Contact lines on stretched soft solids: modelling anisotropic surface stresses

We present fully analytical solutions for the deformation of a stretched soft substrate due to the static wetting of a large liquid droplet, and compare our solutions to recently published experiments (Xu et al. 2018 Soft Matter 14, 916–920 (doi:10.1039/C7SM02431B)). Following a Green’s function approach, we extend the surface-stress regularized Flamant–Cerruti problem to account for uniaxial pre-strains of the substrate. Surface profiles, including the heights and opening angles of wetting ridges, are provided for linearized and finite kinematics. We fit experimental wetting ridge shapes as a function of applied strain using two free parameters, the surface Lamé coefficients. In comparison with experiments, we find that observed opening angles are more accurately captured using finite kinematics, especially with increasing levels of applied pre-strain. These fits qualitatively agree with the results of Xu et al ., but revise values of the surface elastic constants.

A Robust Finite Element Method for Elastic Vibration Problems

A robust finite element method is introduced for solving elastic vibration problems in two dimensions. The temporal discretization is carried out using the {P_{1}}-continuous discontinuous Galerkin (CDG) method, while the spatial discretization is based on the Crouziex–Raviart (CR) element. It is shown after a technical derivation that the error of the displacement (resp. velocity) in the energy norm (resp. {L^{2}} norm) is bounded by {O(h+k)} (resp. {O(h^{2}+k)}), where h and k denote the mesh sizes of the subdivisions in space and time, respectively. Under some regularity assumptions on the exact solution, the error bound is independent of the Lamé coefficients of the elastic material under discussion. A series of numerical results are offered to illustrate numerical performance of the proposed method and some other fully discrete methods for comparison.

Similarity Requirements for Mixed Convective Boundary Layer Flow over Vertical Curvilinear Porous Surfaces with Heat Generation/Absorption

Similarity requirements for three dimensional combined forced and free convective laminar boundary layer flows over the porous inclined vertical curvilinear surfaces with buoyancy effects and heat absorption/generation effects are investigated theoretically. The potential flow in the mainstream and Gabriel lame coefficients outside of the boundary layer are the function of ξ,η. Hence, the external velocity components (Ue, Ve) and Gabriel lame coefficients h1,h2,h3 are independent of ζ. Here, h3ξ,η=1 has been set such that ζ represents actual distance measured normal to the surface. Similarity requirements for an incompressible fluid are sought on the basis of detailed analyses in order to reduce the governing partial differential equations into a set of ordinary differential equations. Finally, different possible cases are exhibited in a tabular form with the inclusion of ΔT variations for onward flow study that are helpful to the future researchers for the flow over the orthogonal curvilinear surfaces.

Estimates for the asymptotic convergence of a non-isothermal linear elasticity with friction

In this paper, we are interested in the study of the asymptotic analysis of a dynamical problem in elasticity with nonlinear friction of Tresca type. The Lamé coefficients of a thin layer are assumed to vary with respect to the thin layer parameter ε and to depend on the temperature. We prove the existence and uniqueness of a weak solution for the limit problem. The proof is carried out by the use of the asymptotic behavior when the dimension of the domain tends to zero.

Thermo-Mechanical Bending Response of Exponentially Graded Thick Plates Resting on Elastic Foundations

The trigonometric shear and normal deformations plate theory is used to study the thermo-mechanical bending analysis of exponentially graded (EG) thick rectangular plates resting on Pasternak elastic foundations. Material properties of the plate are assumed to be graded in the thickness direction according to an exponential law distribution, meaning that Lamé coefficients vary exponentially in a given fixed z-direction. The governing equations are derived from the principle of virtual displacements. The analytical solutions are obtained by using Navier technique and the effects of stiffness of the foundations, thermal loading, and gradient index on thermo-mechanical responses of the plates are discussed. Numerical results for the bending response for EG rectangular plates are investigated and some of them are compared with those available in the literature.