Lectures on Phase Field

1. Front Matter

   Pages i-ix

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2. The Phase-Field Method

   1. Front Matter

      Pages 1-1

      PDF

   2. Introduction

      • Ingo Steinbach, Hesham Salama

      Pages 3-15Open Access

   3. Analytics

      • Ingo Steinbach, Hesham Salama

      Pages 17-29Open Access

   4. Capillarity

      • Ingo Steinbach, Hesham Salama

      Pages 31-39Open Access

   5. Temperature

      • Ingo Steinbach, Hesham Salama

      Pages 41-47Open Access

   6. Concentration

      • Ingo Steinbach, Hesham Salama

      Pages 49-59Open Access

   7. Multi-Phase-Field Approach

      • Ingo Steinbach, Hesham Salama

      Pages 61-68Open Access

   8. Stress–Strain and Fluid Flow

      • Ingo Steinbach, Hesham Salama

      Pages 69-77Open Access

   9. Quantum Phase Field

      • Ingo Steinbach, Hesham Salama

      Pages 79-90Open Access

3. OpenPhase

   1. Front Matter

      Pages 91-91

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   2. Tutorial 1: OpenPhase

      • Ingo Steinbach, Hesham Salama

      Pages 93-102Open Access

   3. Tutorial 2: OpenPhase Examples

      • Ingo Steinbach, Hesham Salama

      Pages 103-113Open Access

4. Back Matter

   Pages 115-122

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This open access textbook fills a gap, in that it introduces readers to the theory and applications of the Phase-Field technique. Phase Field, over the years, has emerged as a standard tool for materials research, just as the Finite-Element technique has in structure mechanics.  Whereas the few existing textbooks on this topic are intended for advanced readers, this one is made accessible to the widest possible audience, through an engaging, lecture format. The content grows out of a course the authors teach for graduate students at Ruhr-University Bochum. Even readers who may, at first, have no clue at all what a “Phase Field” is and for what it is used, are invited on a journey from general physics of thermodynamics and wave mechanics, through applications in all fields of materials science, up to the central questions of physical being. On this journey all the necessary techniques are detailed, mostly formulated in a mathematical language easily understood by engineers and natural scientists.

• Open Access
• Open Access Phase Field textbook
• Phase-Field Methods in Materials Science and Engineering
• Multi-phase-field approach
• Phase-Field in metallic alloys
• evolving microstructures

• Ruhr University Bochum, Bochum, Germany

  Ingo Steinbach, Hesham Salama

Prof. Dr. Ingo Steinbach is a pioneer of the phase-field theory with early publications from 1996. His Multi-Phase-Field approach, with contributions from many other scientists worldwide, forms a standard for multi-phase application in metallurgy and other fields of materials research. Applications range from pattern formation during solidification over solid-state transformation during materials processing to materials degradation and failure. He recently went back to the roots of the phase-field theory in non-linear wave mechanics to propose a Quantum Phase Field Concept of Matter, which forms a new paradigm for understanding the physical world.

Hesham Salama is a Research Associate and a PhD student under the supervision of Prof. Steinbach in the context of the phase-field theory. He is one of the developers of the OpenPhase software project targeted at numerically maximum efficient phase-field simulations.