[ { "id": "https://authors.library.caltech.edu/records/dwtww-vnd56", "eprint_id": 28622, "eprint_status": "archive", "datestamp": "2023-08-20 00:14:39", "lastmod": "2023-10-24 18:01:39", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Biggins-J-S", "name": { "family": "Biggins", "given": "J. S." } }, { "id": "Bhattacharya-K", "name": { "family": "Bhattacharya", "given": "K." }, "orcid": "0000-0003-2908-5469" } ] }, "title": "Characterization of soft stripe-domain deformations in SmC and SmC* liquid-crystal elastomers", "ispublished": "unpub", "full_text_status": "public", "note": "We are grateful for many interesting and important discussions with Professor Mark Warner. This work was carried out during various visits by Biggins to Caltech and Bhattacharya to Cambridge. We gratefully acknowledge the financial support of the CamSURF program at Caltech, the Powell Foundation, the Sims scholarship and the EPSRC.\n\n
Submitted - SmC_Paper_for_Caltech.pdf
", "abstract": "The neo-classical model of SmC (and SmC*) elastomers developed by Warner and Adams predicts a class of \"soft\" (zero energy) deformations. We find and describe the full set of stripe-domains \u2013 laminate structures in which the laminates alternate between two different deformations \u2013 that can form between pairs of these soft deformations. All the stripe-domains fall into two classes, one in which the smectic layers are not bent at the interfaces, but for which, in the SmC* case, the interfaces are charged, and one in which the smectic layers are bent but the interfaces are never charged. Striped deformations significantly enhance the softness of the macroscopic elastic response.", "date": "2008-12-23", "date_type": "published", "publisher": "California Institute of Technology", "id_number": "CaltechSOLIDS:2008.004", "official_url": "https://resolver.caltech.edu/CaltechSOLIDS:2008.004", "rights": "You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.", "funders": { "items": [ { "agency": "CamSURF program, Caltech" }, { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "Sims fund, University of Cambridge" }, { "agency": "Engineering and Physical Sciences Research Council (EPSRC)" } ] }, "local_group": { "items": [ { "id": "Solid-Mechanics-Research-Group" } ] }, "primary_object": { "basename": "SmC_Paper_for_Caltech.pdf", "url": "https://authors.library.caltech.edu/records/dwtww-vnd56/files/SmC_Paper_for_Caltech.pdf" }, "pub_year": "2008", "author_list": "Biggins, J. S. and Bhattacharya, K." }, { "id": "https://authors.library.caltech.edu/records/s7889-26981", "eprint_id": 28623, "eprint_status": "archive", "datestamp": "2023-08-20 00:15:11", "lastmod": "2023-10-24 18:01:41", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bhattacharya-K", "name": { "family": "Bhattacharya", "given": "Kaushik" }, "orcid": "0000-0003-2908-5469" }, { "id": "Schl\u00f6merkemper-A", "name": { "family": "Schl\u00f6merkemper", "given": "Anja" } } ] }, "title": "Stress-induced phase transformations in shape-memory polycrystals", "ispublished": "unpub", "full_text_status": "public", "note": "We are delighted to acknowledge various enlightening and enjoyable discussions with Pierre Suquet and Christian Lexcellent during the course of this work. This work started when AS held a postdoctoral position at the University of Oxford and was continued while AS was affiliated to the Institute for Analysis, Dynamics and Modelling at the University of Stuttgart. The work was completed during KB's sabbatical leave of absence at the Cavendish Laboratory and Clare Hall of Cambridge. We gratefully acknowledge the financial support of the EU TMR Network (FMRX-CT 98-0229, AS), the US Department of Energy (PSAAP, KB), UK EPSRC (KB).\n\nSubmitted - bhatta_schlo_preprint.pdf
", "abstract": "Shape-memory alloys undergo a solid-to-solid phase transformation involving a change of crystal structure. We examine model problems in the scalar setting motivated by the situation when this transformation is induced by the application of stress in a polycrystalline material made of numerous grains of the same crystalline solid with varying orientations. We show that the onset of transformation in a granular polycrystal with homogeneous elasticity is in fact predicted accurately by the so-called Sachs bound based on the ansatz of uniform stress. We also present a simple example where the onset of phase transformation is given by the Sachs bound, and the extent of phase transformation is given by the constant strain Taylor bound. Finally we discuss the stress-strain relations of the general problem using Milton-Serkov bounds.", "date": "2008-12-23", "date_type": "published", "publisher": "California Institute of Technology", "id_number": "CaltechSOLIDS:2008.005", "official_url": "https://resolver.caltech.edu/CaltechSOLIDS:2008.005", "rights": "You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.", "funders": { "items": [ { "agency": "European Union Training and Mobility of Researchers Network (EU TMR)", "grant_number": "FMRX-CT 98-0229, AS" }, { "agency": "Department of Energy (DOE)" }, { "agency": "Engineering and Physical Sciences Research Council (EPSRC)" } ] }, "local_group": { "items": [ { "id": "Solid-Mechanics-Research-Group" } ] }, "primary_object": { "basename": "SOLIDS2008-005v2.pdf", "url": "https://authors.library.caltech.edu/records/s7889-26981/files/SOLIDS2008-005v2.pdf" }, "related_objects": [ { "basename": "bhatta_schlo_preprint.pdf", "url": "https://authors.library.caltech.edu/records/s7889-26981/files/bhatta_schlo_preprint.pdf" } ], "pub_year": "2008", "author_list": "Bhattacharya, Kaushik and Schl\u00f6merkemper, Anja" }, { "id": "https://authors.library.caltech.edu/records/ehbhb-36c73", "eprint_id": 28621, "eprint_status": "archive", "datestamp": "2023-08-19 23:59:23", "lastmod": "2023-10-24 18:01:37", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dondl-P-W", "name": { "family": "Dondl", "given": "Patrick W." } }, { "id": "Bhattacharya-K", "name": { "family": "Bhattacharya", "given": "Kaushik" }, "orcid": "0000-0003-2908-5469" } ] }, "title": "A sharp interface model for the propagation of martensitic phase boundaries", "ispublished": "unpub", "full_text_status": "public", "keywords": "Martensitic phase boundaries, free boundary evolution, sets of finite perimeter, calculus of variations", "note": "This work draws from the doctoral thesis of Patrick Dondl at the California Institute of Technology . We gratefully acknowledge the financial support of the National Science Foundation (ACI-0204932, DMS-0311788).\n\nSubmitted - Dondl-Bhattacharya_SIM.pdf
", "abstract": "A model for the quasistatic evolution of martensitic phase boundaries is presented. The model is essentially the gradient flow of an energy that can contains elastic energy due to the underlying change in crystal structure in the course of the phase transformation and surface energy penalizing the area of the phase boundary. This leads to a free boundary problem with a nonlocal velocity that arises from the coupling to the elasticity equation. We show existence of solutions under a technical convergence condition using an implicit time-discretization.", "date": "2008-11-26", "date_type": "published", "publisher": "California Institute of Technology", "id_number": "CaltechSOLIDS:2008.003", "official_url": "https://resolver.caltech.edu/CaltechSOLIDS:2008.003", "rights": "You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.", "funders": { "items": [ { "agency": "NSF", "grant_number": "ACI-0204932" }, { "agency": "NSF", "grant_number": "DMS-0311788" } ] }, "local_group": { "items": [ { "id": "Solid-Mechanics-Research-Group" } ] }, "primary_object": { "basename": "Dondl-Bhattacharya_SIM.pdf", "url": "https://authors.library.caltech.edu/records/ehbhb-36c73/files/Dondl-Bhattacharya_SIM.pdf" }, "pub_year": "2008", "author_list": "Dondl, Patrick W. and Bhattacharya, Kaushik" }, { "id": "https://authors.library.caltech.edu/records/46y76-5bg40", "eprint_id": 28620, "eprint_status": "archive", "datestamp": "2023-08-19 23:48:44", "lastmod": "2023-10-24 18:01:35", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Givli-S", "name": { "family": "Givli", "given": "Sefi" } }, { "id": "Bhattacharya-K", "name": { "family": "Bhattacharya", "given": "Kaushik" }, "orcid": "0000-0003-2908-5469" } ] }, "title": "A coarse-grained model of the myofibril: overall dynamics and the evolution of sarcomere non-uniformities", "ispublished": "unpub", "full_text_status": "public", "keywords": "Muscle, Sarcomere length, Fokker Planck, Distribution, Instability, Probability, Damage", "note": "This work was carried out when Sefi Givli held a position at the California Institute of Technology. We thank a reviewer for the insightful comment on the typical relaxation time according to Model F. We are grateful to the National Science Foundation (Grant DMS-060667), the Powell Foundation and the Lester Deutch Foundation (Post-doctoral fellowship) for their financial support.\n\nSubmitted - CaltechSolids_2008-002.pdf
", "abstract": "A theoretical framework for predicting the macroscopic behavior of a muscle myofibril based on the collective behavior of sarcomeres is presented. The analysis is accomplished by rigorously transforming the nonlinear dynamics of an assemblage of sarcomeres into a partial differential equation for the probability distribution function of sarcomere lengths in the presence of stochastic temporal fluctuations and biological variability. This enables the study of biologically relevant specimens with reasonable computational effort. The model is validated by a comparison to quantitative experimental results. Further, it reproduces experimental observations that can not be explained by standard single sarcomere models, and provides new insights into muscle function and muscle damage during cyclic loading. We show that the accumulation of overstretched sarcomeres, which is related to muscle damage, depends on a delicate interplay between the dynamics of a large number of sarcomeres and the load characteristics, such as its magnitude and frequency. Further, we show that biological variability rather than stochastic fluctuations are the main source for sarcomere non-uniformities.", "date": "2008-11-04", "date_type": "published", "publisher": "California Institute of Technology", "id_number": "CaltechSOLIDS:2008.002", "official_url": "https://resolver.caltech.edu/CaltechSOLIDS:2008.002", "rights": "You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-060667" }, { "agency": "Powell