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A New Kirchhoff-Love Beam Element and its Application to Polymer Mechanics

Part of the Mechanics and Adaptronics Book Series

DOI: 10.1007/978-3-031-06340-4

ISBN: 978-3-031-06339-8

Publisher: Springer International Publishing - Springer Journals

Sep 22, 2022

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Chapter 1Introduction

Schulz, Matthias C.

Pages: 1 –5

[A large portion of the research in the field of polymer mechanics is concerned with studying experimentally and theoretically the micro-mechanical behavior of single polymer chains and how it determines the macro-mechanical properties of the corresponding polymeric materials . Both domains are...
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Chapter 2Modeling of Slender Bodies

Schulz, Matthias C.

Pages: 7 –41

[In this chapter, it is focused on devising a model for slender bodies that is well suited to be used in simulations of very slender objects such as polymers. It is tried to concisely define the properties of a slender body. Two different parameterizations of rotations are presented and important...
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Chapter 3Finite-Element Formulation of Slender Bodies Modeled by Geometrically Exact Beams

Schulz, Matthias C.

Pages: 43 –92

[In this chapter, the beam theories are used to derive corresponding finite-element formulations.]
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Chapter 4Modeling the Mechanics of Single Polymer Chains in the Finite-Element Framework

Schulz, Matthias C.

Pages: 93 –118

[The Kirchhoff-Love beam and its finite element formulation presented in Sects. 2 and 3 are employed to model the mechanical behavior of polymers. In the remainder of this section, a model for a single polymer chain is presented including both contributions, intrinsic stiffness and temperature...
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Chapter 5Conclusion

Schulz, Matthias C.

Pages: 119 –121

[A new Kirchhoff-Love beam theory was presented based on the strong enforcement of the Kirchhoff constraint by removing two translational degrees of freedom. Based on this theory two new geometrically exact Kirchhoff-Love beam elements, referred to as ψl\documentclass[12pt]{minimal}...

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