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A micromechanically based couple-stress model of an elastic two-phase composite. (English) Zbl 1003.74006

Summary: We determine couple-stress moduli and characteristic lengths of heterogeneous materials. The study is set in the context of a planar (two-dimensional) two-phase composite with linear non-couple-stress (classical) elastic constituents, and with a single microstructural length scale (inclusion spacing) in an equilateral triangular array, We use an approach which allows a replacement of this composite by an approximating couple-stress continuum. We determine effective material parameters from the response of a unit cell under either displacement, displacement-periodic, or traction boundary conditions. We carry out computations of all the moduli by varying the stiffness ratio of both phases, so as to cover a range of very different materials from porous solids through composites with rigid inclusions. It is found that the three boundary conditions result in hierarchies of couple-stress moduli. In addition, we observe that these three boundary conditions also result in a hierarchy of characteristic lengths.

MSC:

74A40 Random materials and composite materials
74Q15 Effective constitutive equations in solid mechanics
74E30 Composite and mixture properties
74M25 Micromechanics of solids
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