A constitutive model for dry metamorphosed snow is proposed, within the framework of elasto-viscoplasticity, which is able to reproduce the most relevant features of the macroscopic behaviour of snow, particularly its time and rate dependency. The basic ideas for modelling stem from the conceptual forms proposed for bonded geomaterials, such as cemented soils or soft rocks. The high viscosity of snow is accounted for by adopting an overstress approach, suitably modified. An evolution law for the curvature-driven process of sintering, by which intergranular ice necks form and grow, is established. The system of constitutive equations is then numerically integrated via a fully implicit time stepping scheme. Selected results from finite element simulations of laboratory tests, available in the literature, are presented. Copyright © 2009 John Wiley & Sons, Ltd.
viernes, 20 de noviembre de 2009
Numerical integration of an elastic-viscoplastic constitutive model for dry metamorphosed snow
A constitutive model for dry metamorphosed snow is proposed, within the framework of elasto-viscoplasticity, which is able to reproduce the most relevant features of the macroscopic behaviour of snow, particularly its time and rate dependency. The basic ideas for modelling stem from the conceptual forms proposed for bonded geomaterials, such as cemented soils or soft rocks. The high viscosity of snow is accounted for by adopting an overstress approach, suitably modified. An evolution law for the curvature-driven process of sintering, by which intergranular ice necks form and grow, is established. The system of constitutive equations is then numerically integrated via a fully implicit time stepping scheme. Selected results from finite element simulations of laboratory tests, available in the literature, are presented. Copyright © 2009 John Wiley & Sons, Ltd.
On explicit two-derivative Runge-Kutta methods
Abstract The theory of Runge-Kutta methods for problems of the form y′ = f(y) is extended to include the second derivative y′′ = g(y): = f′(y)f(y). We present an approach to the order conditions based on Butcher’s algebraic theory of trees (Butcher, Math Comp 26:79–106,
1972), and derive methods that take advantage of cheap computations of the second derivatives. Only explicit methods are considered
here where attention is given to the construction of methods that involve one evaluation of f and many evaluations of g per step. Methods with stages up to five and of order up to seven including some embedded pairs are presented. The first
part of the paper discusses a theoretical formulation used for the derivation of these methods which are also of wider applicability.
The second part presents experimental results for non-stiff and mildly stiff problems. The methods include those with the
computation of one second derivative (plus many first derivatives) per step, and embedded methods for changing stepsize as
well as those involving one first derivative (plus many second derivatives) per step. The experiments have been performed
on standard problems and comparisons made with some standard explicit Runge-Kutta methods.
1972), and derive methods that take advantage of cheap computations of the second derivatives. Only explicit methods are considered
here where attention is given to the construction of methods that involve one evaluation of f and many evaluations of g per step. Methods with stages up to five and of order up to seven including some embedded pairs are presented. The first
part of the paper discusses a theoretical formulation used for the derivation of these methods which are also of wider applicability.
The second part presents experimental results for non-stiff and mildly stiff problems. The methods include those with the
computation of one second derivative (plus many first derivatives) per step, and embedded methods for changing stepsize as
well as those involving one first derivative (plus many second derivatives) per step. The experiments have been performed
on standard problems and comparisons made with some standard explicit Runge-Kutta methods.
- Content Type Journal Article
- Category Original Paper
- DOI 10.1007/s11075-009-9349-1
- Authors
- Robert P. K. Chan, University of Auckland Department of Mathematics Private Bag 92019 Auckland 1142 New Zealand
- Angela Y. J. Tsai, University of Auckland Department of Mathematics Private Bag 92019 Auckland 1142 New Zealand
- Journal Numerical Algorithms
- Online ISSN 1572-9265
- Print ISSN 1017-1398
A stabilized Lagrange multiplier method for the finite element approximation of contact problems in elastostatics
Abstract In this work we consider a stabilized Lagrange (or Kuhn–Tucker) multiplier method in order to approximate the unilateral contact
model in linear elastostatics. The particularity of the method is that no discrete inf-sup condition is needed in the convergence
analysis. We propose three approximations of the contact conditions well adapted to this method and we study the convergence
of the discrete solutions. Several numerical examples in two and three space dimensions illustrate the theoretical results
and show the capabilities of the method.
model in linear elastostatics. The particularity of the method is that no discrete inf-sup condition is needed in the convergence
analysis. We propose three approximations of the contact conditions well adapted to this method and we study the convergence
of the discrete solutions. Several numerical examples in two and three space dimensions illustrate the theoretical results
and show the capabilities of the method.
- Content Type Journal Article
- DOI 10.1007/s00211-009-0273-z
- Authors
- Patrick Hild, Université de Franche-Comté Laboratoire de Mathématiques de Besançon, CNRS UMR 6623 16 route de Gray 25030 Besançon Cedex France
- Yves Renard, Université de Lyon, CNRS, INSA-Lyon, ICJ UMR 5208, LaMCoS UMR 5259 69621 Villeurbanne France
- Journal Numerische Mathematik
- Online ISSN 0945-3245
- Print ISSN 0029-599X
Geometry of Configuration Spaces of Tensegrities
Abstract Consider a graph G with n vertices. In this paper we study geometric conditions for an n-tuple of points in ℝ
d
to admit a nonzero self-stress with underlying graph G. We introduce and investigate a natural stratification, depending on G, of the configuration space of all n-tuples in ℝ
d
. In particular we find surgeries on graphs that give relations between different strata. Further we discuss questions related
to geometric conditions defining the strata for plane tensegrities. We conclude the paper with particular examples of strata
for tensegrities in the plane with a small number of vertices.
d
to admit a nonzero self-stress with underlying graph G. We introduce and investigate a natural stratification, depending on G, of the configuration space of all n-tuples in ℝ
d
. In particular we find surgeries on graphs that give relations between different strata. Further we discuss questions related
to geometric conditions defining the strata for plane tensegrities. We conclude the paper with particular examples of strata
for tensegrities in the plane with a small number of vertices.
- Content Type Journal Article
- DOI 10.1007/s00454-009-9229-4
- Authors
- Franck Doray, Universiteit Leiden Mathematisch Instituut P.O. Box 9512 2300 RA Leiden The Netherlands
- Oleg Karpenkov, Universiteit Leiden Mathematisch Instituut P.O. Box 9512 2300 RA Leiden The Netherlands
- Jan Schepers, Universiteit Leiden Mathematisch Instituut P.O. Box 9512 2300 RA Leiden The Netherlands
- Journal Discrete and Computational Geometry
- Online ISSN 1432-0444
- Print ISSN 0179-5376
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