The multiplicative deformation split for shells with application to growth, chemical swelling, thermoelasticity, viscoelasticity and elastoplasticity

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:174

Article

Sauer, Roger A.¹  Ghaffari, Reza¹  Gupta, Anurag² 

[1] Rhein Westfal TH Aachen, Aachen Inst Adv Study Computat Engn Sci AICES, Templergraben 55, D-52056 Aachen, Germany

[2] Indian Inst Technol Kanpur, Dept Mech Engn, Kanpur 208016, Uttar Pradesh, India

关键词: Curvilinear coordinates;    Inelastic shells;    Irreversible thermodynamics;    Multiplicative decomposition;    Nonlinear shell theory;    Kirchhoff-Love kinematics;   

DOI  :  10.1016/j.ijsolstr.2019.06.002

来源: Elsevier

【 摘 要 】

This work presents a general unified theory for coupled nonlinear elastic and inelastic deformations of curved thin shells. The coupling is based on a multiplicative decomposition of the surface deformation gradient. The kinematics of this decomposition is examined in detail. In particular, the dependency of various kinematical quantities, such as area change and curvature, on the elastic and inelastic strains is discussed. This is essential for the development of general constitutive models. In order to fully explore the coupling between elastic and different inelastic deformations, the surface balance laws for mass, momentum, energy and entropy are examined in the context of the multiplicative decomposition. Based on the second law of thermodynamics, the general constitutive relations are then derived. Two cases are considered: Independent inelastic strains, and inelastic strains that are functions of temperature and concentration. The constitutive relations are illustrated by several nonlinear examples on growth, chemical swelling, thermoelasticity, viscoelasticity and elastoplasticity of shells. The formulation is fully expressed in curvilinear coordinates leading to compact and elegant expressions for the kinematics, balance laws and constitutive relations. (C) 2019 Elsevier Ltd. All rights reserved.

【 授权许可】

Free