Comment on “Ultralow magnetostrictive flexible ferromagnetic nanowires” by G. Muscas, P. E. Jönsson, I. G. Serrano, Ö. Vallin, and M. V. Kamalakar, Nanoscale, 2021, 13, 6043–6052

A strain field (εxx) in Ti/Co/Al nanowires on the PEN substrate subjected to uniaxial stress. The applied stress perpendicular to the nanowire length leads to very low strain in nanowires (about 30 times lower than the macroscopic strain).

Fiber Rearrangement and Matrix Compression in Soft Tissues: Multiscale Hypoelasticity and Application to Tendon

It is widely accepted that the nonlinear macroscopic mechanical behavior of soft tissue is governed by fiber straightening and re-orientation. Here, we provide a quantitative assessment of this phenomenon, by means of a continuum micromechanics approach. Given the negligibly small bending stiffness of crimped fibers, the latter are represented through a number of hypoelastic straight fiber phases with different orientations, being embedded into a hypoelastic matrix phase. The corresponding representative volume element (RVE) hosting these phases is subjected to “macroscopic” strain rates, which are downscaled to fiber and matrix strain rates on the one hand, and to fiber spins on the other hand. This gives quantitative access to the fiber decrimping (or straightening) phenomenon under non-affine conditions, i.e. in the case where the fiber orientations cannot be simply linked to the macroscopic strain state. In the case of tendinous tissue, such an RVE relates to the fascicle material with 50 μm characteristic length, made up of crimped collagen bundles and a gel-type matrix in-between. The fascicles themselves act as parallel fibers in a similar matrix at the scale of a tissue-related RVE with 500 μm characteristic length. As evidenced by a sensitivity analysis and confirmed by various mechanical tests, it is the initial crimping angle which drives both the degree of straightening and the shape of the macroscopic stress-strain curve, while the final linear portion of this curve depends almost exclusively on the collagen bundle elasticity. Our model also reveals the mechanical cooperation of the tissue’s key microstructural components: while the fibers carry tensile forces, the matrices undergo hydrostatic pressure.

Point defects

Examples of intrinsic and extrinsic point defects are discussed. Models of point defects in a continuum as misfitting spheres are solved for rigid and deformablemisfitting spheres. Free surfaces alter significantly the formation volume of a point defect even when the point defect is far from any free surface. Many point defects have non-sperical symmetry, and it is then better to consider defect forces exerted by the point defect on neighbouring atoms. Defect forces capture the symmetry of the point defect in its local environment. Interaction energies between point defects and between point defects and other sources of stress are expressed conveniently and with physical transparency in terms of dipole, quadrupole etc. tensors of point defects and derivatives of the Green’s function. The dipole tensor is experimentally measurable through the lambda-tensor, which measures the derivative of the macroscopic strain of a crystal with concentration of the point defect.

Hashin–Shtrikman bounds of periodic linear elastic media with cubic symmetry

Based on the Hashin–Shtrikman variational principle, novel bounds on the effective shear moduli of a two-phase periodic composite are derived. The composite constituents are assumed to be isotropic, while the microstructure is assumed to exhibit cubic symmetry. A solution of the subsidiary boundary value problem is expressed as a double contraction of a fourth-order cubic tensor with the applied macroscopic strain. The bounds for cubic shear moduli are new, while the bounds for the bulk modulus are equal to the classical ones. The new bounds are verified for composites with the cubic, frame, octet and cubic + octet structures. It is shown that they are nearly attained for the cubic, octet and cubic + octet structures.