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ON THE INCREMENTAL CONSTITUTIVE RELATIONS AND COMPATIBILITY EQUATIONS FOR THIN SHAPE MEMORY ALLOY SHELLS UNDERGOING NON-ISOTHERMAL PHASE TRANSITIONS

Volume 14, Issue 1, 2023, pp. 1-27
DOI: 10.1615/CompMechComputApplIntJ.2022044513
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Sergey I. Zhavoronok
Department of Mechanics of Smart and Composite Materials and Systems, Institute of Applied Mechanics of Russian Academy of Sciences, Moscow, Russian Federation; Department of Applied Mathematics and Informatics, Moscow State University of Civil Engineering, Russian Federation

ABSTRACT

A new formulation of the constitutive equations for thin shape memory alloy shells is obtained on the background of the once coupled phenomenological model of "smeared" non-isothermal thermoelastic phase transitions. The shell is considered under the canonical Kirchhoff assumptions and defined on a two-dimensional manifold corresponding to its mid-surface. The inverse incremental relations express small increments of tangent and bending strain tensors through small tensor increments of tangent forces, bending couples, and martensite volume ratio while the thermodynamic temperature is a given scalar field. Contrarily to the extrinsic problem statement, such constitutive equations do not require either complex analytical inversion or numerical inversion at every point of the deformation pattern. The appropriate compatibility equations for small increments of the tangent forces and bending couples' tensors are derived, and the intrinsic incremental formulation of the geometrically linear theory of thin-walled shape memory alloy shells is proposed.

KEY WORDS: shape memory alloys, phenomenological modeling, thermoelastic non-isothermal phase transitions, thin shape memory shells, incremental constitutive equations, incremental compatibility equations, intrinsic shell theories
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THE EFFECT OF DIFFERENT WINDING CONFIGURATIONS ON THE CRUSHING RESPONSE OF HELICAL WOUND WOVEN GLASS/EPOXY COMPOSITE TUBES Saurabh Kureel, V. Murari INFLUENCE OF PLY ORIENTATION ON INTERLAMINAR FRACTURE TOUGHNESS OF CARBON/EPOXY COMPOSITES Ashok Kumar Prodduturi, Ravinder Reddy Pinninti, Kumara Swami Gupta AVSS PREPARATION AND THERMOELECTRIC PROPERTIES OF Cux/Bi2Te3 COMPOSITES Fanguo Li, Shihong Lu, Luteng Liu, Junping Li, Zhang Zhang, Peimei Yan, Yile Pan ELASTOPLASTIC CONSTITUTIVE MODEL AND MECHANICAL BEHAVIOR OF UNSATURATED LOESS Xuansheng Cheng, Guanjie Qi, Xinhai Zhou, Shanglong Zhang DEVELOPMENT AND QUALIFICATION OF CNT-CFRP COMPOSITE COMPONENTS FOR SPACE APPLICATIONS Yogesh Ghotekar, Dhaval Vartak, Jay Parmar, Nandini Deshpande, Vimal Shah, Nitin Sharma, Bala Satyanarayana MULTI-OBJECTIVE OPTIMIZATION OF THE PROCESS PARAMETERS USING HYBRID TAGUCHI-GREY RELATIONAL ANALYSIS OF BASALT/JUTE FIBER-REINFORCED COMPOSITES Vimalanand Suthenthiraveerappa, Shenbaga Velu Pitchumani, Venkatachalam Gopalan, Muthukumaran Gunasegeran, Anandhan Venugopal, Anish Subramonia

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Effect of Filler Content and Size on the Flexural Strength and Hardness of Pure Iron Powder Filled Laminated Fiberglass Epoxy Composites Youcef Gheid, Abdennacer Chemami, Hamza Aouaichia, Khmissi belkaid
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