Crack problem within the context of implicitly constituted quasi-linear viscoelasticity Academic Article

abstract

• A quasi-linear viscoelastic relation that stems from an implicit viscoelastic constitutive body containing a crack is considered. The abstract form of the response function is given first in [Formula: see text], [Formula: see text], due to power-law hardening; second in [Formula: see text] due to limiting small strain. In both the cases, sufficient conditions on admissible response functions are formulated, and corresponding existence theorems are proved rigorously based on the variational theory and using monotonicity methods. Due to the presence of a Volterra convolution operator, an auxiliary-independent variable of velocity type is employed. In the case of limiting small strain, the generalized solution of the problem is provided within the context of bounded measures and expressed by a variational inequality.

authors

• Rajagopal, Kumbakonam

published proceedings

• MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

author list (cited authors)

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

citation count

• 14

complete list of authors

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

publication date

• February 2019

publisher

• World Scientific Publishing  Publisher

published in

• Mathematical Models and Methods in Applied Sciences (M3AS)  Journal

keywords

• Crack Problem
• Existence Theorem
• Generalized Solution
• Implicit Constitutive Response
• Limiting Small Strain
• Monotonicity Method
• Power-law Hardening
• Quasi-linear Viscoelasticity
• Variational Inequality
• Variational Theory
• Volterra Convolution Operator

Digital Object Identifier (DOI)

• 10.1142/S0218202519500118

start page

• 355

end page

• 372

volume

• 29

issue

• 2

URL

• http://dx.doi.org/10.1142/s0218202519500118