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Peridynamic Multiscale Models for the Mechanics of Materials

Title: Peridynamic Multiscale Models for the Mechanics of Materials: Constitutive Relations, Upscaling from Atomistic Systems, and Interface Problems.
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Name(s): Seleson, Pablo D, author
Gunzburger, Max, professor directing thesis
Rikvold, Per Arne, university representative
El-Azab, Anter, committee member
Peterson, Janet, committee member
Shanbhag, Sachin, committee member
Lehoucq, Richard B., committee member
Parks, Michael L., committee member
Department of Scientific Computing, degree granting department
Florida State University, degree granting institution
Type of Resource: text
Genre: Text
Issuance: monographic
Date Issued: 2010
Publisher: Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: This dissertation focuses on the non local continuum peridynamics model for the mechanics of materials, related constitutive models, its connections to molecular dynamics and classical elasticity, and its multiscale and multimodel capabilities. A more generalized role is defined for influence functions in the state-based peridynamic model which allows for the strength of non local interactions to be modulated. This enables the connection between different peridynamic constitutive models, establishing a hierarchy that reveals that some models are special cases of others. Furthermore, this allows for the modulation of the strength of non local interactions, even for a fixed radius of interactions between material points in the peridynamics model. The multiscale aspect of peridynamics is demonstrated through its connections to molecular dynamics. Using higher-order gradient models, it is shown that peridynamics can be viewed as an up-scaling of molecular dynamics, preserving the relevant dynamics under appropriate choices of length scales. The state-based peridynamic model is shown to be appropriate for the description of multiscale and multimodel systems. A formulation for nonlocal interface problems involving scalar fields is presented, and derivations of non local transmission conditions are derived. Specializations that describe local, non local, and local/non local transmission conditions are considered. Moreover, the convergence of the non local transmission conditions to their classical local counterparts is shown. In all cases, results are illustrated by numerical experiments.
Identifier: FSU_migr_etd-0273 (IID)
Submitted Note: A Dissertation submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Degree Awarded: Degree Awarded: Fall Semester, 2010.
Date of Defense: Date of Defense: July 20, 2010.
Keywords: Interface Problems, Upscaling, Continuum Mechanics, Peridynamics, Multiscale, Nonlocality
Bibliography Note: Includes bibliographical references.
Advisory committee: Max Gunzburger, Professor Directing Thesis; Per Arne Rikvold, University Representative; Anter El-Azab, Committee Member; Janet Peterson, Committee Member; Sachin Shanbhag, Committee Member; Richard B. Lehoucq, Committee Member; Michael L. Parks, Committee Member.
Subject(s): Physical sciences
Mathematics
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_migr_etd-0273
Owner Institution: FSU

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Seleson, P. D. (2010). Peridynamic Multiscale Models for the Mechanics of Materials: Constitutive Relations, Upscaling from Atomistic Systems, and Interface Problems. Retrieved from http://purl.flvc.org/fsu/fd/FSU_migr_etd-0273