Mechanics of Material Forces

1. Front Matter

   Pages i-xv

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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

6. Dislocations & Peach-Koehler-Forces

   1. Self-Driven continuous Dislocations and Growth

      • Marcelo Epstein

      Pages 129-139

   2. Role of the Non-Riemannian Plastic Connection in Finite Elasto-Plasticity with Continuous Distribution of Dislocations

      • Sanda Cleja-Tigoiu

      Pages 141-148

   3. Peach-Koehler Forces within the Theory of Nonlocal Elasticity

      • Markus Lazar

      Pages 149-158

7. Multiphysics & Microstructure

   1. On the Material Energy-Momentum Tensor in Electrostatics and Magnetostatics

      • Carmine Trimarco

      Pages 161-171

   2. Continuum Thermodynamic and Variational Models for Continua with Microstructure and Material Inhomogeneity

      • Bob Svendsen

      Pages 173-180

   3. A Crystal Structure-Based Eigentransformation and its Work-Conjugate Material Stress

      • Chien H. Wu

      Pages 181-189

8. Fracture & Structural Optimization

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

      • Reinhold Kienzler, George Herrmann

      Pages 193-202

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.

• Transformation
• linear optimization
• mathematical physics
• mechanics
• modeling
• modelling
• optimization
• simulation
• stability

• University of Kaiserslautern, Germany

  Paul Steinmann

• Université Pierre et Marie Curie, Paris, France

  Gérard A. Maugin

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