On the Relationship between the Logarithmic Strain Rate and the Stretching Tensor.

Die Barodesie ist ein Materialmodell für granulare Materialien, das gewisse Ähnlichkeiten mit der Hypoplastizität aufweist. Sie wurde von Kolymbas eingeführt und basiert auf den Hypothesen von Goldscheider für das asymptotische Bodenverhalten. Gängige Beziehungen der Bodenmechanik, wie z. B. die Beziehung für die Steifigkeit von Ohde bzw. Janbu, eine Spannungs‐Dilatanz‐Beziehung und Prinzipien der Critical State Soil Mechanics, lassen sich leicht in das vorgestellte Modell einbeziehen. In diesem Artikel werden die Konzepte der Barodesie an einfachen und bekannten Beispielen (zum Teil eindimensional) erklärt. Der Text ist damit ein guter Einstieg in die Barodesie und Materialmodellierung.

show abstract

“…Für Quaderverformungen ist die Zeitrate des Tensors der logarithmischen Verzerrungen

\frac{italicdε}{italicdt} = \dot{ε}

gleich dem Stretchingtensor . Allgemein gilt für kleine Verzerrungen: D ≈ ε̇ .…”

Section: Begriffe Und Notationunclassified

Konzepte der Barodesie

2018

View full text Add to dashboard Cite

show abstract

“…The logarithmic description 1 is arguably the simplest approach to finite plasticity, suitable for the phenomenological description of isotropic polycrystalline metals if the structure of geometrically linear theories is used with respect to the Lagrangian logarithmic strain. In this paper we do not consider hypoelastic-plastic models [72,22,43,96] in which, contrary to hyperelastic models, the potential character of the elastic energy is ignored [42,52]. Otherwise, they are simply the hyperelastic models rewritten in a suitable incremental form.…”

Section: Preliminariesmentioning

confidence: 99%

The exponentiated Hencky-logarithmic strain energy: part III—coupling with idealized multiplicative isotropic finite strain plasticity

Neff

Ghiba

2015

Continuum Mech. Thermodyn.

View full text Add to dashboard Cite

We investigate an immediate application in finite strain multiplicative plasticity of the family of isotropic volumetric-isochoric decoupled strain energieswhere ∂ χ is the subdifferential of the indicator function χ of the convex elastic domain Ee(Wiso, Σe, 1 3 σ 2 y ) in the mixedvariant Σe-stress space and Σe = F T e DF e Wiso(Fe). While W eH may loose ellipticity, we show that loss of ellipticity is effectively prevented by the coupling with plasticity, since the ellipticity domain of W eH on the one hand, and the elastic domain in Σe-stress space on the other hand, are closely related. Thus the new formulation remains elliptic in elastic unloading at any given plastic predeformation. In addition, in this domain, the true-stress-true-strain relation remains monotone, as observed in experiments.

show abstract

“…For the large deformation of isotropic elastic bodies, we adopt the following elastic constitutive equations :

bold-italicT MathClass-rel= bold-italicC MathClass-punc: bold-italicE (i.e., \overset{bold-italicT}{true} MathClass-rel= bold-italicC MathClass-punc: bold-italicD) MathClass-punc,

where T is the Cauchy stress tensor, E is the Hencky strain tensor,

\overset{bold-italicT}{true}

is the Jaumann rate of the Cauchy stress, D is the stretching tensor, and C is the fourth order elasticity tensor described as

C_{ijkl} MathClass-rel= λ δ_{ij} δ_{kl} MathClass-bin+ 2 μ δ_{ik} δ_{jl} MathClass-punc,

where λ and μ are the Lame's parameters.…”

Section: Constitutive Equationsmentioning

confidence: 99%

Floating stress‐point integration meshfree method for large deformation analysis of elastic and elastoplastic materials

Ônishi

Amaya

2012

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARY A new meshfree formulation of stress‐point integration, called the floating stress‐point integration meshfree method, is proposed for the large deformation analysis of elastic and elastoplastic materials. This method is a Galerkin meshfree method with an updated Lagrangian procedure and a quasi‐implicit time‐advancing scheme without any background cell for domain integration. Its new formulation is based on incremental equilibrium equations derived from the incremental virtual work equation, which is not generally used in meshfree formulations. Hence, this technique allows the temporal continuity of the mechanical equilibrium to be naturally achieved. The details of the new formulation and several examples of the large deformation analysis of elastic and elastoplastic materials are presented to show the validity and accuracy of the proposed method in comparison with those of the finite element method. Copyright © 2012 John Wiley & Sons, Ltd.

show abstract

On the Relationship between the Logarithmic Strain Rate and the Stretching Tensor.

Cited by 7 publications

References 0 publications

Konzepte der Barodesie

Konzepte der Barodesie

The exponentiated Hencky-logarithmic strain energy: part III—coupling with idealized multiplicative isotropic finite strain plasticity

Floating stress‐point integration meshfree method for large deformation analysis of elastic and elastoplastic materials

Contact Info

Product

Resources

About