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Cell adhesion to the extracellular matrix is accomplished by the clustering of receptor–ligand bonds into focal contacts on the cell-substrate interface. The contractile forces applied onto these focal contacts lead to elastic deformation of the surrounding, which results into a cellular mechanosensory capability that plays a key role in cell adhesion, spreading, and migration, among many others. The mechanosensitivity can be manipulated by the substrate anisotropy, by which focal contacts may align into certain directions so to minimize the total mechanical potential energy. Using the elastic anisotropic contact analysis, this work systematically analyzes the dependence of the alignment on the elastic anisotropy, and more importantly, the direction of the inclined contractile forces. The contact displacement fields are a complex function of the elastic constants, so simple analysis based on tensile or shear softest direction cannot properly predict the alignment orientation. It is also proved that if these focal contacts are of elongated shape, the major axis will be parallel to the alignment direction.

The pure boundary element method (BEM) is effective for the solution of a large class of problems. The main appeal of this BEM (reduction of the problem dimension by one) is tarnished to some extent when a fundamental solution to the governing equations does not exist as in the case of nonlinear problems. The easy to implement local point interpolation method applied to the strong form of differential equations is an attractive numerical approach. Its accuracy deteriorates in the presence of Neumann-type boundary conditions which are practically inevitable in solid mechanics. The main appeal of the BEM can be maintained by a judicious coupling of the pure BEM with the local point interpolation method. The resulting approach, named the LPI-BEM, seems versatile and effective. This is demonstrated by considering some linear and nonlinear elasticity problems including multi-physics and multi-field problems.

Frictionless contact between an arbitrarily-shaped rigid indenter and an elastically anisotropic film-on-substrate system can be regarded as being superposed incrementally by a flat-ended punch contact, the shape and size of which are determined by the indenter shape, indentation depth (or applied load) and elastic properties of film and substrate. For typical nanoindentation applications, the indentation modulus can thus be approximated from the response of a circular contact with pressure of the form of [1 - (r/a)²]^-1/2, where r is the radial coordinate and a is the contact radius. The surface-displacement Green's function for elastically anisotropic film-on-substrate system is derived in closed-form by using the Stroh formalism and the two-dimensional Fourier transform. The predicted dependence of the effective modulus on the ratio of film thickness to contact radius agrees well with detailed finite element simulations. Implications in evaluating film modulus by nanoindentation technique are also discussed.

The compliance matrix for a general anisotropic material is usually expressed in an arbitrarily chosen coordinate system, which brings some confusion or inconvenience in identifying independent elastic material constants and comparing elastic properties between different materials. In this paper, a unique stiffest orientation-based standardized compliance matrix is established, and 18 independent elastic material constants are clearly shown. During the searching process for the stiffest orientation, it is interesting to find from our theoretical analysis and an example that a material with isotropic tensile stiffness does not definitely possess isotropic elasticity. Therefore, the ratio between the maximum and minimum tensile stiffnesses, although widely used, is not a correct measure of anisotropy degree. Alternatively, a simple and correct measure of anisotropy degree based on the maximum shear-extension coupling coefficient in all orientations is proposed. However, for a two-dimensional constitutive relation, both the stiffness ratio and the shear-extension coupling coefficient can be adopted as proper measures of anisotropy degree.

The problem of Rayleigh waves polarized in a plane of symmetry of an anisotropic linear elastic medium is investigated in terms of displacements. The implicit secular equation is derived and subsequently rearranged into a system of three polynomial equations, which is convenient for further analysis of the problem. Next, a new straightforward procedure based on Vieta’s formulas is developed to reduce the system into a single explicit quartic secular equation. Numerical examples describing both approaches are presented for two monoclinic materials “diopside” and “microcline”.

In this work, dislocation master-equations valid for anisotropic materials are derived in terms of kernel functions using the framework of micromechanics. The second derivative of the anisotropic Green tensor is calculated in the sense of generalized functions and decomposed into a sum of a $1/R^3$-term plus a Dirac $\delta$-term. The first term is the so-called “Barnett-term” and the latter is important for the definition of the Green tensor as fundamental solution of the Navier equation. In addition, all dislocation master-equations are specified for Somigliana dislocations with application to 3D crack modeling. Also the interior Eshelby tensor for a spherical inclusion in an anisotropic material is derived as line integral over the unit circle.

The interaction of anisotropic point defects in anisotropic media is studied in the framework of anisotropic elasticity with eigendistortion. For this purpose, key-equations and their solutions for anisotropic point defects in an anisotropic medium based on the anisotropic Green tensor are derived. The material force, interaction energy and torque between two point defects as well as between a point defect and a dislocation loop are given. We discuss the so-called contact terms and point out similarities between elastic, electric, and magnetic dipoles. The plastic, the elastic and the total volume changes caused by an anisotropic point defect in an anisotropic material and the related Eshelby factor are determined. Thereby, the Eshelby factor is given in terms of the Eshelby tensor.

To allow for “relativistic”-like core contraction effects, an anisotropic regularization of steadily moving straight dislocations of arbitrary orientation is introduced, with two scale parameters $a_{\parallel }$ and $a_{\perp }$ along the direction of motion and transverse to it, respectively. The dislocation core shape is an ellipse. When $a_{\perp }/a_{\parallel }\to 0$, the model reduces to the Peierls–Eshelby dislocation, the fields of which are non-differentiable on the slip plane. For finite $a_{\parallel }$ and $a_{\perp }$, fields are everywhere differentiable. Applying the author’s so-called “causal” Stroh formalism to the model, explicit expressions for the regularized fields in anisotropic elasticity are derived for any velocity. For faster-than-wave velocities, Mach-cone angles are found insensitive to the ratio $a_{\parallel }/a_{\perp }$, as must be. However, the larger $a_{\parallel }$, the weaker the intensity of the cone branches. An expression is given for the radiative dissipative force opposed to motion. From this expression, it is inferred that the concept of a “radiation-free” intersonic velocity can, when not applicable, be replaced by that of a “least-radiation” velocity.