Geometric Conditions Research Articles

Heat Exchanger Improvement of a Counter-Flow Dew Point Evaporative Cooler Through COMSOL Simulations

Due to modern comfort demands and global warming, heating, ventilation, and air conditioning (HVAC) systems are widely used in many homes and buildings. However, HVAC based on the Vapor Compression System (VCS) is a major energy consumer, accounting for 20–50% of a building’s energy consumption and responsible for 29% of the world’s CO2 emissions. Dew-point evaporative coolers offer a sustainable alternative yet face challenges, e.g., dew point and wet bulb effectiveness. Given the above, dew point evaporative cooling systems may find a place to dethrone conventional air conditioning systems. This research aims to design a dew point evaporative cooler system with better performance in terms of dew point and wet bulb effectiveness. In terms of methodology, a heat exchanger as part of a counter-flow dew point cooling system was designed and analyzed using COMSOL simulations under different representative climatic, geometric, and dimensional conditions, taking into account turbulent flow. Next, our model was compared with other cooling systems. The results show that our model performs similarly to other cooling systems, with an error of around 6.89% in the output temperature at low relative humidity (0–21%). In comparison, our system is more sensitive to humidity in the climate, whereas heat pumps can operate in high humidity. The average dew point and wet bulb effectiveness were also higher than reported in the literature, at 91.38% and 147.84%, respectively. In addition, there are some potential limitations of the simulations in terms of the assumptions made about atmospheric conditions. For this reason, the results cannot be generalized but must be considered as a starting point for future research and technology development projects.

Application of Differential Equations on the Ricci Curvature of Contact CR-Warped Product Submanifolds of S2n+1(1) with Semi-Symmetric Metric Connection

In this paper, we explore the uses of Obata’s differential equation in relation to the Ricci curvature of an odd-dimensional sphere that possesses a semi-symmetric metric connection. Specifically, we establish that, given certain conditions, the underlying submanifold can be identified as an isometric sphere. Additionally, we investigate the impact of specific differential equations on these submanifolds and demonstrate that, when certain geometric conditions are met, the base submanifold can be characterized as a special type of warped product.

Connectivity of Parameter Regions of Multistationarity for Multisite Phosphorylation Networks

The parameter region of multistationarity of a reaction network contains all the parameters for which the associated dynamical system exhibits multiple steady states. Describing this region is challenging and remains an active area of research. In this paper, we concentrate on two biologically relevant families of reaction networks that model multisite phosphorylation and dephosphorylation of a substrate at n sites. For small values of n, it had previously been shown that the parameter region of multistationarity is connected. Here, we extend these results and provide a proof that applies to all values of n. Our techniques are based on the study of the critical polynomial associated with these reaction networks together with polyhedral geometric conditions of the signed support of this polynomial.

Influence of convection during droplet evaporation on corrosion product distribution in CFRP-AA2024 galvanic couple: Modeling and experimental approaches

This work aims to clarify the impact of convection, generated within an electrolyte droplet during evaporation, on the distribution of Al(OH)3 in the CFRP-AA2024 system. Both Finite Element and experimental approaches were employed to determine whether convection is significant or negligible. By coupling the Navier–Stokes and Nernst–Planck equations with appropriate geometric and boundary conditions, the transient distribution of corrosion products was numerically tracked. The results showed that Al(OH)3 preferentially deposits on the CFRP surface, a pattern absent when convection is excluded. Experiments confirmed that internal convective currents can transport the Al(OH)3 compound, aligning with the numerical predictions.

Large unions of generalized integral sections on elliptic surfaces

Let f : X → B f \colon X \to B be a nonisotrivial complex elliptic surface and let D ⊂ X \mathcal {D} \subset X be an integral divisor dominating B B . We study finiteness related properties of generalized ( S , D ) (S, \mathcal {D}) -integral sections σ : B → X \sigma \colon B \to X of X X where S ⊂ B S \subset B is arbitrary. These integral sections σ \sigma are algebraic and satisfy the geometric condition f ( σ ( B ) ∩ D ) ⊂ S f ( \sigma (B) \cap \mathcal {D})\subset S . For S ⊂ B S \subset B finite, the set of ( S , D ) (S, \mathcal {D}) -integral sections of X X is finite by the well-known Siegel theorem. In this article, we establish a general quantitative finiteness result for large unions of ( S , D ) (S, \mathcal {D}) -integral sections in which both the subset S S and the divisor D \mathcal {D} are allowed to vary in families where notably S S is not necessarily finite or countable. Some applications to generalized unit equations over function fields are also obtained.

