PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Becky Halpenny.

Title:"The Peridynamic Theory of Solid Mechanics"
Seminar:Ph.D. Thesis Defense
Speaker:Kun Zhou, Adviser: Qiang Du
Abstract:
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
Date:12 / 19 / 2011
Time:01:30pm - 03:30pm