The State of Deformation in Earthlike Self-Gravitating Objects

  • Wolfgang H. Müller
  • Wolf Weiss

Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Also part of the SpringerBriefs in Continuum Mechanics book sub series (BRIEFSCONTINU)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Wolfgang H. Müller, Wolf Weiss
    Pages 1-18
  3. Wolfgang H. Müller, Wolf Weiss
    Pages 19-49
  4. Wolfgang H. Müller, Wolf Weiss
    Pages 51-81
  5. Wolfgang H. Müller, Wolf Weiss
    Pages 83-95
  6. Wolfgang H. Müller, Wolf Weiss
    Pages 97-107
  7. Back Matter
    Pages 109-111

About this book


This book presents an in-depth continuum mechanics analysis of the deformation due to self-gravitation in terrestrial objects, such as the inner planets, rocky moons and asteroids. Following a brief history of the problem, modern continuum mechanics tools are presented in order to derive the underlying field equations, both for solid and fluid material models. Various numerical solution techniques are discussed, such as Runge-Kutta integration, series expansion, finite differences, and (adaptive) FE analysis. Analytical solutions for selected special cases, which are worked out in detail, are also included. All of these methods are then applied to the problem, quantitative results are compared, and the pros and cons of the analytical solutions and of all the numerical methods are discussed. The book culminates in a multi-layer model for planet Earth according to the PREM Model (Preliminary Earth Model) and in a viscoelastic analysis of the deformation problem, all from the viewpoint of rational continuum theory and numerical analysis.


Finite Element Analysis Finite Difference Analysis Newton's Law of Gravity Preliminary Earth Model PREM Self-Gravitation Shooting Solution Method Telluric Objects Telluric Planet

Authors and affiliations

  • Wolfgang H. Müller
    • 1
  • Wolf Weiss
    • 2
  1. 1.Technische Universität BerlinBerlinGermany
  2. 2.Weierstraß-Ins. für Angewandte Anal. & SBerlinGermany

Bibliographic information

  • DOI
  • Copyright Information The Author(s) 2016
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-319-32578-1
  • Online ISBN 978-3-319-32580-4
  • Series Print ISSN 2191-530X
  • Series Online ISSN 2191-5318
  • Buy this book on publisher's site
Industry Sectors
Materials & Steel
Consumer Packaged Goods
Energy, Utilities & Environment
Oil, Gas & Geosciences