Contractibility of the Rips complexes of Integer lattices via local domination

We prove that for each positive integer n n , the Rips complexes of the n n -dimensional integer lattice in the d 1 d_1 metric (i.e., the Manhattan metric, also called the natural word metric in the Cayley graph) are contractible at scales above n 2 ( 2 n − 1 ) n^2(2n-1) , with the bounds arising from the Jung constants. We introduce a new concept of locally dominated vertices in a simplicial complex, upon which our proof strategy is based. This allows us to deduce the contractibility of the Rips complexes from a local geometric condition called local crushing. In the case of the integer lattices in dimension n n and a fixed scale r r , this condition entails the comparison of finitely many distances to conclude that the corresponding Rips complex is contractible. In particular, we are able to verify that for n = 1 , 2 , 3 n=1,2,3 , the Rips complex of the n n -dimensional integer lattice at scale greater or equal to n n is contractible. We conjecture that the same proof strategy can be used to extend this result to all dimensions n n .

Particulate fouling simulation in unit micropore using a hydrodynamically coupled Lagrangian framework

Predicting and mitigating pore clogging is challenging for the sustainable operation of water treatment systems. During transport and filtration through membrane micropores, buoyant contaminants in water gradually deposit on the surface, reducing the membrane's lifespan and performance, and sometimes completely blocking the pores. To alleviate the negative effects of fouling and to ensure sustainable operation, it is necessary to understand the fundamental mechanisms of fouling and to predict the probability of fouling formation under specific geometrical and material conditions. In this study, multiscale simulations are conducted to understand the fundamental mechanisms of particulate fouling at a microscopic level based on a Lagrangian framework incorporating inter-particle hydrodynamic interactions. We investigate both dead-end and cross-flow filtration, considering the direction of the feed stream relative to the unit micropore. The results elucidate the quantitative background of fouling history, which agrees with experimental findings. Depending on the level of hydrodynamic stress specific to the clog location and the nature of inter-particle interactions, deformation or resuspension of the clog is observed, competing with deposition, which leads to a two-way fouling history. Dominant deposition leads to micropore clogging, and to the best of the authors' knowledge, this is the first study to observe complete blockage and subsequent reopening. With this approach, the microscopic backgrounds between permanent and temporary pore blocking are distinguished. This study is expected to provide useful insights for controlling operational conditions to optimize anti-fouling performance in the transport and filtration through micropores.

Near-real-time atmospheric and oceanic science products of Himawari-8 and Himawari-9 geostationary satellites over the South China Sea

Abstract. The initial release of near-real-time (NRT) atmospheric and oceanic science products from Japanese Himawari-8 and Himawari-9 (H8/9) geostationary (GEO) satellites over the South China Sea (SCS) was unveiled in 2024. The primary objective behind crafting these NRT H8/9 satellite products is to facilitate weather and marine environment monitoring, enhance maritime security, and aid ocean navigation, among other purposes. As part of this investigation, a novel NRT data processing system was devised to generate a variety of regional H8/9 GEO satellite science products within a resolution of 10 min and a gridded resolution of 0.05° × 0.05° from 3 November 2022 to the present. This algorithm system was built upon the preceding Fengyun (FY) geostationary satellite algorithm test bed (FYGAT), which was the prototype of the FY-4 GEO meteorological satellite science product operational processing system. These regional H8/9 GEO satellite science products encompass a range of crucial data such as cloud mask, fraction, height, phase, optical, and microphysical properties; layered precipitable water; and sea surface temperature. We subjected these products to rigorous evaluations against high-quality analogous satellite products and reanalysis data spanning 1 year in 2023. The validations underscore a strong consistency between the H8/9 GEO satellite atmospheric and oceanic science products over the SCS and the referenced products. Nevertheless, slight discrepancies in these satellite science products were identified, primarily stemming from variations in sensor/dataset characteristics, retrieval algorithms, and geometric conditions. These outcomes demonstrate the suitability of the first edition of NRT atmospheric and oceanic science products of H8/9 satellites over the SCS in supporting the intended quantitative applications. This NRT GEO satellite data record is publicly accessible through the File Transfer Protocol (FTP) provided by the Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai) in China. Free access to the dataset is possible via https://doi.org/10.6084/m9.figshare.25015853 (Liu et al., 2024).

