Homogenization and fracture models for thermoviscoelastic solids /
In this study, mathematical techniques are developed
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
1998.
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| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=732843591&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | In this study, mathematical techniques are developed for obtaining averaged (homogenized) constitutive equations for heterogeneous linear thermoviscoelastic solids. Homogenization principles will be developed for the cases wherein no internal boundaries are present, and also where internal boundaries in the form of sharp cracks are present, thus resulting in damage dependent macroscopic constitutive equations. The microthermomechanics problem will first be formulated, followed by the construction of the locally averaged equations resulting from the homogenization process. It will be shown that homogenized conservation laws and constitutive equations take the same form as do the local equations when locally linear thermoviscoelastic media are considered. However, the resulting homogenized constitutive equations will be nonlinear in the case wherein time dependent damage occurs. In addition, for materials of convolution type at the local scale, the homogenized equations will be shown to contain a term that depends on the time derivative of the strain localization tensor. Example problems will be discussed and the homogenized results will be given for these examples in order to demonstrate the technique. A cohesive zone is introduced ahead of a crack tip in order to avoid the singularity at the crack tip. By applying thermodynamics to the cohesive zone and the surrounding body, a fracture criterion will be established so that the inelastic energy dissipation both in the cohesive zone and the surrounding bulk material can be distinguished from the energy released by fracture, and the propagation of crack can be predicted. In addition, the cohesive zone constitutive equation is constructed utilizing the Helmholtz free energy in the form of a single hereditary integral for a nonlinear viscoelastic material. The resulting constitutive model for the cohesive zone contains an internal state variable which represents the damage state within the cohesive zone. When the cohesive zone opening displacement is known, the energy release rate in the cohesive zone is thus history dependent in terms of the damage state, the length of separation in the cohesive zone and the geometric configuration of the cohesive zone opening displacement. Example results contained herein demonstrate this effect. |
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| Item Description: | Vita. |
| Physical Description: | xiii, 79 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilm Inc. |
| Bibliography: | Includes bibliographical references: pages 72-78. |