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An Introduction to Nonlinear Finite Element Analysis$
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J. N. Reddy

Print publication date: 2004

Print ISBN-13: 9780198525295

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198525295.001.0001

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Material Nonlinearities and Coupled Problems

Material Nonlinearities and Coupled Problems

(p.389) 10 Material Nonlinearities and Coupled Problems
An Introduction to Nonlinear Finite Element Analysis


Oxford University Press

Nonlinearities arise from two independent sources: nonlinearity due to changes in the geometry or position of the material particles of a continuum, which is called the geometric nonlinearity, and nonlinearity due to the nonlinear material behavior, which is called material nonlinearity. In fluid mechanics and coupled fluid flow and heat transfer, geometric nonlinearity arises as a result of the spatial (or Eulerian) description of motion, and they enter the equations of motion through material time derivative term. This chapter considers material nonlinear formulations and discusses nonlinear elastic and elastic plastic material models for solids and power-law model for viscous incompressible fluids. Nonlinear elastic problems are discussed, along with the small deformation theory of plasticity, ideal plasticity, strain hardening plasticity, elastic plastic analysis of a bar, non-Newtonian fluids, governing equations in cylindrical coordinates, power-law fluids, White-Metzner fluids, and finite element models.

Keywords:   material nonlinearity, finite element models, nonlinear elastic problems, small deformation theory of plasticity, non-Newtonian fluids, heat transfer, ideal plasticity, incompressible fluids, power-law fluids

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