Numerical Investigation of Two-Phase Shock Waves in CO2 Flows Using a Modified Hertz–Knudsen Model

Abstract Understanding the complex behavior of two-phase shocks in CO2 flows is essential for a variety of applications, including carbon capture and storage () and transcritical refrigeration cycles. This study presents a comprehensive numerical investigation of two-phase shock waves using the multispecies user-defined real gas model in Ansys Fluent. The simulations are performed for de-Laval nozzles, exploring the two-phase shock features for three-dimensional (3D), two-dimensional (2D), and two-dimensional axisymmetric geometries. The nonequilibrium condensation, subsequent evaporation, and denucleation occurring across the shock are modeled through a set of user-defined scalar transport equations implemented within Ansys Fluent. The two-phase computational fluid dynamics (CFD) simulations are carried out in proximity to the critical point where real gas effects are relevant. The CO2 real gas properties are computed using an in-house Python code and integrated into the solver via user-defined functions as external look-up tables. This study provides valuable insights into the physical processes underlying two-phase shocks in CO2 flows and their sensitivity to geometric variations and thermodynamic conditions. The findings contribute to the development and modification of predictive models and optimized designs for systems involving two-phase CO2 flows. The results highlight the influence of geometry configurations and thermodynamic conditions on shock location and intensity, providing comparisons for shock waves occurring in two-phase flows and supercritical single-phase flows.

Susceptibility of hydraulic structures to internal erosion: modeling of suffusion process

Internal erosion is a primary cause of hydraulic structure failure, manifesting as two key phenomena: piping erosion and suffusion. These processes differ in their geometrical and hydraulic boundary conditions, resulting in varying levels of failure risk. Piping erosion is the more hazardous and rapid process, often leading to immediate failure if not promptly addressed. In contrast, suffusion gradually alters the permeability of the medium, potentially culminating in failure after a prolonged period of development. In this study, we propose a model for suffusion based on Darcy’s law, Papamichos' erosion law, and Einstein's viscosity evolution relation. The model describes the temporal evolution of the average porosity in the porous medium, the concentration of eroded particles in the fluid, and the mass of particles eroded, while highlighting the impact of hydraulic and mechanical parameters, such as the erosion coefficient and maximum porosity, on this evolution. The numerical solution is obtained using the finite difference method, with the sample discretized into elementary layers. For discretization, an explicit off-centered scheme was adopted. The simulation results reveal that suffusion is strongly influenced by soil hydraulic and mechanical parameters, particularly the erosion coefficient (λ) and final porosity (Ømax).

A holistic study of the effect of geometrical and processing conditions on the static mechanical performance of LPBF strut elements

Laser powder bed fusion (LPBF) enables geometrical designs of great complexity, such as metamaterials. These structures are founded on elemental struts printed at various orientations and sizes. Understanding how these design variables affect mechanical properties is crucial for optimizing component performance. This work aims to systematically investigate the impact between these design variables on defects, roughness, geometrical deviations, and microstructure of Ti-6Al-4V elemental struts and correlate them with mechanical properties. The analysis shows that smaller strut diameters present an increased sensitivity to defects, reducing ductility by 45.8% on average as the diameter decreases from 1.5 mm to 0.5 mm. When compared to vertical struts, horizontally printed struts of 1.5 mm, 1 mm, and 0.5 mm present on average a respective reduction in ductility of 57.4%, 59.8%, and 70.9%, and a respective reduction in the ultimate strength of 13.3%, 24.5%, 61.2%. This has been associated with warping and increased roughness caused by dross formation. Finally, the study shows the complex interaction of process parameters' effect with the struts' orientation and size. These findings pose the basis for a more accurate and optimal mechanical design of cellular metamaterials, from the underlying material perspective.

