For more information about this meeting, contact Becky Halpenny.
| Title: | "The Peridynamic Theory of Solid Mechanics" |
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| Seminar: | Ph.D. Thesis Defense |
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| Speaker: | Kun Zhou, Adviser: Qiang Du |
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| Abstract: |
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| The peridynamic model proposed by Silling is an integral-type
nonlocal continuum theory. It depends crucially upon the non-locality of
the force interactions and does not explicitly involve the notion of
deformation gradients. It provides a more general framework than the
classical theory for problems involving discontinuities or other
singularities in the deformation. In this dissertation, we review the
recent developed peridynamic models including the ordinary bond-based,
state-based models and non-ordinary triclinic model. The linear ordinary
bond-based peridynamic model is analyzed under a rigorous analytical
framework. Meanwhile the relation between the peridynamic energy space
and fractional sobolev spaces is established for various micromodulus
functions. And for better assisting the nonlocal mechanical modeling and
nonlocal mathematical analysis, a vector calculus for the nonlocal
operators is developed. Nonlocal analogs of several theorem and
identities of the vector calculus for differential operators are also
presented. Relationships between the nonlocal operators and their
differential counterparts are established. We further apply the nonlocal
vector calculus to express the constitutive relation for the ordinary
state-based peridynamic elastic material. The linear peridynamic models
and associated nonlocal volume-constraints problems are defined and
analyzed within the nonlocal vector calculus framework. Especially, the
well-posedness of the ordinary state-based peridynamic model for a
linear homogeneous and anisotropic material is demonstrated. Moreover,
we establish relation between the classical elasticity and nonlocal
peridynamic theory as the nonlocal horizon converges to zero. And under
the mathematical framework introduced, we conduct the numerical analysis
of the finite-dimensional approximations to the bond-based peridynamic
models. A posterior error estimator for the peridynamic model is also
proposed and studied. Finally we list the open issues involved in the
peridynamic theory. |
Room Reservation Information
| Room Number: | MB113 |
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| Date: | 12 / 19 / 2011 |
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| Time: | 01:30pm - 03:30pm |
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