On theoretical and numerical methods in the theory of porous media based on polar and non-polar elasto-plastic solid materials

Ehlers, Wolfgang; Volk, Wolfram

doi:10.1016/s0020-7683(98)00086-9

Cited by 117 publications

(99 citation statements)

References 18 publications

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“…In this case it is likely that in the quasi-static elastic limit (Campbell 2002) force chains (Howell, Behringer & Veje 1999), the contact fabric (Toiya, Stambaugh & Losert 2004;Sun & Sundaresan 2011) and shear bands (Wu, Bauer & Kolymbas 1996;Ehlers & Volk 1998) play an important role. In contrast, for large inertial numbers there is a transition to a low-density granular gas dominated by particle collisions (Jenkins & Savage 1983;Goldhirsch 2003).…”

Section: N T Graymentioning

confidence: 99%

Well-posed and ill-posed behaviour of the -rheology for granular flow

et al. 2015

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In light of the successes of the Navier-Stokes equations in the study of fluid flows, similar continuum treatment of granular materials is a long-standing ambition. This is due to their wide-ranging applications in the pharmaceutical and engineering industries as well as to geophysical phenomena such as avalanches and landslides. Historically this has been attempted through modification of the dissipation terms in the momentum balance equations, effectively introducing pressure and strain-rate dependence into the viscosity. Originally, a popular model for this granular viscosity, the Coulomb rheology, proposed rate-independent plastic behaviour scaled by a constant friction coefficient µ. Unfortunately, the resultant equations are always ill-posed. Mathematically ill-posed problems suffer from unbounded growth of short-wavelength perturbations, which necessarily leads to grid-dependent numerical results that do not converge as the spatial resolution is enhanced. This is unrealistic as all physical systems are subject to noise and do not blow up catastrophically. It is therefore vital to seek well-posed equations to make realistic predictions. The recent µ(I)-rheology is a major step forward, which allows granular flows in chutes and shear cells to be predicted. This is achieved by introducing a dependence on the non-dimensional inertial number I in the friction coefficient µ. In this paper it is shown that the µ(I)-rheology is well-posed for intermediate values of I, but that it is ill-posed for both high and low inertial numbers. This result is not obvious from casual inspection of the equations, and suggests that additional physics, such as enduring force chains and binary collisions, becomes important in these limits. The theoretical results are validated numerically using two implicit schemes for non-Newtonian flows. In particular, it is shown explicitly that at a given resolution a standard numerical scheme used to compute steady-uniform Bagnold flow is stable in the well-posed region of parameter space, but is unstable to small perturbations, which grow exponentially quickly, in the ill-posed domain.

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Section: N T Graymentioning

confidence: 99%

Well-posed and ill-posed behaviour of the -rheology for granular flow

et al. 2015

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“…When the microdeformation reduces to its skew symmetric part, the Cosserat model is retrieved [10,16]. The microdeformation is to be compared to the deformation gradient:…”

Section: Micromorphic Model As a Special Casementioning

confidence: 99%

Micromorphic vs. Phase-Field Approaches for Gradient Viscoplasticity and Phase Transformations

Forest

Ammar

Appolaire

2011

Advances in Extended and Multifield Theories for Continua

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Abstract. Strain gradient models and generalized continua are increasingly used to introduce characteristic lengths in the mechanical behavior of materials with microstructure. On the other hand, phase-field models have proved to be efficient tools to simulate microstructure evolution due to thermodynamical processes in the presence of mechanical deformation. It is shown that both methods have strong connections from the point of view of thermomechanical field theory. A general formulation of thermomechanics with additional degrees of freedom is presented that encompasses both applications as special cases. It is based on the introduction of additional power of internal forces introducing generalized stresses. The current knowledge in the formulation of physically non-linear constitutive equations is used to develop strongly coupled elastoviscoplastic material models involving phase transformation and moving boundaries.

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“…Für den Zusammenhang zwischen den mikropolaren Spannungenσ und den elastischen mikropolaren Verzerrungen ε e =ε −ε p wird ein um den schiefsymmetrischen Anteil des Verzerrungstensors erweiterter Hookescher Ansatz gewählt [1]:σ = 2 µε e sym + λ (ε e · I) I + 2 µ cεe skw .…”

Section: Kinematik Und Konstitutivannahmen Mikropolarer Materialienunclassified

“…Dazu wird eine für Reibungsmaterialien geeignete Fließfläche F verwendet [2] und um die Invarianten des schiefsymmetrischen Teils des Spannungstensors sowie des Momentenspannungstensors erweitert [1]. Desweiteren wird ein plastisches Potential G definiert:…”

Section: Kinematik Und Konstitutivannahmen Mikropolarer Materialienunclassified

Inverses Rechnen zur Identifikation der Materialparameter des Cosserat‐Kontinuums

Scholz

Ehlers

2003

Proc Appl Math and Mech

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Bei der Anwendung der Cosserat‐Theorie treten neben den Verschiebungsfreiheitsgraden zusätzliche Rotationsfreiheitsgrade auf. Zur Beschreibung der Deformation wurden demzufolge ein nicht‐symmetrischer Verzerrungstensor sowie ein Krümmungstensor eingeführt. Diesen erweiterten Deformationsmaßen werden über konstitutive Beziehungen ein nicht‐symmetrischer Spannungstensor sowie ein Momentenspannungstensor zugeordnet. Dabei treten neue Materialparameter (z. B. die interne Länge) auf, deren Identifikation das Ziel der vorgestellten Arbeit ist. Da die zusätzlichen Rotationsfreiheitsgrade nur bei inhomogener Deformation aktiviert werden, sind zur Bestimmung der Materialparameter des Cosserat‐Kontinuums inhomogene Versuche sowie deren Nachrechnung als Randwertproblem erforderlich. Dazu stehen an Hostun‐Sand durchgeführte Biaxialversuche zur Verfügung.

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On theoretical and numerical methods in the theory of porous media based on polar and non-polar elasto-plastic solid materials

Cited by 117 publications

References 18 publications

Well-posed and ill-posed behaviour of the -rheology for granular flow

Well-posed and ill-posed behaviour of the -rheology for granular flow

Micromorphic vs. Phase-Field Approaches for Gradient Viscoplasticity and Phase Transformations

Inverses Rechnen zur Identifikation der Materialparameter des Cosserat‐Kontinuums

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