From a thin membrane to an unbounded solid : dynamics and instabilities in radial motion of nonlinearly viscoelastic spheres
Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2018.
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | eng |
| Published: |
Massachusetts Institute of Technology
2019
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/120231 |
| _version_ | 1826194936845828096 |
|---|---|
| author | Chen, Zhantao |
| author2 | Tal Cohen. |
| author_facet | Tal Cohen. Chen, Zhantao |
| author_sort | Chen, Zhantao |
| collection | MIT |
| description | Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2018. |
| first_indexed | 2024-09-23T10:04:11Z |
| format | Thesis |
| id | mit-1721.1/120231 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T10:04:11Z |
| publishDate | 2019 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1202312019-04-12T22:29:46Z From a thin membrane to an unbounded solid : dynamics and instabilities in radial motion of nonlinearly viscoelastic spheres Chen, Zhantao Tal Cohen. Massachusetts Institute of Technology. Department of Mechanical Engineering. Massachusetts Institute of Technology. Department of Mechanical Engineering. Mechanical Engineering. Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2018. Cataloged from PDF version of thesis. Includes bibliographical references (pages 85-88). In this thesis, a theoretical investigation of the dynamic motion of spherically symmetric bodies is presented, considering nonlinear viscoelastic material responses. To explore the stability thresholds of the dynamic motion and to compare them with available formula for the quasi-static limit, the present formulation employs a generalized constitutive relation and accounts for different loading scenarios. Specifically for instantaneously applied load, by studying the entire spectrum of radii ratios of the spherical body, ranging from a thin membrane to an unbounded medium, we show that geometric effects can significantly reduce the dynamic stability limit while viscoelasticity has a stabilizing effect. Additionally, we show that in finite spheres, rate-dependence can induce a bifurcation of the long-time response. The stability thresholds derived in this thesis, together with their geometric and constitutive sensitivities, can inform the design of more resilient material systems that employ soft materials in dynamic settings, with examples including seismic bearings that are designed to absorb shocks but often fail due to rupture of internal cavities, and thin inflatable membrane structures like rubber balloons, which may exhibit snap-through instabilities and consequent ruptures. By accounting for rate-dependence, the results of this thesis also shed light on the response of biological materials to dynamic load and the possible instabilities that can lead to injury in vulnerable organs, such as the brain and the lungs. Moreover, while modern therapeutic ultrasound techniques intentionally generate cavities within the tissue, the present investigation of the material response to harmonic excitations across various frequencies can lead to safer practice. by Zhantao Chen. S.M. 2019-02-05T15:59:40Z 2019-02-05T15:59:40Z 2018 2018 Thesis http://hdl.handle.net/1721.1/120231 1083122538 eng MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission. http://dspace.mit.edu/handle/1721.1/7582 90 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mechanical Engineering. Chen, Zhantao From a thin membrane to an unbounded solid : dynamics and instabilities in radial motion of nonlinearly viscoelastic spheres |
| title | From a thin membrane to an unbounded solid : dynamics and instabilities in radial motion of nonlinearly viscoelastic spheres |
| title_full | From a thin membrane to an unbounded solid : dynamics and instabilities in radial motion of nonlinearly viscoelastic spheres |
| title_fullStr | From a thin membrane to an unbounded solid : dynamics and instabilities in radial motion of nonlinearly viscoelastic spheres |
| title_full_unstemmed | From a thin membrane to an unbounded solid : dynamics and instabilities in radial motion of nonlinearly viscoelastic spheres |
| title_short | From a thin membrane to an unbounded solid : dynamics and instabilities in radial motion of nonlinearly viscoelastic spheres |
| title_sort | from a thin membrane to an unbounded solid dynamics and instabilities in radial motion of nonlinearly viscoelastic spheres |
| topic | Mechanical Engineering. |
| url | http://hdl.handle.net/1721.1/120231 |
| work_keys_str_mv | AT chenzhantao fromathinmembranetoanunboundedsoliddynamicsandinstabilitiesinradialmotionofnonlinearlyviscoelasticspheres |