general constitutive models that are applied to 2D and 3D continuum elements. The focus of the present development is on aggregate interlock and crack closing behaviour, which is examined from available experimental data. A contact function is derived and is used to differentiate between three contact states. These states are named open, where there is no contact, interlock, for which the stresses depend upon the nearest distance to the contact surface and closed, for which the stresses depend upon the relative displacements directly. The model is developed within an elasto-plastic framework using effective stresses, which are related to the total stresses via a contact proportion function. The relationship between the effective normal and shear yield stresses is found to be parabolic and the yield shear stress to be dependent upon the opening and embedment displacements. The performance of the model is assessed against experimental data from shear-normal tests and it is concluded that the model is able to represent the key characteristics of the behaviour of formed cracks in concrete.

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“…Several researchers tried to improve this type of methods (Nilson [162] (1968), Grootenboer et al [163] (1981), Feenstra et al [164] (1991), Rots [165] (1991), Xie and Gerstle [166] (1995), Bittencourt and Ingraffea [167] (1995), Riddell et al [168] (1997), Ruiz et al [169] (2001), Galvez et al [170] (2002), Prasad and Krishnamoorthy [171] (2002), Dias-da-Costa [172] (2009)). Nevertheless, all numerical tests that are encountered in the literature are strictly limited to simple structural Page 101 of 272 member implementations pointing the major disadvantage of this approach when it comes to multi-member RC structures.…”

Section: Discrete Crack Modelsmentioning

confidence: 99%

Detailed three - dimensional nonlinear hybrid simulation for the analysis of large - scale reinforced concrete structures

