Couple stress theory for solids

By Ali Reza Hadjesfandiari, G. Dargush. 2011

575 citations recorded by the source corpus.

By relying on the definition of admissible boundary conditions, the principle of virtual work and some kinematical considerations, we establish the skew-symmetric character of the couple-stress tensor in size-dependent continuum representations of matter. This fundamental result, which is independent of the material behavior, resolves all difficulties in developing a consistent couple stress theory. We then develop the corresponding size-dependent theory of small deformations in elastic bodies, including the energy and constitutive relations, displacement formulations, the uniqueness theorem for the corresponding boundary value problem and the reciprocal theorem for linear elasticity theory. Next, we consider the more restrictive case of isotropic materials and present general solutions for two-dimensional problems based on stress functions and for problems of anti-plane deformation. Finally, we examine several boundary value problems within this consistent size-dependent theory of elasticity.

Subfields: Biomedical Engineering, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/59b937bab573b49e4ec94bb8544ffbc7b16fc60b

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In Biomedical Engineering

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Dynamic compressive behaviour of cellular materials: A review of phenomenon, mechanism and modelling (2018, unknown): “generalised continuum mechanics [263-266]) are still needed for different types of cellular materials.”
On some fundamental misunderstandings in the indeterminate couple stress model. A comment on recent papers of A.R. Hadjesfandiari and G.F. Dargush (2016, background): “In a series of papers which are either published [14, 13] or available as preprints [16, 15, 12, 17, 18] Hadjesfandiari and Dargush have reconsidered the linear indeterminate couple stress model.”
Size-dependent piezoelectricity (2012, background): “Recently, Hadjesfandiari and Dargush (2011) have resolved the troubles in the existing size-dependent continuum mechanics.”