On some fundamental misunderstandings in the indeterminate couple stress model. A comment on recent papers of AR Hadjesfandiari and GF Dargush

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:81

Article

Neff, Patrizio¹  Muench, Ingo²  Ghiba, Ionel-Dumitrel^1,3,4  Madeo, Angela^5,6 

[1] Univ Duisburg Essen, Fak Math, Lehrstuhl Nichtlineare Anal & Modellierung, Thea Leymann Str 9, D-45127 Essen, Germany

[2] Karlsruhe Inst Technol, Inst Struct Anal, Kaiserstr 12, D-76131 Karlsruhe, Germany

[3] Alexandru Ioan Cuza Univ, Dept Math, Blvd Carol 1,11, Iasi 700506, Romania

[4] Romanian Acad, Iasi Branch, Octav Mayer Inst Math, Iasi 700505, Romania

[5] Univ Lyon INSA, Lab Genie Civil & Ingn Environm, Batiment Coulomb, F-69621 Villeurbanne, France

[6] Int Ctr M&MOCS Math & Mech Complex Syst, Palazzo Caetani, Cisterna Di Lat, Italy

关键词: Modified couple stress model;    Symmetric Cauchy stresses;    Boltzmann axiom;    Symmetry of couple stress tensor;    Generalized continua;    Microstructure;    Size effects;    Strain gradient elasticity;    Conformal invariance;    Gradient elasticity;    Consistent traction boundary conditions;   

DOI  :  10.1016/j.ijsolstr.2015.11.028

来源: Elsevier

【 摘 要 】

In a series of papers which are either published [Hadjesfandiari, A., Dargush, G. F., 2011a. Couple stress theory for solids. Int. J. Solids Struct. 48 (18), 2496-2510; Hadjesfandiari, A., Dargush, G. F., 2013. Fundamental solutions for isotropic size-dependent couple stress elasticity. Int. J. Solids Struct. 50 (9),1253-1265.] or available as preprints [Hadjesfandiari, A., Dargush, G. F., 2010. Polar continuum mechanics. Preprint arXiv:1009.3252; Hadjesfandiari, A. R., Dargush, G. F., 2011b. Couple stress theory for solids. Int. J. Solids Struct. 48, 2496-2510; Hadjesfandiari, A. R., 2013. On the skew-symmetric character of the couple-stress tensor. Preprint arXiv:1303.3569; Hadjesfandiari, A. R., Dargush, G. F., 2015a. Evolution of generalized couple-stress continuum theories: a critical analysis. Preprint arXiv:1501.03112; Hadjesfandiari, A. R., Dargush, G. F., 2015b. Foundations of consistent couple stress theory. Preprint arXiv:1509.06299] Hadjesfandiari and Dargush have reconsidered the linear indeterminate couple stress model. They are postulating a certain physically plausible split in the virtual work principle. Based on this postulate they claim that the second-order couple stress tensor must always be skew-symmetric. Since they do not consider that the set of boundary conditions intervening in the virtual work principle is not unique, their statement is not tenable and leads to some misunderstandings in the indeterminate couple stress model. This is shown by specifying their development to the isotropic case. However, their choice of constitutive parameters is mathematically possible and we show that it still yields a well-posed boundary value problem. (C) 2015 Elsevier Ltd. All rights reserved.

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