An implicit gradient formulation for microplane Drucker-Prager plasticity

Zreid, Imadeddin; Kaliske, Michael

doi:10.1016/j.ijplas.2016.04.013

Cited by 59 publications

(21 citation statements)

References 48 publications

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“…Standard gradient damage models are regularly used to model failure. [33][34][35] Even though, from the algorithmic and structural point of view, these models are similar to the variational approaches, the physical background is relatively different. 36 A distinctive drawback of gradient damage models is the lack of the Γ-convergence property.…”

Section: Introductionmentioning

confidence: 99%

Variational eigenerosion for rate‐dependent plasticity in concrete modeling at small strain

Qinami

Pandolfi

Kaliske

2019

Numerical Meth Engineering

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Summary In the context of eigenfracture scheme, the work at hand introduces a variational eigenerosion approach for inelastic materials. The theory seizes situations where the material accumulates large amounts of plastic deformations. For these cases, the surface energy entering the energy balance equation is rescaled to favor fracture, thus energy minimization delivers automatically the crack‐tracking solution also for inelastic cases. The minimization approach is sound and preserves the mathematical properties necessary for the Γ‐limit proof, thus the existence of (local) minimizers is guaranteed by the Γ‐convergence theory. Although it is not possible to demonstrate that the obtained minimizers are global, satisfactory results are obtained with the local minimizers provided by the method. Furthermore, with the goal of addressing the constitutive behavior of concrete, a Drucker‐Prager viscoplastic consistency model is introduced in the microplane setting. The model delivers a rate‐dependent three‐surface smooth yield function that requires hardening and hardening‐rate parameters. The independent evolution of viscoplasticity in different microplanes induces anisotropy in the mechanical response. The sound performance of the model is illustrated via numerical examples for both rate‐independent and rate‐dependent plasticity.

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Section: Introductionmentioning

confidence: 99%

Variational eigenerosion for rate‐dependent plasticity in concrete modeling at small strain

Qinami

Pandolfi

Kaliske

2019

Numerical Meth Engineering

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“…Macroscopic plastic yielding occurs due to frictional sliding of particles or formation and compression of voids in porous material at microscale. Numerical works of Zreid and Kaliske [20,21] demonstrate the sound predictive capacity of the Drucker-Prager model in recovering the experimentally determined mechanical behaviour of concrete that comprises a matrix of rocky material and a binder. On the other hand, Griffith's criterion [22] is among the most popular theories to describe fracturing in linear elastic materials.…”

Section: Introductionmentioning

confidence: 90%

Multiphase-field modelling of crack propagation in geological materials and porous media with Drucker-Prager plasticity

et al. 2020

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A multiphase-field approach for elasto-plastic and anisotropic brittle crack propagation in geological systems consisting of different regions of brittle and ductile materials is presented and employed to computationally study crack propagation. Plastic deformation in elasto-plastic materials such as frictional, granular or porous materials is modelled with the pressure-sensitive Drucker-Prager plasticity model. This plasticity model is combined with a multiphase-field model fulfilling the mechanical jump conditions in diffuse solid-solid interfaces. The validity of the plasticity model with phase-inherent stress and strain fields is shown, in comparison with sharp interface finite element solutions. The proposed model is capable of simulating crack formation in heterogeneous multiphase systems comprising both purely elastic and inelastic phases. We investigate the influence of different material parameters on the crack propagation with tensile tests in single- and two-phase materials. To show the applicability of the model, crack propagation in a multiphase domain with brittle and elasto-plastic components is performed.

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“…Nachfolgend werden die Kernpunkte des Modells skizziert. Eine detailliertere Herleitung und Analyse des Modells ist in nachzulesen. Das Modell basiert auf der Auswertung des Fließkriteriums für effektive Spannungen, die anschließend für die Ermittlung der Materialschädigung benutzt werden.…”

Section: Deterministisches Simulationsmodell Für Betontragwerke – Graunclassified

“…Dabei ist der Übergangsbereich zwischen der ursprünglichen Fließfläche und den Kappen von besonderer Bedeutung, da hier nicht stetige Übergänge zu numerischen Schwierigkeiten führen. Im hier beschriebenen Modell wird die in Bild gezeigt Fließfunktion

\begin{matrix} left \\ f^{mic} (σ_{normalD}^{normale}, σ_{normalV}^{normale}, κ) = \frac{3}{2} {bold-italicσ}_{normalD}^{normale} \cdot σ_{normalD}^{normale} - f_{1}^{2} (σ_{normalV}^{normale}, κ) \\ f_{normalc} (σ_{normalV}^{normale}, κ) f_{normalt} (σ_{normalV}^{normale}, κ) \end{matrix}

verwendet, die in entwickelt und detailliert vorgestellt ist. Sie basiert auf der Auswertung der durch ein hochgestelltes „e“ bezeichneten effektiven (d. h. ungeschädigten) volumetrischen und deviatorischen Spannungsanteile

σ_{normalV}^{normale}

und

σ_{normalD}^{normale}

sowie der Verfestigungsvariable κ .…”

Section: Deterministisches Simulationsmodell Für Betontragwerke – Graunclassified

Zur Fortentwicklung des Microplane‐Modells für die numerische Analyse von Betonstrukturen

et al. 2019

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Weltweit ist Stahlbeton der meist angewendete Baustoff im Bauwesen. Grundlage einer qualitativ hochwertigen und effizienten deterministischen Analyse ist die nichtlineare numerische Modellierung. Aus der Vielzahl der aktuellen Entwicklungen ist die Beschreibung der Betoncharakteristiken mit dem Microplane‐Modell ausgewählt. Die wesentlichen Aspekte und Vorteile der Vorgehensweisen werden vorgestellt und an sehr anschaulichen praktischen Beispielen gezeigt. Die Implementierung der Modelle in kommerzielle Programme ist weit vorangeschritten, sodass eine breite Nutzung zukünftig möglich sein wird. Der vorliegende Beitrag wurde am 19. Okt. 2018 im Rahmen des 22. Dresdner Baustatik Seminars präsentiert.

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An implicit gradient formulation for microplane Drucker-Prager plasticity

Cited by 59 publications

References 48 publications

Variational eigenerosion for rate‐dependent plasticity in concrete modeling at small strain

Variational eigenerosion for rate‐dependent plasticity in concrete modeling at small strain

Multiphase-field modelling of crack propagation in geological materials and porous media with Drucker-Prager plasticity

Zur Fortentwicklung des Microplane‐Modells für die numerische Analyse von Betonstrukturen

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