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Thermomechanics of Viscoplasticity

Fundamentals and Applications

  • Book
  • © 2009

Overview

Authors:
  1. Milan Micunovic
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  • Includes a detailed description of the geometry of thermo-deformation with local evolving natural state configuration
  • A comparative review of various models of thermodynamics including classical, rational, statistical, and endochronic, with a special approach to inelastic high speed histories
  • Provides a comparative review of various models of thermodynamics (classical, rational, endochronic, statistical) with special approach to inelastic high speed histories
  • Introduces quasi-rate independence and its application to plastic waves, ratcheting, and diffuse localization
  • A tensor representation approach to thermo-inelastic coupled fields connected to a generalized associativity of flow rule; includes a comparison with the J2 approach
  • Discussion of Drucker, Iliushin, and Hill postulates; special attention devoted to the slight disorder of polycrystal grains
  • Quasi-rate independence and its application to plastic waves, ratcheting and diffuse localization;
  • Micromechanics based on the micro grain approach leading to a reduced number of material constants
  • Especially useful to the emergent field of biomechanics
  • Examines micromechanics based on micro grain approach leading to reduced number of material constants
  • Provides biaxial cruciform specimen Hopkinson bar results
  • Reexamines the Hill’s yield function for nonproportional stress-thermo-strain histories

Part of the book series: Advances in Mechanics and Mathematics (AMMA, volume 20)

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Table of contents (11 chapters)

  1. Front Matter

    Pages 1-22
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  2. Theoretical and Experimental Aspects

    1. Front Matter

      Pages 1-1
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    2. Physical and Geometrical Background

      • Milan V. Mićunović
      Pages 7-31

    3. Crystalline Materials with Thermo-inelastic Memory

      • Milan V. Mićunović
      Pages 33-45

    4. Normality Rule? Plastic Work Extremals and Related Topics

      • Milan V. Mićunović
      Pages 47-59

    5. Thermodynamics of Inelasticity

      • Milan V. Mićunović
      Pages 61-79

    6. Some Multiaxial Viscoplastic Experiments: Relation to Tensor Functions

      • Milan V. Mićunović
      Pages 81-97

  3. Some General Problems

    1. Front Matter

      Pages 1-1
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    2. Viscoplasticity of Ferromagnetics

      • Milan V. Mićunović
      Pages 101-119

    3. Self-Consistent Method and Quasi-Rate-Dependent Polycrystals

      • Milan V. Mićunović
      Pages 121-143

    4. Inelastic Micromorphic Polycrystals

      • Milan V. Mićunović
      Pages 145-166

  4. Applications of the Theory

    1. Front Matter

      Pages 1-1
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    2. Plastic Wave Propagation in Hopkinson Bar

      • Milan V. Mićunović
      Pages 171-192

    3. Ratchetting Phenomenon at Low Strain Rates for AISI

      • Milan V. Mićunović
      Pages 193-201

    4. Stress and Strain Measures for Orthotropic Metals at Large Nonproportional Plastic Strain Histories

      • Milan V. Mićunović
      Pages 203-222

  5. Back Matter

    Pages 1-26
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Keywords

About this book

As any human activity needs goals, mathematical research needs problems. —David Hilbert Mechanics is the paradise of mathematical sciences. —Leonardo da Vinci Mechanics and mathematics have been complementary partners since N- ton’s time, and the history of science shows much evidence of the bene?cial in?uence of these disciplines on each other. Driven by increasingly ela- rate modern technological applications, the symbiotic relationship between mathematics and mechanics is continually growing. However, the increasingly large number of specialist journals has generated a duality gap between the partners, and this gap is growing wider. Advances in Mechanics and Mathematics (AMMA) is intended to bridge the gap by providing multidisciplinary publications that fall into the two f- lowing complementary categories: 1. An annual book dedicated to the latest developments in mechanics and mathematics; 2. Monographs, advanced textbooks, handbooks, edited volumes, and selected conference proceedings. The AMMA annual book publishes invited and contributed compreh- sive research and survey articles within the broad area of modern mechanics and applied mathematics. The discipline of mechanics, for this series, includes relevantphysicalandbiologicalphenomenasuchas:electromagnetic,thermal, viii Series Preface and quantum e?ects, biomechanics, nanomechanics, multiscale modeling, - namical systems, optimization and control, and computation methods. - pecially encouraged are articles on mathematical and computational models and methods based on mechanics and their interactions with other ?elds. All contributions will be reviewed so as to guarantee the highest possible sci- ti?c standards. Each chapter will re?ect the most recent achievements in the area.

Reviews

From the reviews: “This book exposes in a concise manner the essentials of the modern theory of viscoplasticity in relation with its basic thermomechanical foundations … . In that sense the book represents a true … contribution to the field. … addresses professionals or younger readers (graduate students, PhDs, research engineers) who want to apprehend a difficult subject matter that pertains to both continuum mechanics … and its applications in materials science. … It is generally well and concisely written and … generously documented.” (Gérard A. Maugin, Mathematical Reviews, Issue 2010 c)

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