Large deformation analysis of soft biomaterials

A possible form for the strain energy function for soft biomaterials is proposed. Application to the fundamental problems of simple elongation of a cylindrical bar and simultaneous inflation and extension of a circular cylindrical tube is discussed. Results give a good least square fit to experimental data found in the literature for papillary muscle and artery.     

Sliding of the wigner solid from the coupled plasmon-ripplon surface deformation

The Wigner solid (WS) on a liquid⁴He surface is accompanied with the periodic surface deformation, i.e. the ripplons whose wavevectors equal the reciprocal WS lattice vectors. This unique situation plays a crucial role in the dynamics of the WS. We have performed an extensive measurement of the ac Corbino conductivity _xx. The WS conductivity shows extremely nonlinear behavior, and it jumps abruptly at a certain input voltage. The threshold input voltage V_th varies as V_thB^–0.8f^–1n_s ^1.5E, where B, f, n_s, and E are magnetic field, frequency, electron density and pressing electric field, respectively. We have interpreted the _xx jump as the collective sliding of the electrons out of the surface deformation.     

骨组织工程用多孔HA生物材料的制备

用PVB、NH4HCO3和(NH4)2CO3粒子作造孔剂,制备了骨组织工程用多孔HA生物材料.讨论了烧结工艺和造孔剂含量等对材料结构的影响.研究表明,较佳的烧结工艺为1200℃烧结4h,烧结后样品主要是HA相.造孔剂PVB、(NH4)2CO3、NH4HCO3含量分别为10vol%、15vol%和20vol%时,多孔HA陶瓷拥有大于100μm和5～50 μm的贯通孔,具有较好的孔连通性与孔结构,有利于细胞和组织的生长以及营养输送;其最大孔隙率为50.3%,抗压强度为6.33MPa.     

Fatigue behavior of porous biomaterials manufactured using selective laser melting

Porous titanium alloys are considered promising bone-mimicking biomaterials. Additive manufacturing techniques such as selective laser melting allow for manufacturing of porous titanium structures with a precise design of micro-architecture. The mechanical properties of selective laser melted porous titanium alloys with different designs of micro-architecture have been already studied and are shown to be in the range of mechanical properties of bone. However, the fatigue behavior of this biomaterial is not yet well understood. We studied the fatigue behavior of porous structures made of Ti6Al4V ELI powder using selective laser melting. Four different porous structures were manufactured with porosities between 68 and 84% and the fatigue S–N curves of these four porous structures were determined. The three-stage mechanism of fatigue failure of these porous structures is described and studied in detail. It was found that the absolute S–N curves of these four porous structures are very different. In general, given the same absolute stress level, the fatigue life is much shorter for more porous structures. However, the normalized fatigue S–N curves of these four structures were found to be very similar. A power law was fitted to all data points of the normalized S–N curves. It is shown that the measured data points conform to the fitted power law very well, R² = 0.94. This power law may therefore help in estimating the fatigue life of porous structures for which no fatigue test data is available. It is also observed that the normalized endurance limit of all tested porous structures (< 0.2) is lower than that of corresponding solid material (c.a. 0.4).     

Dynamic mechanical properties of hydroxyapatite-reinforced and porous starch-based degradable biomaterials

It has been shown that blends of starch with a poly(ethylene-vinyl-alcohol) copolymer, EVOH, designated as SEVA-C, present an interesting combination of mechanical, degradation and biocompatible properties, specially when filled with hydroxyapatite (HA). Consequently, they may find a range of applications in the biomaterials field. This work evaluated the influence of HA fillers and of blowing agents (used to produce porous architectures) over the viscoelastic properties of SEVA-C polymers, as seen by dynamic mechanical analysis (DMA), in order to speculate on their performances when withstanding cyclic loading in the body. The composite materials presented a promising performance under dynamic mechanical solicitation conditions. Two relaxations were found being attributed to the starch and EVOH phases. The EVOH relaxation process may be very useful in vivo improving the implants performance under cyclic loading. DMA results also showed that it is possible to produce SEVA-C compact surface/porous core architectures with a mechanical performance similar to that of SEVA-C dense materials. This may allow for the use of these materials as bone replacements or scaffolds that must withstand loads when implanted.     

Nonlinear compressive deformation of viscoelastic porous materials

Two nonlinear viscoelastic solutions are presented for a porous, foam type material. The first is for the hydrostatic compression of the foam, while the second is for the one-dimensional compression of an infinite slab of the material. Relative to the particular viscoelastic constitutive equation employed, the first solution is exact, whereas the second, obtained through the use of a physical hypothesis, is approximate. Both solutions predict the macroscopic, average stress in the foam, required by the corresponding deformation processes. The theoretical results are compared with experimental measurements on a foam material at a porosity of 48.5%. The effect of material hysteresis is revealed and discussed.     