Modified Easley formula for elastic critical global shear buckling stress of corrugated steel webs considering real boundary conditions

The real juncture between corrugated steel webs (CSWs) and flanges follows a multi-segmented line, distinct from that of flat steel webs. Classic methods may yield significant deviations in predicting the elastic global shear buckling capacity of CSWs of various scales due to their failure to consider real boundary constraints. Therefore, a universally applicable formula for calculating the elastic critical global shear buckling stress of CSWs, which accounts for real boundary conditions, is proposed. This formula is pertinent to both large-scale engineering CSWs and small-scale testing CSWs. This study commenced with a comprehensive reassessment of the elastic global shear buckling calculation method. Subsequently, the influence of geometric parameter ratios on the elastic critical global buckling stress was examined. The primary parameter was identified and employed to improve the global buckling coefficient. The proposed calculation method was validated using different corrugation configurations, including 1000-type, 1200-type, 1600-type, 1800-type, and 2000-type CSWs, as well as other CSWs used in experimental settings. These results were compared with those obtained from other reference methods. Findings indicate that the accuracy of the classic theoretical method is affected by variations in both boundary conditions and geometric dimensions due to the constraint effect of real boundary conditions. Under the real boundary conditions, the elastic critical global shear buckling stress of CSWs with simply supported boundary conditions is close to that of CSWs with consolidated boundary conditions. The ratio of web height to corrugation depth primarily affects the elastic global shear buckling capacity, which decreases as the ratio increases. The Easley formula can be modified based on the web height to corrugation depth ratio. Comparisons of numerous numerical and theoretical results reveal that the proposed calculation method exhibits commendable computational precision. In comparison to alternative formulas, the proposed method demonstrates enhanced consistency for calculating CSWs with varying geometric dimensions and boundary conditions, thereby demonstrating its favorable applicability. These conclusions provide valuable reference for the shear design of CSWs.

Evaluating the Performance of Ensemble Machine Learning Algorithms Over Traditional Machine Learning Algorithms for Predicting Fire Resistance in FRP Strengthened Concrete Beams

In recent years, fiber-reinforced polymers (FRP) have emerged as a highly effective solution for strengthening reinforced concrete (RC) structures. However, accurately assessing the fire resistance of FRP-strengthened members remains a significant challenge due to the limited guidance available in current building codes, often leading to conservative and cost-intensive evaluations. Experimental testing and numerical analysis required for such assessments are resource-demanding, highlighting the need for more efficient methods. This study investigates the application of machine learning (ML) techniques to predict the fire resistance of FRP-strengthened RC beams. Twelve ML models, including eight ensemble methods and four traditional approaches, were employed. The models were trained using a comprehensive dataset comprising over 21,000 data points obtained from numerical simulations and experimental tests. The dataset captured variations in geometric configurations, insulation strategies, loading conditions, and material properties. To enhance predictive accuracy, Bayesian optimization and k-fold cross-validation were applied for model tuning, while the Shapley Additive Explanations (SHAP) method was utilized to assess the relative importance of features influencing fire resistance. Among the models tested, Extreme Gradient Boosting (XGBoost), Categorical Boosting (CatBoost), Light Gradient Boosting (LGBoost), and Gradient Boosting (GRB) demonstrated superior performance, achieving accuracy rates exceeding 92%. Key factors identified as significantly affecting fire resistance included loading ratio, area of tensile reinforcement, insulation depth, concrete cover thickness, and FRP area. The findings underscore the potential of ensemble ML techniques over traditional methods for accurately predicting the fire resistance of FRP-strengthened RC beams, offering critical insights for optimizing design practices and enhancing structural fire safety.

Application of phase space file secondary computation method in cell dose distribution

Phase space files can store the particle information in one or more planes of radiation particles simulated by the Monte Carlo (MC) method. The secondary calculation method based on phase space files is commonly used to improve the efficiency of MC simulations. However, it is still unclear whether phase space files are applicable for microdosimetric evaluations. In this study, voxel-type and mesh-type monolayer cell population models of different sizes were constructed, and phase space files of secondary electrons generated by photons with different initial energies were obtained using the MC software -- PHITS. The overall average dose caused by the secondary electron phase space files in the region of interest and their microdosimetric distribution within cells were calculated and compared with the results caused by the initial photons under the same geometric conditions. The results showed that the adoption of secondary electron phase space files had almost no impact on the evaluation of macroscopic average dose, with deviations lower than 3% compared to the overall dose caused by the initial photons in the Petri dish. For microdosimetric distributions of the voxel-type model and the two different morphologies of mesh-type cell models, with a macroscopic accumulated dose of 1 mGy, the relative deviation of the cell dose distribution generated by the initial photons and the phase space files was below 10% and the total computation time of phase space files was below 2% of initial photon's. For accumulated doses of 10, 50, and 100 mGy, the relative deviation of the cell nucleus specific energy obtained by secondary electrons and initial photons was greater than 10%. As the size of the culture dish increased, the differences in cell dose distributions also increased, with the root mean square error (RMSE) and coefficient of variation (Cv) of dose distributions both exceeding 30%. In conclusion, this study assessed the effectiveness of the secondary calculation method utilizing phase space files for dose evaluation at the cellular scale. This research offers essential technical support and theoretical foundations for the utilization of this approach in microdosimetric investigations at the cellular level.

