Volume 21, Nº 1 (2018)

Indentation testing, also refereed to as tonometry in medical diagnostics, is one of the most frequently used methods for studying the properties of soft biological tissues. In the case of lymphedematous tissues, characterized by abnormal accumulation of excess interstitial fluid, the indentation method constitutes an objective alternative for the standard manual palpation test, that is used for evaluation of elastic modulus and time dependent tissue response related to finding parameters of effective compression therapy. This paper focuses on the numerical modelling of a deep indentation test for which the flat cylindrical tip with a surface area of 1 cm2 penetrates the tissue at a constant rate until 1 cm depth is reached. The indentation generates large deformations of skin and subcutaneous tissue and squeezing of part of the interstitial fluid from the compressed region. The skin is modelled as an isotropic neo-Hookean solid and subcutaneous tissue is modelled as a fluid saturated porous matrix. The effective stress law, isotropic neo-Hookean elastic matrix and the Darcy's type of interaction force between phases are adopted for the subcutaneous tissue. The finite element simulations deliver results for time dependent indentation force and pore pressure under the indenter for different and relevant to real tissues properties. The role of the properties and the presence of skin are analysed. The values of maximum reaction force and relaxation time are compared and evaluated as descriptors of mechanical properties of tissues.

Active control of friction by ultrasonic vibration is a well-known effect with numerous technical applications ranging from press forming to micromechanical actuators. Reduction of friction is observed with vibration applied in any of the three possible directions (normal to the contact plane, in the direction of motion and in-plane transverse). In this work, we consider the multi-mode active control of sliding friction, where phase-shifted oscillations in two or more directions act at the same time. Our analysis is based on a macroscopic contact-mechanical model that was recently shown to be well-suited for describing dynamic frictional processes. For simplicity, we limit our analysis to a constant, load-independent normal and tangential stiffness and two superimposed phase-shifted harmonic oscillations, one of them being normal to the plane and the other in the direction of motion. As in previous works utilizing the present model, we assume a constant local coefficient of friction, with reduction of the observed force of friction arising entirely from the macroscopic dynamics of the system. Our numerical simulations show that the resulting law of friction is determined by just three dimensionless parameters. Depending on the values of these parameters, three qualitatively different types of behavior are observed: (a) symmetric velocity-dependence of the coefficient of friction (same for positive and negative velocities), (b) asymmetric dependence with respect to the sign of the velocity, but with zero force at zero velocity, and (c) asymmetric dependence with nonzero force at zero velocity. The latter two cases can be interpreted as a "dynamic ratchet" (b) and an actuator (c).

A multilevel approach is used to numerically investigate physical and mechanical properties of titanium-based bcc alloys and their behavior under conditions identical to selective laser sintering. Plastic properties of P-Ti-Nb alloy are calculated within the first principles approach. An algorithm is proposed and tested to optimize the calculations and reduce their number by more than 5 times. A molecular dynamics method is employed to study structural changes of titanium and niobium powder particles during sintering and to calculate adhesion characteristics of nanoparticles of the produced alloy depending on the external action. The simulation results are in good agreement with the known experimental data and can be used as input data both for numerical models of a higher spatial scale and for the optimization of production parameters of titanium alloys by additive technologies.

There has been a long debate about the validity of asperity models in the contact between rough surfaces, much of it concentrated on relatively minor aspects of the solution for the special case of Gaussian random processes for roughness, like the exact value of the area-load slope or the extent of the linear regime. It is shown here that in the case of adhesion, the behavior is extremely sensitive to the shape of the height distribution. We show for example results for Weibull distributions, which has been suggested in a number of practical cases from macroscopic to nanoscopic roughness. Pull-off force is found to vary by several orders of magnitude both lower and higher than in the Gaussian case, whereas the "stickiness" criterion on the adhesion parameter changes by an order of magnitude. Additionally, in some operations like chemical-mechanical polishing, tails are almost completely removed and a sharp peak develops instead of a tail: modeling this with contact on the bounded side of the Weibull distribution, stickiness seems to occur for any level of roughness. Pome qualitative comparison with recent numerical experiments is attempted.

We discuss contact stiffness and adhesion of flat-ended cylindrical indenters with a graded material the elastic coefficient of which is a power-function of the depth with an exponent 1 < k < 3. So far, only graded materials with k < 1 have been considered in the literature as the stiffness of the medium becomes zero when k is approaching 1. However, it is known that the case of incompressible media is an exception. We argue that in this case the final stiffness can be defined up to values of k < 3. The interval 1 < k < 3, which has not been considered earlier occurs to be of special interest, since for k > 1 the adhesive properties of contacts change qualitatively from "brittle" to very tough even in the case of a purely elastic material.

Here we consider melting of an ultrathin lubricant layer between two atomically smooth solid surfaces taking into account the stress dependence of the lubricant shear modulus and its decrease with increasing stress (strain). In the adiabatic approximation with the stress relaxation time far longer than strain and temperature relaxation times, a Langevin equation is written and its respective Fokker-Planck equation is derived using the Stratonovich calculus. Phase diagrams for the steady case are presented illustrating the effect of the system parameters on the lubricant behavior. A joint numerical and analytical analysis demonstrates a very close match between probability distributions at different parameters. It is shown that in a limited stress range, a self-similar mode of dry friction is established showing up in self-similar behavior of stress time series.