Narrow Results

We consider the macroscopic model derived by Degond and Motsch from a time-continuous version of the Vicsek model, describing the interaction orientation in a large number of self-propelled particles. In this paper, we study the influence of a slight modification at the individual level, letting the relaxation parameter depend on the local density and taking in account some anisotropy in the observation kernel (which can model an angle of vision).

The main result is a certain robustness of this macroscopic limit and of the methodology used to derive it. With some adaptations to the concept of generalized collisional invariants, we are able to derive the same system of partial differential equations, the only difference being in the definition of the coefficients, which depend on the density. This new feature may lead to the loss of hyperbolicity in some regimes.

We then provide a general method which enables us to get asymptotic expansions of these coefficients. These expansions shows, in some effective situations, that the system is not hyperbolic. This asymptotic study is also useful to measure the influence of the angle of vision in the final macroscopic model, when the noise is small.

We consider an anisotropic first-order ODE aggregation model in two dimensions and its approximation by a second-order relaxation system. The relaxation model contains a small parameter $𝜀$, which can be interpreted as inertia or (non-dimensionalized) response time. We examine rigorously the limit $𝜀\to 0$ of solutions to the relaxation system. Of major interest is how discontinuous (in velocities) solutions to the first-order model are captured in the zero-inertia limit. We find that near such discontinuities, solutions to the second-order model perform fast transitions within a time layer of size ${𝒪}({𝜀}^{2/3})$. We validate this scale with numerical simulations.

Waves propagating through heterogeneous media experience scattering that can convert a coherent pulse into small incoherent fluctuations. This may appear as attenuation for the transmitted front pulse. The classic O’Doherty–Anstey theory describes such a transformation for scalar waves in finely layered media. Recent observations for seismic waves in the earth suggest that this theory can explain a significant component of seismic attenuation. An important question to answer is then how the O’Doherty–Anstey theory generalizes to seismic waves when several wave modes, possibly with the same velocity, interact. An important aspect of the O’Doherty–Anstey theory is the statistical stability property, which means that the transmitted front pulse is actually deterministic and depends only on the statistics of the medium but not on the particular medium realization when the medium is modeled as a random process. It is shown in this paper that this property generalizes in the case of elastic waves in a nontrivial way: the energy of the transmitted front pulse, but not the pulse shape itself, is statistically stable. This result is based on a separation of scales technique and a diffusion-approximation theorem that characterize the transmitted front pulse as the solution of a stochastic partial differential equation driven by two Brownian motions.

In this paper, the mechanical responses of a recently developed hyperelastic model for the neo-Hookean solids with aligned continuous cylindrical pores under finite homogeneous deformation that can capture the anisotropic compressibility as well as the coupling between the volumetric and deviatoric behaviours are examined. To this end, the strain energy function of this hyperelastic compressible transversely isotropic model contains terms for the coupling of volumetric and deviatoric behaviours. It is shown that, the asymptotic response of this anisotropic compressible model under extreme loading situations is considerably different from that of incompressible models. The unstable behaviour of the porous solid under hydrostatic stress/strain loadings is discussed in detail. When a general simple 2D shear deformation is applied to this porous solid in i₁ – i₂ plane, the normal stress in the third axial direction (i₃) is nonzero. The loss of monotonicity of the stress tensor under off-axis simple 2D shear loading is demonstrated as well.

Mechanical behaviors of artificial elastic tubes are studied to see if the fibre orientation in these vessels is optimal by comparison with those of human artery. By optimal we mean that the strengths of stretching and inflation in the vessels are equally good. Artificial thin film tubes have many applications in the food and fruit packing industry. In this paper, the wall of thin-film elastic tubes is considered as a fibre-reinforced membrane with two families of fibres and a uniform matrix material. Their mechanical properties are determined using a structure-based constitutive law. The constitutive parameters are inversely estimated from two separate uniaxial tensile tests in the circumferential and longitudinal directions. The inflation model for the elastic tubes and human common carotid artery are developed to investigate their breaking characteristics, and to explore the optimal fibre orientations. Results show that the fibre orientation has an important effect on the break behavior of the elastic tubes, and the tubes investigated are much weaker in the circumferential direction. On the other hand, the fibre orientation is close to the optimal state in the human common carotid artery.

Theoretical formulas for predicting the undrained shear strength of K₀ consolidated soft clays under the stress path related to triaxial and plane strain tests are presented within the framework of critical state soil mechanics. An inclined elliptical yield surface is adopted to take account of the initial anisotropic stress state. The undrained strength is determined by combining the undrained stress path in the volumetric stress–strain space and the initial yield surface in the deviator-mean stress space. The derived mathematical expressions are functions of the critical state frictional angle, the plastic volumetric strain ratio and the overconsolidation ratio, which can be simplified into the solutions for isotropically consolidated clays under triaxial tests or under plane strain tests. The results calculated by using the theoretical formulas obtained in this paper are in good agreement with the available collected test results. It indicates that these new formulas are applicable to triaxial and plane strain tests on normally and lightly to moderately overconsolidated soft clays.