Slope stability/instability analysis of advanced nanocomposite reinforced column structure under mechanical loading via coupled Carrera unified formulation, layer-wise and Laplace transform approaches

This study presents a comprehensive investigation into the slope stability and instability of column structures made of Triply Periodic Minimal Surfaces (TPMS) under mechanical loading. TPMS structures, known for their high strength-to-weight ratio, are increasingly used in engineering applications, particularly in lightweight structures. However, their stability behavior under complex loading conditions remains largely unexplored. To address this gap, we employ a coupled approach integrating the Carrera Unified Formulation (CUF), the Layer-Wise (LW) theory, and Laplace Transform techniques. The CUF framework, known for its versatility in modeling structural behavior across different geometrical and loading configurations, is utilized to capture the mechanical response of the TPMS-based columns. The LW theory further enhances the model by accurately representing the through-thickness behavior, particularly crucial for layered or composite TPMS structures. Finally, the Laplace Transform approach is applied to efficiently solve the governing differential equations, reducing the computational complexity of time-dependent mechanical analyses. A parametric study investigates the influence of various geometrical parameters, material properties, and loading conditions on the stability of the structures. The results highlight the critical factors influencing slope stability, including the interplay between the TPMS geometry and material distribution. Moreover, the findings offer insights into failure mechanisms, providing a basis for optimizing the design of TPMS-based columns for enhanced mechanical performance. This work contributes to advancing the theoretical understanding of TPMS structures, offering novel methodologies for slope stability analysis in complex mechanical systems.

Enhancement of heat transfer characteristics in wavy microchannel heat sinks with streamlined micropins within convergent-divergent flow passages

In the current study, the heat transfer characteristics of a novel design microchannel with a wavy sinusoidal convergent-divergent wall structure featuring streamlined pins have been numerically investigated under laminar flow conditions. Various amplitudes, wavelengths, pin heights, and Reynolds numbers are considered as parameters. The thermal and hydraulic characteristics are analyzed in terms of Nusselt number, Fanning friction factor, and Performance Evaluation Criteria number (PEC), which evaluates the heat transfer enhancement against the associated pressure drop. It is revealed that increasing the amplitude and decreasing wavelength, along with moderate pin heights, significantly augment heat transfer. The streamlined pins effectively direct the flow, and the resulting secondary flow and chaotic advection considerably enhance heat transfer in the designed configuration. The study demonstrates that the heat transfer can be improved by a factor of 4.79 compared to a straight microchannel. Under these geometric and flow conditions, the pressure drop increases by a factor of 9.87, and the PEC is found to be around 2.23. A multi-objective optimization study using the Non-dominated Sorting Genetic Algorithm (NSGA-II) is conducted with Genetic Aggregation Response Surface Methodology to evaluate the impact of various parameters on thermal-flow performance and to identify the optimal design with material quantity variation. According to the optimal results, a 5 % increase in material can augment thermal-flow performance by approximately 206.6 % compared to traditional microchannels. Finally, practical correlations for the Nusselt number and friction factor, accounting for various parameters, have been developed to facilitate in designing of microchannel cooling systems.

The hysteretic Aw–Rascle–Zhang model

AbstractA novel hyperbolic system of partial differential equations is introduced to model traffic flows. This system comprises three equations, with two being linearly degenerate; its main feature is the inclusion of a hysteretic term in a generalized Aw–Rascle–Zhang (ARZ) model. First, a maximum principle for the diffusive version of the model is proven. Then, it is demonstrated that a solution to the Riemann problem exists, which is unique among solutions that are monotone in velocity; all waves exploited in the construction have suitable viscous profiles. Through several examples it is shown how, as a consequence of different driving habits, the system can model the decay, emergence, or persistence of stop‐and‐go waves (a feature that is missing in the ARZ model), and such behavior is characterized by a simple geometric condition. Furthermore, the model allows the study of traffic flows with a mixture of drivers whose hysteresis loops are either clockwise or counterclockwise. In particular, the presence of sufficiently many of the former dampens speed oscillations.

