Journal
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
Volume 101, Issue 11, Pages -Publisher
WILEY-V C H VERLAG GMBH
DOI: 10.1002/zamm.202100103
Keywords
biaxial loading; implicit constitutive theories; porous solids; stress concentration
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Funding
- Office of Naval Research
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This paper investigates stress concentration in a hole of a slab subjected to biaxial loading in a material where constitutive relation depends on density, finding that the stress concentration can be significantly higher than in classical linearized elasticity theory.
Most solid bodies are porous and in such bodies we expect the material properties to vary with porosity and hence with the density. Such bodies whose properties depend on the density cannot be described by the classical linearized elastic constitutive relation when they are undergoing small deformations, as the material moduli cannot depend on density. A constitutive relation which is valid in the small displacement gradient range wherein the material moduli are dependent on the density can be developed by linearizing implicit constitutive relations for describing elastic bodies introduced recently by Rajagopal [1]. In this paper, we determine the stress concentration due to a hole in a slab that is subject to biaxial loading in a body described by such a constitutive relation. We find that the stress concentration can be much as 147% higher than that for classical linearized elasticity for the range of loadings considered in the study.
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