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

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• 作者：Patrizio Neff^a ; ^{patrizio.neff@uni-due.de" class="auth_mail" title="E-mail the corresponding author} ; Ingo Mü ; nch^b ; ^{ingo.muench@kit.edu" class="auth_mail" title="E-mail the corresponding author} ; Ionel-Dumitrel Ghiba ; ^a ; ^c ; ^d ; ^{dumitrel.ghiba@uni-due.de" class="auth_mail" title="E-mail the corresponding author} ; ^{dumitrel.ghiba@uaic.ro" class="auth_mail" title="E-mail the corresponding author} ; Angela Madeo^e ; ^f ; ^{angela.madeo@insa-lyon.fr" class="auth_mail" title="E-mail the corresponding author}
• 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
• 刊名：International Journal of Solids and Structures
• 出版年：2016
• 出版时间：1 March 2016
• 年：2016
• 卷：81
• 期：Complete
• 页码：233-243
• 全文大小：572 K

文摘

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.