Effects of shot-peening on surface contact angles of biomaterials

It was shown previously that (i) if the surface of a biomaterial is covered with TiO₂ (tetragonal structure oxide), it shows a high initial contact angle and a high change rate in contact angle (i.e. a higher spreading process); while (ii) cubic structure oxides show relatively lower spreading rates in 1% NaCl solution at 25°C. Shot-peening has been applied to biomaterials (especially titanium and its alloys) to improve their fatigue strength. It is well known that shot-peening causes surface roughening. The effects of surface roughness on wettability are not well documented. Therefore, in the present study, the effects of shot peening on the initial contact angle and changes in it as a function of time, were investigated. In addition, the spontaneous half-cell potential of all tested biomaterials were measured to correlate the wettability phenomenon to initial surface chemistry. Pure titanium and its alloys, including Ti-6AI-4V and NiTi alloys, AISI Type 316L stainless, Co-Cr alloy, and pure nickel, were mechanically polished, shot-peened and pre-oxidized at 300°C for 30 min in pure oxygen. It was found that (i) shot-peening homogenized the surface conditions in terms of initial contact angles, (ii) TiO₂ oxide shows a higher spreading coefficient, while cubic structure oxides show a lower value, and (iii) the spreading coefficient was correlated to the magnitude of the spontaneous half-cell potential.     

Localization of deformation in rate sensitive porous plastic solids

The effect of material rate sensitivity on the localization of deformation in a porous visco-plastic solid is examined under plane strain tension and axisymmetric tension conditions. The plastic flow rule proposed by Gurson [3], modified to account for material rate sensitivity, is adopted to model the plastic softening behavior that arises due to void nucleation and growth. An initial imperfection in the form of a planar band is assumed and a material instability is sought as the deformation proceeds. Comparisons are made with the results of a rate-independent analysis [10]. The present rate-dependent results show that the retardation effect on flow localization is larger when the material is more rate-sensitive, and that, with a given rate sensitivity, the retardation effect on flow localization is greater in plane strain tension than in axisymmetric tension. Results are also obtained by employing parameter values representative of spheroidized carbon steels studied by Fisher [21], and the predictions of the model are in good agreement with experimental observations.     

Modeling plastic deformation and fracture of porous materials

Strain hardening of a porous material was numerically modeled. The corresponding stress-strain (σ-ε) curves, the ultimate strength, and the strain at break were calculated for iron with a relative porosity in the interval from 0 to 30%. Anomalous behavior of these characteristics is observed at a porosity corresponding to the percolation transition from isolated pores to the “infinite” pore cluster. The proposed model adequately describes the available experimental data.     

A fully coupled model for diffusion-induced deformation in polymers

Polymers that mechanically respond to the presence of a diffusing fluid/solvent have found various applications in drug delivery, tissue scaffolding, sensors and actuators. These applications involve understanding of both the diffusion process and the evolution of the deformation of the polymers during the diffusion process. For example, in a polymeric actuator one might be interested in the extent of deformation one can achieve given a solvent environment and the time in which it can be achieved. There are two key aspects in modeling such behavior. First, the displacement gradients involved are usually large, especially in problems such as “self-assembly.” Second, since the diffusion occurs in a deforming polymeric medium, an appropriate diffusion model that includes the effect of the deformed state of the body as well as the interaction between the polymeric medium and the diffusing fluid has to be considered. In effect, this results in the diffusion and equilibrium equation being fully coupled and nonlinear. In this work, we model diffusion-induced deformation in an elastic material including large deformations based on thermodynamics framework. For the chemical potential, we use the Flory–Huggins potential adapted to include the effect of stress in the polymers. Using the model, we simulate folding and bending of a rectangular polymeric strip by simultaneous solution of the diffusion equation as well as the equilibrium equation using the finite element method. Parametric studies are also conducted in order to examine the effect of material parameters on the diffusion and deformation behaviors. Finally, using the coupled diffusion–deformation model we simulate deformations of composite domains comprising of polymeric constituents with different diffusion–deformation behaviors in order to achieve various interesting “self-assembly” shapes.     

Mixed isogeometric analysis of strongly coupled diffusion in porous materials

In this paper, we develop a mixed isogeometric analysis approach based on subdivision stabilization to study strongly coupled diffusion in solids in both small and large deformation ranges. Coupling the fluid pressure and the solid deformation, the mixed formulation suffers from numerical instabilities in the incompressible and the nearly incompressible limit due to the violation of the inf‐sup condition. We investigate this issue using subdivision‐stabilized nonuniform rational B‐spline (NURBS) elements, as well as different families of mixed isogeometric analysis techniques, and assess their stability through a numerical inf‐sup test. Furthermore, the validity of the inf‐sup stability test in poromechanics is supported by a mathematical proof concerning the corresponding stability estimate. Finally, two numerical examples involving a rigid strip foundation on saturated soil and a swelling hydrogel structure are presented to validate the stability and to demonstrate the robustness of the proposed approach.     

