Kontinuumsmechanik

Betten, Josef

doi:10.1007/978-3-642-56562-5

Cited by 78 publications

(40 citation statements)

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“…If the flock is linear, that is all planes of the flock share a common line, then the resulting generalised quadrangle is isomorphic to H(3, q 2 ). There exist nonlinear flocks, and so nonclassical flock quadrangles, and these have been classified for all q 37, q = 32 (see [6], [11], [2]). For instance, if q is a prime power congruent to 2 modulo 3, there exist non-linear flock quadrangles known as the Fisher-ThasWalker-Kantor generalised quadrangles.…”

Section: Main Theoremmentioning

confidence: 99%

“…The partial quadrangle PQ (2,25,8) has an associated strongly regular graph with parameters (v, k, λ, µ) = (378, 52, 1, 8). According to [5,Remark 4.3], the parameters of the strongly regular graph above were new at the time of the construction of their 3 · A 7 -hemisystem, and hence we have constructed a second strongly regular graph with these parameters, that is inequivalent to the one known before.…”

Section: Main Theoremmentioning

confidence: 99%

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A hemisystem of a nonclassical generalised quadrangle

Bamberg

Clerck

Durante

2008

Des. Codes Cryptogr.

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The concept of a hemisystem of a generalised quadrangle has its roots in the work of B. Segre, and this term is used here to denote a set of points H such that every line l meets H in half of the points of l. If one takes the point-line geometry on the points of the hemisystem, then one obtains a partial quadrangle and hence a strongly regular point graph. The only previously known hemisystems of generalised quadrangles of order (q, q (2)) were those of the elliptic quadric Q(-)(5, q) , q odd. We show in this paper that there exists a hemisystem of the Fisher-Thas-Walker-Kantor generalised quadrangle of order (5, 5(2)), which leads to a new partial quadrangle. Moreover, we can construct from our hemisystem the 3 . A (7)-hemisystem of Q-(5, 5), first constructed by Cossidente and Penttila

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Section: Main Theoremmentioning

confidence: 99%

Section: Main Theoremmentioning

confidence: 99%

A hemisystem of a nonclassical generalised quadrangle

Bamberg

Clerck

Durante

2008

Des. Codes Cryptogr.

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“…Here, C is an isotropic fourth-order elastic tensor defined by C = λ1 ⊗ 1 + 2µI or expressed in index notation [9,10] as…”

Section: A Chaboche Viscoplastic Law At Small Deformationsmentioning

confidence: 99%

“…This function arises in the plastic potential function and can be used to adjust the center α of the elastic domain. † In some cases, for instance for anisotropic materials, the normality rule cannot furnish complete constitutive equations, as has been pointed out by Betten [9,10] in more detail. Therefore, he developed modified flow rules for both incompressible and compressible anisotropic materials.…”

Section: A Chaboche Viscoplastic Law At Small Deformationsmentioning

confidence: 99%

“…In the theory of finite deformation the tensorial Hencky measure of strain and strain rate plays a central role (see Fitzgerald [19] and Betten [9]) because it can be decomposed into a sum of an isochoric distorsion and a volume change. The problem to present the logarithmic function Y = ln X or Y i j = {ln X} i j as an isotropic tensor function has been solved by Betten [7,8].…”

Section: The Extended Viscoplastic Law At Finite Strainsmentioning

confidence: 99%

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Modeling of finite strain viscoplasticity based on the logarithmic corotational description

Lin

Betten²,

Brocks

2006

Arch Appl Mech

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It has been proven that the deformation rate is identical to the logarithmic corotational rate of the spatial logarithmic strain. Based on the logarithmic corotational description we present an extension of a Chaboche's infinitesimal viscoplastic law for finite strain cases. An additive decomposition of the logarithmic corotational rate of the logarithmic strain, implicitly included in an internal dissipation inequality, is applied for the extension. Functionally, this additive decomposition corresponds to the additive decomposition of the material derivative of the logarithmic strain used in infinitesimal inelastic problems. Using the additive decomposition and replacing the material time derivatives of all second-order tensors in the infinitesimal viscoplastic law with the corresponding logarithmic corotational rates we arrive at a new finite viscoplastic law with nonlinear isotropic and kinematic hardening. The numerical algorithms suitable for the finite element implementation of this law are formulated and several numerical examples are presented. These numerical examples prove that the finite viscoplastic law and the algorithms are effective and reliable.

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Constitutive Modeling of the Mechanical Behavior of Trabecular Bone – Continuum Mechanical Approaches

Öchsner

Hosseini

2010

Biomechanics of Hard Tissues

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Typical uniaxial stress-strain curves for different types of bones are shown in Figure 6.1 for the compressive regime. For all the curves, an initial linear elastic behavior can be observed. The common approach is to describe this elastic part on the basis of Hooke's law, cf. Sections 6.3.1-6.3.4. This elastic range is followed by a strong nonlinear behavior of almost constant stress (so-called stress plateau). At higher strains, some curves show a strong increase in the stress where densification begins.These macroscopic stress-strain curves are similar to the behavior known from completely different types of materials such as cellular polymers and metals or even concrete. Although the deformation mechanism on the microlevel can be completely different, a common approach is to use the constitutive equations of metal plasticity to describe the nonelastic behavior, cf. [1-3]. As we see in this chapter, bones have some kind of cellular or porous structure, and the classical equations of full dense metals (e.g., von Mises or Tresca) must be extended by at least the hydrostatic pressure to account for the fact that such a material is even in the plastic range compressible. This general theory of a yield or failure surface based on stress invariants is introduced in Section 6.3.5. Many extensions of this theory are known for bones. However, the main focus is to thoroughly introduce the concept of a yield and limit surface so that possible extensions (e.g., by damage variables or the consideration of anisotropy) are easier to incorporate.Many different approaches to derive new constitutive equations are known. Nowadays, the finite element method is the standard tool in computational engineering and advanced analysis tools (e.g., µCT) allow an extremely detailed imaging of bone structure. More and more powerful computer hardware (RAM and CPU) enables and supports this trend. However, there are approaches based on simplified model structures that reveal some advantages compared to these highly computerized approaches. Thus, some classical model structures are presented in the second part of the chapter. These simpler models are, in many cases, able to consider the major physical effect and may finally yield a mathematical equation to

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Kontinuumsmechanik

Cited by 78 publications

References 0 publications

A hemisystem of a nonclassical generalised quadrangle

A hemisystem of a nonclassical generalised quadrangle

Modeling of finite strain viscoplasticity based on the logarithmic corotational description

Constitutive Modeling of the Mechanical Behavior of Trabecular Bone – Continuum Mechanical Approaches

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