0
Review Articles

Stresses, Singularities, and a Complementary Energy Principle for Large Strain Elasticity

[+] Author and Article Information
Yu-Chen Gao1

Institute of Mechanics, School of Civil Engineering and Architecture, Beijing Jiaotong University, Beijing 100044, China

Ming Jin

Institute of Mechanics, School of Civil Engineering and Architecture, Beijing Jiaotong University, Beijing 100044, Chinajinmingjinming@hotmail.com

Guan-Suo Dui

Institute of Mechanics, School of Civil Engineering and Architecture, Beijing Jiaotong University, Beijing 100044, China

1

Deceased.

Appl. Mech. Rev 61(3), 030801 (May 06, 2008) (16 pages) doi:10.1115/1.2909715 History: Published May 06, 2008

This article reviews three aspects of large strain elasticity. First, various conjugate stress tensors to strain tensors are reviewed. Many researchers have studied the theory of large strain elasticity. Many stress tensors including the Cauchy stress tensor, the first and the second Piola–Kirchhoff stress tensor, and the Jaumann stress tensor have been proposed to describe the stress state at a point. Recently, the first author of this article proposed a concept of “base forces” to reveal the essence of stress state. By the concept of base forces, the description of the stress state becomes clearer than other stress tensors. We attempt to take base forces as a basic point of view to deal with a review in which different descriptions of stress state are discussed and compared. The governing equations and boundary conditions expressed by the base forces are given. Second, this article reviews the solution of some singularity problems for large strain elasticity, i.e., problems of stress singularity at a crack or a notch tip, at the point of application of a concentrated force and at the vertex of contact in rubberlike materials. Methods of getting the singularity index of stress by using base forces are introduced and compared to earlier work. Complementary energy principles for large strain elasticity have eluded researchers for nearly 100years. A review of some important advances in this is also given, and a new complementary energy principle related to base forces is introduced.

FIGURES IN THIS ARTICLE
<>
Copyright © 2008 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

A half-space under a concentrated tensile load

Grahic Jump Location
Figure 2

A rectangular hexahedron element on current configuration

Grahic Jump Location
Figure 3

A parallel hexahedron element in the current configuration; its original shape was a rectangular box

Grahic Jump Location
Figure 4

A parallel hexahedron element in the current configuration

Grahic Jump Location
Figure 5

Three sides of a tetrahedron and the forces acting on them

Grahic Jump Location
Figure 6

A crack in an infinity plane

Grahic Jump Location
Figure 7

The deformation pattern of a crack tip field

Grahic Jump Location
Figure 8

A cone of revolution

Grahic Jump Location
Figure 9

Across section of the half-space compressed by a point load

Grahic Jump Location
Figure 10

The deformation of two typical triangles in SH and EX domains

Grahic Jump Location
Figure 11

A cross section of a rubber notch contacted by a rigid wedge, where 2A is the wedge angle and 2B is the notch angle

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In