A frictional sliding contact model is established for the anisotropic piezoelectric/piezomagnetic composites indented by a flat or circular stamp. The characteristic equation related to monoclinic anisotropic piezoelectric/piezomagnetic composites is of tenth-order. The stated problem is reduced to integral equations whose kernels present an unconventional singularity. Parametric studies reveal that both the volume fraction of the composites and the friction coefficient could significantly affect the tribological behaviors. Numerical results show that the surface quantities have a singularity or spike at the stamp edge, and that the magneto-electro coupling in piezoelectric/piezomagnetic composites does not exist in any single phase.

An anisotropic hyperelastic constitutive model with tension–shear coupling was developed for woven composite reinforcements based on fiber reinforced continuum mechanics theory. The strain energy of the model was additively decomposed into two parts nominally representing the fiber stretches and fiber–fiber interaction considering shear–tension coupling, respectively. Experimental data were used to identify material parameters orderly and simply in the constitutive model for a specific balanced plain woven carbon fabric. The developed model was validated by comparing numerical results with picture-frame shear tests under different pre-stretch ratios, and was then applied to the simulation of a hemispherical stamping experiment, demonstrating that the developed constitutive model is highly suitable to characterize the nonlinear and anisotropic mechanical behaviors of woven composite reinforcements under large deformation. The proposed model establishes a theoretical foundation for more accurate forming simulation and processing optimization of woven fabric composites.

In this work, large deformation of incompressible, hyperelastic membranes based on the quasi-linear viscoelasticity (QLV) theory is formulated. Time integration algorithm and the expression for consistent fourth-order tangent tensor are presented. The formulation covers isotropic as well as anisotropic polymeric and biological materials. To solve numerical examples, a nonlinear finite element formulation in the Lagrangian framework is developed. Finally, several examples are provided to investigate the applicability of the present formulation. It is found that the numerical results are in good agreement with the analytical and experimental results available in the literature.

Gas hydrate-bearing sediments (GHBS) are considered a significant potential energy source. However, the decomposition of hydrates can lead to various geological hazards. Therefore, a comprehensive investigation into the mechanical properties of GHBS is essential to ensure the safe extraction of gas hydrate. This paper presents a constitutive model for GHBS that incorporates anisotropy, based on the theory of thermodynamics. To account for the effects of hydrate filling and cementing, two parameters are introduced into the dissipation function of the model. The filling effect is expressed through the densification mechanism, which increases the density of the host sediment. The cementing effect is represented by the enhanced expansion of the yield surface. The yield function incorporates the spacing ratio $r$ and the teardrop shape parameter $\alpha$, which govern the shape of the yield surface, as well as the anisotropy angle ${𝜃}_n$, which signifies the anisotropic evolution law. The physical significance of these parameters is also elucidated. The anisotropic evolution is described by an exponential function. The proposed model is compared to both the test results and the existing constitutive model, and it is found that it provides more accurate predictions of the mechanical properties of GHBS.

The analysis of the filamentary structure of the cosmo as well as that of the internal structure of the polar ice suggests the development of models based on three-dimensional (3D) point processes. A point process, regarded as a random measure, can be expressed as a sum of Delta Dirac measures concentrated at some random points. The integration with respect to the point process leads the continuous wavelet transform of the process itself. As possible mother wavelets, we propose the application of the Mexican hat and the Morlet wavelet in order to implement the scale-angle energy density of the process, depending on the dilation parameter and on the three angles which define the direction in the Euclidean space. Such indicator proves to be a sensitive detector of any variation in the direction and it can be successfully implemented to study the isotropy or the filamentary structure in 3D point patterns.

The creep behavior of an anisotropic rotating disc of functionally gradient material (FGM) has been investigated in the present study using Hill's yield criteria and the creep behavior in this case is assumed to follow Sherby's constitutive model. The stress and strain rate distributions are calculated for disc having different types of anisotropy and the results obtained are compared graphically. It is concluded that the anisotropy of the material has a significant effect on the creep behavior of the FGM disc. It is also observed that the FGM disc shows better creep behavior than the non-FGM disc.

Anisotropy of a Gaussian field with stationary increments is related with the anisotropy of its spectral density. Such Gaussian fields can be used for modelling anisotropic homogeneous media, which leads to try to simulate these ones and identify parameters. This paper is a first attempt in these two directions. We first show how such Gaussian fields can be written as a random series, which is a first step for simulation purposes. There is anisotropy of the Gaussian field when its spectral density has a different power law in each direction. The exponent in a given direction can be obtained from an integration of the field on the orthogonal hyperplanes, as proved by the two last authors in ⁴. We then show how this property can be used to propose an estimator of this exponent.