A general method to synthesize planar overconstrained mechanism

Traditionally, planar overconstrained mechanisms has been explained through special geometry, which often lacks clarity and specificity. This paper addresses this challenge by introducing two explicit criteria for analyzing and synthesizing planar overconstrained mechanisms. With the criteria, one may synthesize new planar overconstrained systematically and confidently. To create new planar overconstrained mechanisms, three approaches are employed: the parallelogram-aided approach, the stretch-rotation approach, and an optimization-based method. Given that the mobility of mechanisms is independent of the choice of the ground link and that the mathematical treatment of function generation is straightforward, this paper proposes a systematic approach for synthesizing novel function cognates. By combining these approaches, new types of overconstrained mechanisms are discovered. Leveraging advanced computational tools, a special geometric condition for function cognates of inverted slider cranks is found for the first time. Through inversion, the coupler cognates for slider cranks are also identified. The success of these results indicates that the proposed criteria are explicit and crucial for discovering new mechanisms, and the concept may be extended to spherical or spatial cases.

Performance analysis of natural draft power plant cooling tower: Mathematical modeling of cross-flow type, application in capital cities of Iranian provinces

Cooling towers are heat exchangers that reduce the hot water temperature produced by process equipment through heat and mass transfer between water and air stream. This study investigates the performance of cross-flow cooling towers under various geometrical, physical, and environmental conditions. For this purpose, thermodynamic modeling of the cross-flow cooling tower was conducted, and the governing equations were numerically solved using the finite difference method. Unlike previous studies, the effects of water droplet deformation into an elliptical shape during its fall along the cooling tower were also considered. This deformation, which influences the drag coefficient, Reynolds number of the water droplets, droplet surface area, and its cross-section area, along with the incorporation of buoyancy force in the droplet momentum equation, led to an improvement in the results. Consequently, the maximum computational error in this case was reduced to 1.97 %, compared to the scenario where droplet deformation and buoyancy force were neglected. The change in geometrical parameters of the tower in Tehran and Rasht was investigated, revealing that increasing the outlet radius of the tower from 20 m to 22.5 m decreased the outlet water temperature by 1.21 °C and 0.67 °C and increased the thermal efficiency of the tower by 4.94 % and 2.88 % respectively, while increasing the tower height from 100 m to 120 m, only decreased the outlet water temperature by 0.47 °C and 0.26 °C, and increased the thermal efficiency of the tower by 1.89 % and 1.09 % respectively. Additionally, the cooling tower performance was assessed in the centers of different provinces .of Iran. Results showed that with an initial droplet radius of 1 mm and an inlet water temperature of 50 °C, the maximum and minimum temperature reductions occurred in Shahrekord by 20.16 °C and Bandarabbas by 12.37 °C, respectively.

The effect of unintended porosity on the first compressive stress maximum of alumina hollow sphere-filled bimodal composite metal foams

Bimodal composite metal foams made from Al99.5 aluminium and quasi-eutectic Sr-modified AlSi12 matrix were investigated, where the bimodality was introduced by two alumina hollow sphere sets with nominal diameters of Ø7.0 and Ø2.4 mm in various volume concentrations. The research aimed to determine the effect of the cell structure (especially the unintended porosity) on the first compressive stress maximum, depending on the applied matrix material. The various features of the cell structure were quantitatively measured in composite metal foams by filtering raw computed tomography analysis data. The casting porosity, the wetting porosity, the porosity from the various-sized hollow spheres, and the partially matrix-filled hollow spheres have been successfully distinguished based on volumetric and geometrical conditions, such as sphericity and compactness. The unintended porosity (as the sum of the casting porosity and the wetting porosity) influences the first compressive stress maximum of the Al99.5 matrix composite metal foams. In contrast, for the AlSi12Sr bimodal foams, the results correlated with the total porosity values. The first compressive stress maximum could be estimated well from the compressive yield strength of the matrix and the total porosity of the foam.