Foundation" }, { "agency": "Lester Deutsch Foundation" } ] }, "local_group": { "items": [ { "id": "Solid-Mechanics-Research-Group" } ] }, "primary_object": { "basename": "CaltechSolids_2008-002.pdf", "url": "https://authors.library.caltech.edu/records/46y76-5bg40/files/CaltechSolids_2008-002.pdf" }, "pub_year": "2008", "author_list": "Givli, Sefi and Bhattacharya, Kaushik" }, { "id": "https://authors.library.caltech.edu/records/1a03w-6rj82", "eprint_id": 28618, "eprint_status": "archive", "datestamp": "2023-08-19 21:39:58", "lastmod": "2023-10-24 18:01:31", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Porter-M-A", "name": { "family": "Porter", "given": "Mason A." } }, { "id": "Daraio-C", "name": { "family": "Daraio", "given": "Chiara" }, "orcid": "0000-0001-5296-4440" }, { "id": "Herbold-E-B", "name": { "family": "Herbold", "given": "Eric B." } }, { "id": "Szelengowicz-I", "name": { "family": "Szelengowicz", "given": "Ivan" } }, { "id": "Kevrekidis-P-G", "name": { "family": "Kevrekidis", "given": "P. G." }, "orcid": "0000-0002-7714-3689" } ] }, "title": "Highly Nonlinear Solitary Waves in Periodic Dimer Granular Chains", "ispublished": "unpub", "full_text_status": "public", "keywords": "highly nonlinear waves, acoustic metamaterials, granular chains, solitons, phononic crystals", "note": "Author preprint.\n\nWe acknowledge support from the Caltech Information Science and Technology initiative (M.A.P.), start-up funds from Caltech (C.D.), and NSFDMS and CAREER (P.G.K.). I.S. performed his work as a visiting student of GALCIT at Caltech. We thank A. Molinari and V.F. Nesterenko for useful discussions.\n\nSubmitted - Porter2007.002.pdf
", "abstract": "We report the propagation of highly nonlinear solitary waves in heterogeneous, periodic granular media using experiments, numerical simulations, and theoretical analysis. We examine periodic arrangements of particles in experiments in which stiffer/heavier beads (stainless steel) are alternated with softer/lighter ones (polytetrafluoroethylene beads). We find excellent agreement between experiments and numerics in a model with Hertzian interactions between adjacent beads, which in turn agrees very well with a theoretical analysis of the model in the long-wavelength regime that we derive for heterogeneous environments and general bead interactions. Our analysis encompasses previously-studied examples as special cases and also provides key insights on the influence of the dimer lattice on the properties (width and propagation speed) of the obtained highly nonlinear wave\nsolutions.", "date": "2007-12-15", "date_type": "published", "publisher": "Physical Review E", "id_number": "CaltechSOLIDS:2007.002", "official_url": "https://resolver.caltech.edu/CaltechSOLIDS:2007.002", "rights": "You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.", "local_group": { "items": [ { "id": "Solid-Mechanics-Research-Group" } ] }, "primary_object": { "basename": "Porter2007.002.pdf", "url": "https://authors.library.caltech.edu/records/1a03w-6rj82/files/Porter2007.002.pdf" }, "pub_year": "2007", "author_list": "Porter, Mason A.; Daraio, Chiara; et el." }, { "id": "https://authors.library.caltech.edu/records/y3a3d-rzt86", "eprint_id": 28617, "eprint_status": "archive", "datestamp": "2023-08-19 21:29:30", "lastmod": "2023-10-24 18:01:29", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Liu-Liping", "name": { "family": "Liu", "given": "Liping" } } ] }, "title": "Solutions to the Eshelby Conjectures", "ispublished": "unpub", "full_text_status": "public", "note": "Submitted - SolidsLiu2007001.pdf
", "abstract": "We present solutions to the Eshelby conjectures based on a variational inequality. We first discuss the meanings of the original Eshelby's statement. By Fourier analysis, we establish the connection between the homogeneous Eshelby inclusion problem and the classic Newtonian potential problem. We then proceed to the solutions of the Eshelby conjectures. Under some hypothesis on the material properties and restricted to connected inclusions with Lipschitz boundary, we show that one version of the Eshelby conjectures is valid in all dimensions and the other version is valid in two dimensions. We also show the existence of multiply-connected inclusions in all dimensions and the existence of non-ellipsoidal connected inclusions in three and higher dimensions such that, in physical terms and in the context of elasticity, some uniform eigenstress of the inclusion induces uninform strain on the inclusion. We numerically calculate these special inclusions based on the finite element method.", "date": "2007-11-29", "date_type": "published", "publisher": "Caltech Library", "id_number": "CaltechSOLIDS:2007.001", "official_url": "https://resolver.caltech.edu/CaltechSOLIDS:2007.001", "rights": "You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.", "local_group": { "items": [ { "id": "Solid-Mechanics-Research-Group" } ] }, "primary_object": { "basename": "SolidsLiu2007001.pdf", "url": "https://authors.library.caltech.edu/records/y3a3d-rzt86/files/SolidsLiu2007001.pdf" }, "pub_year": "2007", "author_list": "Liu, Liping" } ]