Nonlinear elasticity with limiting small strain for cracks subject to non-penetration. Academic Article

abstract

• A major drawback of the study of cracks within the context of the linearized theory of elasticity is the inconsistency that one obtains with regard to the strain at a crack tip, namely it becoming infinite. In this paper we consider the problem within the context of an elastic body that exhibits limiting small strain wherein we are not faced with such an inconsistency. We introduce the concept of a non-smooth viscosity solution which is described by generalized variational inequalities and coincides with the weak solution in the smooth case. The well-posedness is proved by the construction of an approximation problem using elliptic regularization and penalization techniques.

authors

• Rajagopal, Kumbakonam

published proceedings

• Math Mech Solids

author list (cited authors)

• Itou, H., Kovtunenko, V. A., & Rajagopal, K. R.

citation count

• 28

complete list of authors

• Itou, Hiromichi||Kovtunenko, Victor A||Rajagopal, Kumbakonam R

publication date

• June 2017

publisher

• SAGE Publications  Publisher

published in

• Mathematics and Mechanics of Solids  Journal

keywords

• Generalized Solution
• Limiting Small Strain
• Nonlinear Crack With Non-penetration
• Nonlinear Elasticity
• Penalization
• Regularization
• Variational Inequality

PubMed Central ID

• 29750007

Digital Object Identifier (DOI)

• 10.1177/1081286516632380

start page

• 1334

end page

• 1346

volume

• 22

issue

• 6

URL

• http://dx.doi.org/10.1177/1081286516632380