Uncertainty analysis of thermo-hydro-mechanical coupled processes in heterogeneous porous media

In this paper we present an uncertainty analysis of thermo-hydro-mechanical (THM) coupled processes in a typical geothermal reservoir in crystalline rock. Fracture and matrix are treated conceptually as an equivalent porous medium, and the model is applied to available data from the Urach Spa and Falkenberg sites (Germany). The finite element method (FEM) is used for the numerical analysis of fully coupled THM processes, including thermal water flow, advective–diffusive heat transport, and thermoelasticity. Non-linearity in system behavior is introduced via temperature and pressure dependent fluid properties. Reservoir parameters are considered as spatially random variables and their realizations are generated using conditional Gaussian simulation. The related Monte-Carlo analysis of the coupled THM problem is computationally very expensive. To enhance computational efficiency, the parallel FEM based on domain decomposition technology using message passing interface (MPI) is utilized to conduct the numerous simulations. In the numerical analysis we considered two reservoir modes: undisturbed and stimulated. The uncertainty analysis we apply captures both the effects of heterogeneity and hydraulic stimulation near the injection borehole. The results show the influence of parameter ranges on reservoir evolution during long-term heat extraction, taking into account fully coupled thermo-hydro-mechanical processes. We found that the most significant factors in the analysis are permeability and heat capacity. The study demonstrates the importance of taking parameter uncertainties into account for geothermal reservoir evaluation in order to assess the viability of numerical modeling.     

Surface behaviour of biomaterials: The theta surface for biocompatibility

“Biomaterials” are non-living substances selected to have predictable interactions with contacting biological phases, in applications ranging from medical/dental implants to food processing to control of biofouling in the sea. More than 30 years of empirical observations of the surface behaviours of various materials in biological settings, when correlated with the contact-angle-determined Critical Surface Tensions (CST) for these same materials, support the definition of the “theta surface”. The “theta surface” is that characteristic expression of outermost atomic features least retentive of depositing proteins, and identified by the bioengineering criterion of having measured CST between 20 and 30 mN/m. Biomaterials applications requiring strong bioadhesion must avoid this range, while those requiring easy release of accumulating biomass should have “theta surface” qualities. Selection of blood-compatible materials is a main example. It is forecast that future biomaterials will be safely and effectively translated directly to clinical use, without requiring animal testing, based on laboratory data for CST, protein denaturation, and cell spreading alone.     

Analysis of plane porous emitters with surface combustion and a heated article

Computational dependences are obtained for porous emitters, taking account of the influence of the velocity and heat of combustion of the injectant, the thermophysical properties, the porosity of the packing, and the degrees of the interacting media.     

Effective moduli of hyperelastic porous media at large deformation

Summary.  Among the parameters affecting the overall material properties of porous media, the most significant involve the micromechanical morphology, the matrix material behavior and the applied load range. Considering a unit cell for the porous medium, several approaches of the material response are developed, which yield the effective properties of the medium. Numerical results are presented and compared with experimental or analytical data available in literature. Proposed formulations impose several material characterizations ranging from linear elastic to incompressible hyperelastic. In the case of nonlinear materials, a special formulation has been developed permitting prediction of the porous material moduli. This formulation considers a special nonlinear form for the strain energy function under specific loading conditions. The proposed method yields simple formulas approximating the effective moduli of porous media, which are useful for design purposes. Received August 3, 2001; revised August 14, 2002 Published online: January 16, 2003 Acknowledgements The first of the authors is grateful to his mentor Dr. Paul J. Blatz for his encouragement all these years for continuous research on the nonlinear theories of hyperelastic materials.     

XPS characterization of surface modified titanium alloys for use as biomaterials

Three different Ti alloys of biomedical interest have been studied by means of X-ray photoelectron spectroscopy (XPS) to determine their surface chemical composition in both as-received condition and after oxidation at 750 °C in air for different times. Compositions of the investigated alloys were, in wt.%, Ti-7Nb-6Al, Ti-13Nb-13Zr and Ti-15Zr-4Nb. XPS analyses showed a behaviour of the Ti-7Nb-6Al alloy different from that of the two TiNbZr alloys, evidencing the role of the chemical composition of the alloys on the oxidation mechanisms. The oxidation process generates an aluminium-oxide rich surface on the Ti-7Nb-6Al, while in the case of the TiNbZr alloys a titanium-oxide rich layer is formed. The effect of the heat treatment on the contribution of the minority elements at the surface is also discussed.