Markou¹

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S u p e r v i s i n g P r o f e s s o rM a n o l i s P a p a d r a k a k i s A t h e n s , J a n 2 0 1 1 G Ge eo or rg ge e M Ma ar rk ko ou u N a t i o n a l T e c h n i c a l U n i v e r s i t y o f A t h e n s S c h o o l o f C i v i l E n g i n e e r i n g I n s t i t u t e o f S t r u c t u r a l A n a l y s i s a n d S e i s m i c R e s e a r c h ΕυχαριςτίεσΠξσηίζησο ζα ήζεια λα επραξηζηήζσ ηνλ επηβιέπνληά κνπ, Καζεγεηή Μαλόιε Παπαδξαθάθε, γηα ηελ επθαηξία πνπ κνπ έδσζε λα αζρνιεζώ κε εξεπλεηηθά ζέκαηα αηρκήο, ηα νπνία έρνπλ άκεζε εθαξκνγή κέζσ ηεο Μεζόδνπ ησλ Πεπεξαζκέλσλ ηνηρείσλ θαη αθνξνύλ ηελ επίιπζε πξαθηηθώλ πξνβιεκάησλ Πνιηηηθνύ θαη Αεξνλαππεγνύ Μεραληθνύ. Μέζσ ηεο παξαγσγηθήο καο ζπλεξγαζίαο θαη ηεο επηζηεκνληθήο ηνπ θαζνδήγεζεο, θαηάθεξε λα κνπ ππνδείμεη ην απεξηόξηζην ησλ δπλαηνηήησλ κνπ θαη λα ζέζεη ςηινύο εξεπλεηηθνύο ζηόρνπο ζηα πιαίζηα ηεο παξνύζαο Γηαηξηβήο. Γηα όια απηά πνπ κνπ έρεη πξνζθέξεη, ζα ήζεια λα εθθξάζσ ηελ βαζηά κνπ επγλσκνζύλε.Θα ήζεια λα εθθξάζσ έλα κεγάιν επραξηζηώ ζηνλ ζπλάδειθν αιιά θαη θίιν, Τπνςήθην Γηδάθηνξα Μέηζε Παλαγηώηε κε ηνλ νπνίν πεξάζακε ακέηξεηεο ώξεο ζπδεηώληαο επνηθνδνκεηηθά γηα δηάθνξα επηζηεκνληθά ζέκαηα. Δπηπιένλ έλα κεγάιν επραξηζηώ γηα ηελ αληδηνηειή βνήζεηά ηνπ ε νπνία ήηαλ πξαγκαηηθά αλεθηίκεηεο αμίαο.Δλ ζπλερεία, ζα ήζεια λα επραξηζηήζσ ηα άιια δύν κέιε ηεο Σξηκεινύο Δπηηξνπήο, Καζεγεηή Μηραήι Κνηζνβό θαη Δπίθνπξν Καζεγεηή Υξίζην Εέξε, γηα ηηο ελδηαθέξνπζεο ζπδεηήζεηο πνπ είρακε ζε ζέκαηα ηεο Γηδαθηνξηθήο Γηαηξηβήο αιιά θαη ηελ παξνρή βνήζεηαο ζε εξεπλεηηθό επίπεδν, όπνηε απηή είρε δεηεζεί. Οη ζπκβνπιέο θαη ηα ζρόιηά ηνπο βνήζεζαλ ζεκαληηθά ζηε βειηίσζε ηεο παξνύζαο εξγαζίαο.Θα ήζεια λα εθθξάζσ ηελ βαζηά κνπ εθηίκεζε ζηνπο Καζεγεηή Βιάζε Κνπκνύζε θαη Αλαπιεξσηή Καζεγεηή Κσλζηαληίλν πειηόπνπιν, νη νπνίνη ήηαλ πάληα δηαζέζηκνη γηα επνηθνδνκεηηθά ζρόιηα θαη ζπκβνπιέο επί ηνπ εξεπλεηηθνύ κνπ έξγνπ.Δπραξηζηώ όια ηα κέιε ηεο 7-κεινύο επηηξνπήο θαη εηδηθόηεξα ηνλ θαζ. Κάππν, γηα ηα επνηθνδνκεηηθά ηνπο ζρόιηα θαη παξαηεξήζεηο νη νπνίεο βνήζεζαλ ζηελ βειηίσζε ηεο παξνύζαο Γηαηξηβήο.Θα ήζεια επίζεο λα επραξηζηήζσ ηνλ Γξ Γηώξγν ηαπξνπιάθε γηα ηελ ζπλεξγαζία πνπ είρακε ζηα πιαίζηα ηεο εξεπλεηηθήο νκάδαο ηνπ Καζεγεηή Μαλόιε Παπαδξαθάθε θαη ε νπνία ήηαλ πάληνηε επράξηζηε θαη επνηθνδνκεηηθή. Δπίζεο ζα ήζεια λα εθθξάζσ ηελ εθηίκεζή κνπ ζηνπο Γξ. Μηράιε Φξαγθηαδάθε, Γξ. Γεώξγην Λπθίδε, Γξ. Αξηζηείδε Παπαρξεζηίδε θαη Τπνςήθην Γηδάθηνξα Κσλζηαληίλν Παπαληθνιόπνπιν γηα ηηο πνιύηηκεο ζπκβνπιέο ηνπο επί ηνπ εξεπλεηηθνύ κνπ έξγνπ.ηα πιαίζηα ηεο Γηδαθηνξηθήο Γηαηξηβήο εθπνλήζεθαλ δύν Γηπισκαηηθέο θαη κία Μεηαπηπρηαθή Δξγαζία από ηελ ηεθαλία Βαζηινκηρειάθε θαη ηνλ Παλαγηώηε Καξαθίηζην, νη νπνίνη κέζα από ηελ ζρνιαζηηθή ηνπο δνπιεηά ζπληέιεζαλ ζεκαληηθά ζηελ εθηελή παξακεηξηθή δηεξεύλεζε ηνπ θώδηθα πεπεξαζκέλσλ ζηνηρείσλ πνπ αλαπηύρζεθε ζηα πιαίζηα Ευχαριςτύεσ Athens, Jan 2011ii ηνπ εξεπλεηηθνύ απηνύ έξγνπ. Θα ήζεια λα ηνπο επραξηζηήζσ γηα ηελ άξηζηε θαη ζπλάκα επνηθνδνκεηηθή ζπλεξγαζία καο.Θα ήζεια λα επραξηζηήζσ ηνλ Καζεγεηή Κπξηάθν Γηαλλάθνγινπ, ηνλ Λέθηνξα Γήκν Υαξκπή, ηνλ...

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Numerical Study on Crack Dilatancy Part I: Models and Stability Analysis

Cited by 34 publications

References 6 publications

Fundamental Issues in Finite Element Analyses of Localization of Deformation

Fundamental Issues in Finite Element Analyses of Localization of Deformation

Constitutive modelling of aggregate interlock in concrete

Detailed three - dimensional nonlinear hybrid simulation for the analysis of large - scale reinforced concrete structures

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