Computing overall elastic constants of polydisperse particulate composites from microtomographic data

In this paper, we use the well-known Hashin-Shtrikman-Willis variational principle to obtain the overall mechanical properties of heterogeneous polydisperse particulate composites. The emphasis is placed on the efficient numerical integration of complex three-dimensional integrals and on aspects of the anisotropic material response of real tomographically characterized packs. For this purpose, we numerically calculate the complete statistics of real packs, which are numerically or tomographically generated. We use the parallel adaptive sparse Smolyak integration method with hierarchical basis to integrate complex singular integrals containing the product of probability functions and the second derivative of Green's function. Selected examples illustrate both the numerical and physical facets of our work. First, we show the reduction of integral points for integration in spherical coordinates. Then, we comment on the parallel scalability of our method and on the numerical accuracy associated with the integration of a singular function. Next, we validate the solver against the experimental data and verify the results by comparing it to a closed-form expression. To investigate the ability of our scheme to capture the anisotropic nature of packs, we study a lattice type system. Finally, we report on the elastic constants computed for the modeled anisotropic particulate system that is tomographically characterized.     

An error threshold criterion for singular value decomposition modes extracted from PIV data

Singular value decomposition (SVD) is often used as a tool to analyze particle image velocimetry (PIV) data. However, experimental error tends to corrupt higher SVD modes, in which the root mean square velocity value is smaller than the experimental error. Therefore, we suggest that the threshold criterion, $s_k >\sqrt{DT}\epsilon,$s_k >\sqrt{DT}\epsilon, can be used as a rough limit of the validity of SVD modes extracted from experimental data (where s _k is the singular value of mode k, D and T are the number of data sites and time steps, respectively, and e\epsilon is the root mean square PIV error). By synthesizing the relationship between the general SVD procedure and its two special cases—biorthogonal decomposition (BOD) and proper orthogonal decomposition (POD)—we show that our criterion can be used to assess modes extracted by either BOD or POD. We apply our threshold criterion to PIV data of the wake behind a live swimming Giant Danio (Danio aequipinnatus). The biorthogonal decomposition of the fish wake, which is a reverse-Kármán street, reveals that the first four modes are similar to the modes of a regular Kármán street created in the wake of a stationary cylinder and that higher modes are corrupted by experimental error.     

The effect of material properties on the radiation of impact sound from cylinders

A number of studies have investigated engineering methods of reducing forge-hammer noise by means of enclosure, blow reduction and external application of damping materials. Another alternative, in which parts and units are manufactured from metals with high internal damping, has yet to be fully investigated. In a theoretical and experimental study of sound radiation from cylindrical samples, candidate hammer materials are evaluated for potential reduction of radiated energy and energy spectrum. It is shown that the quantity of radiated sound is strongly dependent on the stiffness and damping properties of the candidate tool-steel, forged-iron and cast-iron samples. The rate of attenuation of sound radiation is also shown to be affected in a predictable manner from the (tabulated) properties of the metals.     

Fatigue damage of APC-2 composite assessed from material degradation and non-destructive evaluation data

Quasi-isotropic 45° APC-2 specimens are fatigued under constant amplitude stress reversal load condition. Fatigue induced degradation of the mechanical properties is correlated to data obtained from non-destructive evaluation. C-scan readings were used to define a generic damage severity factor D. It refers to the current fatigue damage state and accounts for the varying severity of damage at the different specimen locations. Analytical expressions are developed to relate D to the axial stiffness, residual strength and interlaminar shear strength. An indication of damage tolerance can thus be made for evaluating the integrity of structural components.     

Development of an efficient numerical model for hail impact simulation based on experimental data obtained from pressure sensitive film

Aircraft are subjects to a number of unpredictable loadings that can seriously affect their performance. In the spirit of ever increasing the safety of passengers, hail impact has been studied. This paper shows the progress that has been made using pressure sensitive film to measure the hail impact event. Moreover, the smooth particle hydrodynamics (SPH) method in LS-DYNA is used to create a numerical model in order to validate the numerical hail model so that it can be used in future advanced simulations of hail impact on components of aircraft. Results show that the SPH method can be effectively used to create a numerical hail model and that pressure sensitive film is a simple and inexpensive tool to capture the experimental data.     

The determination of plough draught—Part I. prediction from soil and meteorological data with cone index as the soil strength parameter

Using cone index as an indication of soil strength, empirical equations are developed in accordance with soil mechanics theory to relate soil moisture content to plough draught. The plough draught equation comprises a quasi-static component dependent on cone index and a dynamic component which is a function of the soil specific weight, plough speed and mouldbard tail angle. It is further argued that the cohesive and frictional components of the cone penetration resistance can be predicted by means of a simple equation comprising a reciprocal function of the square of the soil moisture content and a linear function of the soil specific weight. The cone index equation explained 98% of the experimental data for threthree soils over a wide range of moisture contents. These empirical equations, together with a soil moisture model, provide a method of predicting plough draught directly from soil and meteorological data.     

Reconstruction of the three mechanical material constants of a lossy fluid-like cylinder from low-frequency scattered acoustic fieldsReconstruction des trois constants mécaniques matériels d'un cylindre fluide dissipatif à partir de champs acoustiques basses fréquences

The inverse medium problem for a circular cylindrical domain is studied using low-frequency acoustic waves as the probe radiation. To second order in k₀a (k₀ the wavenumber in the host medium, a the radius of the cylinder), only the first three terms (i.e., of orders 0, ?1 and +1) in the partial wave representation of the scattered field are non-vanishing. This enables the scattered field to be expressed algebraically in terms of the unknown material constants, i.e., the density ρ₁, and the real and imaginary parts of complex compressibility κ₁ of the cylinder. It is shown that these relations can be inverted to yield explicit, decoupled expressions for ρ₁ and κ₁ in terms of the totality of the far-zone scattered field. These expressions furnish accurate estimations of the material parameters provided the probe frequency is low and the radius of the cylinder is known very precisely. To cite this article: T. Scotti, A. Wirgin, C. R. Mecanique 332 (2004).