Elastic characterization of orthotropic plates of any shape via static testing

The paper presents an inverse procedure for identifying elastic properties of isotropic or orthotropic materials from the full-field measurement of the surface displacements of plates under flexural loading configurations. The procedure is based on a numerical–experimental optimisation process which minimizes an error function defined by subtracting the experimental data from the outputs of the numerical analysis. In each iteration the optimisation process updates the values of the elastic constants in a finite element model of the specimen used in the experimental tests. The unknown parameters are simultaneously identified by a single test and without damaging the structural integrity of the specimen. The possibility of using the methodology for characterizing any-shaped plates was investigated. The applicability and the robustness of the procedure were carried out on aluminum and unidirectional Graphite/PEEK laminate specimens. Phase-shifting speckle interferometry was employed to detect the out-of-plane displacement field of a portion of the observed surface of the specimen.     

Effective Cohesive Behavior of Layers of Interatomic Planes

A simple model of cleavage in brittle crystals consists of a layer of material containing N atomic planes separating in accordance with an interplanar potential under the action of an opening displacement δ prescribed on the boundary of the layer. The problem addressed in this work concerns the characterization of the constrained minima of the energy E_N of the layer as a function of δ as N becomes large. These minima determine the effective or macroscopic cohesive law of the crystal. The main results presented in this communication are: (i) the computation of the Γ limit E₀ of E_N as N → ∞; (ii) the characterization of the minimum values of E₀ as a function of the macroscopic opening displacement; (iii) a proof of uniform convergence of the minima of E_N for the case of nearest-neighbor interactions; and (iv) a proof of uniform convergence of the derivatives of E_N, or tractions, in the same case. The scaling on which the present Γ-convergence analysis is based has the effect of separating the bulk and surface contributions to the energy. It differs crucially from other scalings employed in the past in that it renders both contributions of the same order.     

Constitutive branching analysis of cylindrical bodies under in-plane equibiaxial dead-load tractions

Finite homogeneous deformations of hyperelastic cylindrical bodies subjected to in-plane equibiaxial dead-load tractions are analyzed. Four basic equilibrium problems are formulated considering incompressible and compressible isotropic bodies under plane stress and plane deformation condition. Depending on the form of the stored energy function, these plane problems, in addition to the obvious symmetric solutions, may admit asymmetric solutions. In other words, the body may assume an equilibrium configuration characterized by two unequal in-plane principal stretches corresponding to equal external forces. In this paper, a mathematical condition, in terms of the principal invariants, governing the global development of the asymmetric deformation branches is obtained and examined in detail with regard to different choices of the stored energy function. Moreover, explicit expressions for evaluating critical loads and bifurcation points are derived. With reference to neo-Hookean, Mooney-Rivlin and Ogden-Ball materials, a broad numerical analysis is performed and the qualitatively more interesting asymmetric equilibrium branches are shown. Finally, using the energy criterion, a number of considerations are put forward about the stability of the computed solutions.     

A class of linear viscoelastic models based on Bessel functions

In this paper we investigate a general class of linear viscoelastic models whose creep and relaxation memory functions are expressed in Laplace domain by suitable ratios of modified Bessel functions of contiguous order. In time domain these functions are shown to be expressed by Dirichlet series (that is infinite Prony series). It follows that the corresponding creep compliance and relaxation modulus turn out to be characterized by infinite discrete spectra of retardation and relaxation time respectively. As a matter of fact, we get a class of viscoelastic models depending on a real parameter \(\nu > -1\). Such models exhibit rheological properties akin to those of a fractional Maxwell model (of order 1/2) for short times and of a standard Maxwell model for long times.     

Impact of sorption phenomena on multiphase conveying processes

Twin-screw multiphase pumps are employed increasingly to convey multiphase mixtures of crude oil, accompanying fluids, associated gas and solid particles. They are positive displacement pumps and suitable for handling products containing liquid accompanied by large amounts of gas. Experimental investigations on the conveying characteristic, namely measuring the delivered volume flow as a function of the pressure difference, provide results for selected mixtures. By means of the on hand work, the influence of sorption phenomena occurring due to pressure variations alongside the conveying process on the conveying characteristics of twin-screw pumps delivering mixtures of oil and gases is measured. The employed gases are air and carbon dioxide, which differ strongly in solubility in oil. All experiments are conducted in a closed loop test facility, where oil and gas volume flows are mixed before the inlet and separated after the outlet of the multiphase pump. In order to simulate the influence of the suction side pressure drop in the reservoir on the conveying characteristic, packed beds are employed as oil-filed model. Sorption processes inside of the oil-field model and within the multiphase pump affect the conveying behaviour significantly. The two-phase flow in the inlet and outlet pipe is visualised by means of a capacitance tomography system. Results show that the oil fraction of the total delivered volume flow is decreased due to desorption at the pump inlet. The gas fraction at the pump outlet is further decreased due to absorption. Experimental results are compared to calculated solubilities of the on-hand gases in oil and to the theoretically derived gas volume flow fraction expected at the multiphase pump.     

Modeling and Analysis of Seawater Intrusion in the Coastal Aquifer of Eastern Cap-Bon, Tunisia

A numerical model that treats density-dependent variably saturated flow and miscible salt transport is used to investigate the occurrence of seawater intrusion in the Korba aquifer of the eastern coast of Cap-Bon in northern Tunisia. We examine the interplay between pumping regimes and recharge scenarios and its effect on the saline water distribution. More localized simulations are used to examine, in vertical cross sections, the effects of well location and soil type and the role of the vadose zone in possible remediation actions. The exploratory simulations suggest interesting interactions between the unsaturated zone and the saltwater–freshwater interface with possible implications for groundwater exploitation from shallow unconfined coastal aquifers, involving in one case feedback between seawater intrusion and the high pressure head gradients around the pumping-induced drawdown cone and in another case threshold-like interface displacement for tight soils such as clays. The data processing steps undertaken in this GIS and modeling study are described in some detail, and a critical assessment is given of the data availability and of the requirements for successful monitoring and modeling of seawater intrusion risks in heavily exploited coastal aquifers such as those found in the semi-arid regions of the Mediterranean basin. It is shown how, with the aid of GIS, reasonably reliable information can be assembled from maps, surveys, and other sources of geospatial and hydrogeological data, an approach that is necessary in the many regions of the world with acute water resource problems but with limited means for undertaking systematic data acquisition and environmental monitoring actions. Nonetheless the need for more concerted monitoring of relevant parameters and processes and of closer coordination between monitoring and modeling is stressed. An idea of the extent of over-exploitation of the Korba aquifer is obtained by examining the pumping and rainfall/infiltration data, and the simulation results support groundwater pumping as the mechanism for and seawater intrusion as the origin of the salt contamination observed in the soils and subsurface waters of the Korba plain.