Combined Effect Of Heterogeneity Research Articles

Characteristics of crack growth in brittle solids with the effects of material heterogeneity and multi-crack interaction

AbstractDespite the extensive research on crack propagation in brittle solids, numerous unexplored problems still necessitate in-depth study. In this work, we focus on numerical modeling of multi-crack growth, aiming to explore the effect of material heterogeneity and multi-crack interaction on this process. To do this, an improved singular-finite element method (singular-FEM) is proposed with incorporation of heterogeneity and crack interaction. An efficient algorithm is proposed for simulating multi-crack propagation and interaction. Stress singularity near crack tip is reproduced by the singular elements. The singular-FEM is convenient and cost-effective, as the zone far away from crack tips is directly discretized using linear elements, in contrast to the quadratic or transition elements utilized in traditional FEM. Next, the proposed method is validated through benchmark study. Numerical results demonstrate that the superiority of the singular-FEM, which combines the merits of low cost and high accuracy. Then, the mechanics of crack growth are explored in more complex scenarios, accounting for the effects of crack interaction, loading condition and heterogeneity on crack trajectory, stress field and energy release rate. The findings reveal that the combined effect of heterogeneity and crack interaction plays a critical role in the phenomenon of crack growth, and the proposed method is capable of effectively modeling the process.

Combined effects of heterogeneity and non-linearity on the critical time parameters of orthotropic conical shells

The work is devoted to the non-linear dynamic stability of heterogeneous orthotropic truncated conical shells subjected to the combined static and time-dependent axial loads. The basic equations are derived using the finite deflection theory with von Karman–Donnell-type of kinematic non-linearity and reduced to a non-linear differential equation with the time variable coefficient using the superposition principle and Galerkin method. The resulting equation is solved numerically using Runge–Kutta method for variety of an axial loading speed, heterogeneity of features, orthotropic material properties and conical shell characteristics to obtain the non-linear critical time parameters. Finally, the influences of the axial loading speed, non-linearity, heterogeneity and orthotropy on the dimensionless critical time parameters are discussed in detail.

Combined effect of heterogeneity, anisotropy and saturation on steady state flow and transport: Structure recognition and numerical simulation

Natural soil profiles may be interpreted as an arrangement of parts which are characterized by properties like hydraulic conductivity and water retention function. These parts form a complicated structure. Characterizing the soil structure is fundamental in subsurface hydrology because it has a crucial influence on flow and transport and defines the patterns of many ecological processes. We applied an image analysis method for recognition and classification of visual soil attributes in order to model flow and transport through a man‐made soil profile. Modeled and measured saturation‐dependent effective parameters were compared. We found that characterizing and describing conductivity patterns in soils with sharp conductivity contrasts is feasible. Differently, solving flow and transport on the basis of these conductivity maps is difficult and, in general, requires special care for representation of small‐scale processes.

Origin of lateral variation of seismic wave velocities and density in the deep mantle

Strong constraints can be placed on the origin of heterogeneity of seismic wave velocities and density if the observed ratios of various parameters are compared with mineral physics predictions. They include the shear to compressional wave velocity heterogeneity ratio,Rs/p≡ δ logVs/δ logVp, the bulk sound to shear wave velocity heterogeneity ratio,Rϕ/s≡ δ logVϕ/δ logVs, and the density to velocity heterogeneity ratio,Rρ/s,p≡ δ log ρ/δ logVs,p. Using mineral physics considerations, we calculate these ratios in the lower mantle corresponding to the thermal and chemical origin of velocity and density heterogeneity. Both anharmonic and anelastic effects are considered for thermal origin. Anharmonic effects are estimated from the theoretical calculations as well as from laboratory measurements which show a marked increase inRs/pwith pressure from ∼1.5 to ∼2.1 in the lower mantle. Such a trend is marginally consistent with seismological observations showing an increase inRs/pwith depth (from ∼1.7 to ∼3.2 in the lower mantle). However, anharmonic effect alone cannot explain inferred lowRρ/s(<0.2–0.4), and the values ofRs/ppredicted from anharmonic effects are systematically smaller than seismological observations. Anelastic effects must be included to account for these geophysical observations. A new formulation of anelastic effect is developed in which the role of nonlinear temperature dependence of anelasticity is included. When anharmonic and anelastic effects are combined, thermal effects on velocity and density can account for most of the geophysical observations in Earth's lower mantle. Effects other than temperature variations (such as chemical heterogeneity) are required only in the very deep portions of the mantle (deeper than ∼2000–2300 km). A puzzling observation is very large values ofRs/p(>2.7) and corresponding negative values ofRϕ/s(andRρ/s) in the deep lower mantle which cannot be accounted for by thermal or simple chemical heterogeneity such as the heterogeneity in the Fe/(Fe + Mg) and/or Mg/(Mg + Si) ratios. Possible causes of anomalies in this region are discussed, including the role of anisotropy and a combined effect of heterogeneity in Fe and Ca content.

