{"651408":{"#nid":"651408","#data":{"type":"event","title":"PhD Defense by Fabio Sozio ","body":[{"value":"\u003Cdiv\u003E\r\n\u003Cp\u003E\u003Cbr \/\u003E\r\n\u003Cstrong\u003ENonlinear mechanics of non-Euclidean solids\u003Cbr \/\u003E\r\nFabio Sozio\u003Cbr \/\u003E\r\nDr. Arash Yavari (CEE)\u003Cbr \/\u003E\r\nDr. Phanish Suryanarayana (CEE), Dr. David McDowell (ME, MSE), Dr. Julian J. Rimoli (AE), Dr.\u003Cbr \/\u003E\r\nJohn Etnyre (Math)\u003Cbr \/\u003E\r\nTuesday, October 19, 2021 at 12:00 PM\u003Cbr \/\u003E\r\nSustainable Education Building (SEB), Room 122\u003Cbr \/\u003E\r\nIn this thesis we formulate a geometric theory of the nonlinear mechanics of non-Euclidean solids. The\u003Cbr \/\u003E\r\nterm \u0026ldquo;non-Euclidean solids\u0026rdquo; was coined by Henri Poincar\u0026eacute; in 1902, and refers to mathematical objects that\u003Cbr \/\u003E\r\nrepresent solids with distributed eigenstrains, and hence residual stresses. We present a theoretical\u003Cbr \/\u003E\r\nframework for the nonlinear mechanics of accretion (or surface growth) and for continuous dislocation\u003Cbr \/\u003E\r\ndynamics. Accretion is the growth of a deformable solid by the gradual addition of material on its boundary,\u003Cbr \/\u003E\r\nresulting in the formation of a residually-stressed structure. Examples of accretion are the growth of\u003Cbr \/\u003E\r\nbiological tissues and crystals, additive manufacturing, the deposition of thin films, etc. Dislocations are\u003Cbr \/\u003E\r\ncrystallographic line defects whose motion is responsible for plastic slip. Both accretion and dislocation\u003Cbr \/\u003E\r\ndynamics have a close connection with differential geometry; accretion can be seen as the layer-by-layer\u003Cbr \/\u003E\r\nassembly of non-Euclidean solids, while plasticity concerns the study of the evolution of their geometric\u003Cbr \/\u003E\r\nstructure in time. However, plastic slip is a process that involves more information than the change in\u003Cbr \/\u003E\r\ndistances considered in anelasticity and captured by Riemannian geometry; one must consider the torsion\u003Cbr \/\u003E\r\nof an associated Weitzenb\u0026ouml;ck manifold as well. In this thesis we propose a geometric theory of nonlinear\u003Cbr \/\u003E\r\naccretion. The accretion part of the deformation gradient brings each particle to its natural state right before\u003Cbr \/\u003E\r\nits time of attachment, and depends on both the mass flux and the history of deformation during accretion.\u003Cbr \/\u003E\r\nThis tensor is used to construct a material metric. From a geometric perspective, the presence of residual\u003Cbr \/\u003E\r\nstresses in an accreted solid is due to a non-vanishing Riemann curvature tensor associated with the\u003Cbr \/\u003E\r\nmaterial metric, which in turn is related to the incompatibility of the accretion process. In the geometric\u003Cbr \/\u003E\r\nframework, an accreted solid is represented by a foliated manifold, which allows one to express its 3D\u003Cbr \/\u003E\r\ngeometry in terms of the geometry of its layers and of the mass flux. The theory extends to thermal\u003Cbr \/\u003E\r\naccretion. A numerical two-step scheme for nonlinear accretion based on a novel matrix formulation for\u003Cbr \/\u003E\r\nfinite differences is also presented. In the setting of geometric anelasticity, we propose a field theory of\u003Cbr \/\u003E\r\nnonlinear dislocation mechanics in single crystals. The theory relies on the notion of a dislocated lattice\u003Cbr \/\u003E\r\nstructure, described by a triplet of differential 1-forms. Dislocation distributions are represented by a\u003Cbr \/\u003E\r\ncollection of triplets of differential 2-forms. These differential forms constitute a set of internal variables\u003Cbr \/\u003E\r\nwhose evolution equations are formulated in the framework of exterior calculus. This geometric approach\u003Cbr \/\u003E\r\nallows one to study the integrability of the slip surfaces and its implications on the glide motion. The\u003Cbr \/\u003E\r\ngoverning equations are derived using a variational principle of the Lagrange-d\u0026rsquo;Alembert type with a twopotential\u003Cbr \/\u003E\r\napproach to include dissipation. We also take into account the nonholonomic constraints that the\u003Cbr \/\u003E\r\nlattice puts on the motion of dislocations\u003C\/strong\u003E\u003C\/p\u003E\r\n\u003C\/div\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"Nonlinear mechanics of non-Euclidean solids "}],"uid":"27707","created_gmt":"2021-10-05 19:52:29","changed_gmt":"2021-10-05 19:52:29","author":"Tatianna Richardson","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2021-10-19T13:00:00-04:00","event_time_end":"2021-10-19T15:00:00-04:00","event_time_end_last":"2021-10-19T15:00:00-04:00","gmt_time_start":"2021-10-19 17:00:00","gmt_time_end":"2021-10-19 19:00:00","gmt_time_end_last":"2021-10-19 19:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"221981","name":"Graduate Studies"}],"categories":[],"keywords":[{"id":"100811","name":"Phd Defense"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1788","name":"Other\/Miscellaneous"}],"invited_audience":[{"id":"78761","name":"Faculty\/Staff"},{"id":"78771","name":"Public"},{"id":"174045","name":"Graduate students"},{"id":"78751","name":"Undergraduate students"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}