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Mechanics of Material Forces

  • Conference proceedings
  • © 2005

Overview

Editors:
  1. Paul Steinmann

    1. University of Kaiserslautern, Germany

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  2. Gérard A. Maugin

    1. Université Pierre et Marie Curie, Paris, France

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  • Contains all recent developments, both theoretical and numerical, in the field of Eshelbian mechanics
  • Includes supplementary material: sn.pub/extras

Part of the book series: Advances in Mechanics and Mathematics (AMMA, volume 11)

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Table of contents (33 papers)

  1. Front Matter

    Pages i-xv
    Download chapter PDF

  2. 4d Formalism

    1. On Establishing Balance and Conservation Laws in Elastodynamics

      • George Herrmann, Reinhold Kienzler
      Pages 1-11

    2. From Mathematical Physics to Engineering Science

      • Gérard A. Maugin
      Pages 13-22

  3. Evolving Interfaces

    1. The Unifying Nature of the Configurational Force Balance

      • Eliot Fried, Morton E. Gurtin
      Pages 25-32

    2. Generalized Stefan Models

      • Alexandre Danescu
      Pages 33-41

    3. Explicit Kinetic Relation from “First Principles”

      • Lev Truskinovsky, Anna Vainchtein
      Pages 43-50

  4. Growth & Biomechanics

    1. Surface and Bulk Growth Unified

      • Antonio DiCarlo
      Pages 53-64

    2. Mechanical and Thermodynamical Modelling of Tissue Growth Using Domain Derivation Techniques

      • Jean Francois Ganghoffer
      Pages 65-75

    3. Material Forces in the Context of Biotissue Remodelling

      • Krishna Garikipati, Harish Narayanan, Ellen M. Arruda, Karl Grosh, Sarah Calve
      Pages 77-84

  5. Numerical Aspects

    1. Error-Controlled Adaptive Finite Element Methods in Nonlinear Elastic Fracture Mechanics

      • Marcus Rüter, Erwin Stein
      Pages 87-94

    2. Material Force Method. Continuum Damage & Thermo-Hyperelasticity

      • Ralf Denzer, Tina Liebe, Ellen Kuhl, Franz Josef Barth, Paul Steinmann
      Pages 95-104

    3. Discrete Material Forces in the Finite Element Method

      • Ralf Mueller, Dietmar Gross
      Pages 105-114

    4. Computational Spatial and Material Settings of Continuum Mechanics. An Arbitrary Lagrangian Eulerian Formulation

      • Ellen Kuhl, Harm Askes, Paul Steinmann
      Pages 115-125

  8. Fracture & Structural Optimization

    1. Teaching Fracture Mechanics Within the Theory of Strength-of-Materials

      • Reinhold Kienzler, George Herrmann
      Pages 193-202
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Keywords

About this book

The notion dealt with in this volume of proceedings is often traced back to the late 19th-century writings of a rather obscure scientist, C. V. Burton. A probable reason for this is that the painstaking de­ ciphering of this author's paper in the Philosophical Magazine (Vol. 33, pp. 191-204, 1891) seems to reveal a notion that was introduced in math­ ematical form much later, that of local structural rearrangement. This notion obviously takes place on the material manifold of modern con­ tinuum mechanics. It is more or less clear that seemingly different phe­ nomena - phase transition, local destruction of matter in the form of the loss of local ordering (such as in the appearance of structural defects or of the loss of cohesion by the appearance of damage or the exten­ sion of cracks), plasticity, material growth in the bulk or at the surface by accretion, wear, and the production of debris - should enter a com­ mon framework where, by pure logic, the material manifold has to play a prominent role. Finding the mathematical formulation for this was one of the great achievements of J. D. Eshelby. He was led to consider the apparent but true motion or displacement of embedded material inhomogeneities, and thus he began to investigate the "driving force" causing this motion or displacement, something any good mechanician would naturally introduce through the duahty inherent in mechanics since J. L. d'Alembert.

Editors and Affiliations

  • University of Kaiserslautern, Germany

    Paul Steinmann

  • Université Pierre et Marie Curie, Paris, France

    Gérard A. Maugin

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