Combined effects of heterogeneity, anisotropy, and saturation on steady state flow and transport: A laboratory sand tank experiment

Field soils show rather different spreading behavior at different water saturations, frequently caused by layering of the soil material. We performed tracer experiments in a laboratory sand tank. Such experiments complement and help comprehension of field investigations. We estimated, by image analysis, the first two moments of small plumes traveling through a two‐dimensional, heterogeneous medium with strongly anisotropic correlation structure. Three steady state regimes were analyzed. Two main conclusions were drawn. First, low saturation led to very large heterogeneity and to strong preferential flow. Thus the description of the flow paths and the prediction of the solute arrival times require, in this case, more accurate knowledge about the topological structure. Second, saturation‐dependent macroscopic anisotropy is an essential element of transport in unsaturated media. For this reason, small structural soil features should be properly upscaled to give appropriate effective soil parameters to be input in transport models.

Additive partitioning of plant species diversity in an agricultural mosaic landscape

In this paper, we quantify the effects of habitat variability and habitat heterogeneity based on the partitioning of landscape species diversity into additive components and link them to patch-specific diversity. The approach is illustrated with a case study from central Switzerland, where we recorded the presence of vascular plant species in a stratified random sample of 1'280 quadrats of 1 m2 within a total area of 0.23 km2. We derived components of within- and between-community diversity at four scale levels (quadrat, patch, habitat type, and landscape) for three diversity measures (species richness, Shannon index, and Simpson diversity). The model implies that what we measure as within-community diversity at a higher scale level is the combined effect of heterogeneity at various lower levels. The results suggest that the proportions of the individual diversity components depend on the habitat type and on the chosen diversity aspect. One habitat type may be more diverse than another at patch level, but less diverse at the level of habitat type. Landscape composition apparently is a key factor for explaining landscape species richness, but affects evenness only little. Before we can test the effect of landscape structure on landscape species richness, several problems will have to be solved. These include the incorporation of neighbourhood effects, the unbiased estimation of species richness components, and the quantification of the contribution of a landscape element to landscape species richness.

Space, energy and anisotropy effects on diffusion coefficients in the resonance region

Most of the present methods used in reactor calculations assume a priori that the conservation of the total, absorption and transfer cross sections will result in the conservation of the leakage term, div J. This assumption is not valid since it is well known that the leakage of neutrons from a heterogeneous cell is strongly anisotropic. In particular, the neutrons have a tendency to escape more easily in the axial direction. A new method is presented which includes linearly anisotropic scattering, a more adequate definition of the diffusion coefficient in a heterogeneous lattice and explicit energy dependence of the new diffusion coefficient in the resonance region. The study showed that the combined effect of heterogeneity and linear scattering anisotropy gave an increase of up to 29% in the parallel diffusion coefficient of TRX-3 and 5% in the parallel diffusion coefficient of ZPR-6/5. In contrast, the change in the perpendicular diffusion coefficient did not exceed 2% in both systems. These changes in the diffusion coefficients yielded a decrease in Δk k of 0.486% in TRX-3 and 0.188% in ZPR-6/5.