Journal ArticleDOI
Correspondence principles and a generalized J integral for large deformation and fracture analysis of viscoelastic media
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In this paper, a quasi-static deformation and fracture analysis for nonlinear viscoelastic media and sample applications are given. But the authors focus on predicting mechanical work available at the crack tip for initiation and continuation of growth.Abstract:
Methods of quasi-static deformation and fracture analysis are developed for a class of nonlinear viscoelastic media and sample applications are given. Selection of the class of media is guided by actual rheological behavior of monolithic and composite materials as well as the need for simplicity to be able to understand the effect of primary material and continuum parameters on crack growth behavior. First, pertinent aspects of J integral and energy release rate theory for nonlinear elastic media are discussed. Nonlinear viscoelastic constitutive equations are then given, and correspondence principles which establish a simple relationship between mechanical states of elastic and viscoelastic media are developed. These principles provide the basis for the subsequent extension of J integral theory to crack growth in viscoelastic materials. Emphasis is on predicting mechanical work available at the crack tip for initiation and continuation of growth; some examples show how viscoelastic properties and the J integral affect growth behavior. Included is the problem of a crack in a thin layer having different viscoelastic properties than the surrounding continuum. The Appendix gives an apparently new constitutive theory for elastic and viscoelastic materials with changing microstructure (e.g. distributed damage) and indicates the conditions under which the fracture theory in the body of the paper is applicable.read more
Citations
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References
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Journal ArticleDOI
A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks
TL;DR: In this paper, an integral is exhibited which has the same value for all paths surrounding a class of notches in two-dimensional deformation fields of linear or non-linear elastic materials.
Book
Introduction to the mechanics of a continuous medium
TL;DR: In this article, the authors propose a linearized theory of elasticity for tensors, which they call Linearized Theory of Elasticity (LTHE), which is based on tensors and elasticity.
Journal ArticleDOI
On a class of conservation laws in linearized and finite elastostatics
James K. Knowles,Eli Sternberg +1 more
TL;DR: In this article, ESHELBY deduced a surface-integral representation for the force on an elastic singularity or inhomogeneity, which gives rise to a conservation law for regular elastostatic fields appropriate to homogeneous but not necessarily isotropic solids in the presence of infinitesimal deformations.