A Deformation Model for Monotropic Plastic Foams under Compression/Tension Perpendicularly to the Foam Rise Direction

The deformation properties of monotropic plastic foams under uniaxial compression or tension perpendicularly to the foam rise direction are considered. Theoretical results are obtained for the case where the volume- deformation hypothesis is assumed. In order to perform numerical calculations, the foams are devided into three groups with different degrees of monotropy. For these groups, different methods of calculating the numerical value of the relative volume strain are used. The Young's modulus in the plane of isotropy is determined using both the mixed Reuss-Voigt and Voigt averaging. The Poisson ratios are expressed using the Reuss averaging. If only the axial deformation of the load-bearing elements (polymer struts) is allowed for, the results obtained do not agree with experimental data. Therefore, we also take into account the changes in their orientation. The values of Young's modulus and Poisson ratios are obtained for a wide range of degrees of extension of the model cell. A comparison of the theoretical results with the experimental data available shows a satisfactory agreement.     

A Deformation Model of Monotropic Plastic Foams in Shear Perpendicularly to the Isotropy Plane

Based on an ellipsoidal model for the cellular structure of monotropic plastic foams, their deformational properties in shear perpendicularly to the isotropy plane are predicted. The theoretical results are obtained for the case of pure shear. The deformation energy is calculated by the method of coordinates assuming that the polymer struts of the structure can change both their length and orientation. Numerical values of shear moduli are found for monotropic and isotropic plastic foams, which agree satisfactorily with the experimental data for polyurethane and polyvinylchloride foams available in the literature.     

Structural Modeling in the Mechanics of Porous Materials

A new method for analyzing the deformation behavior of rigid and elastic foams with a small volume content of solid phase ( < 0.2) is developed. Various structural models for describing the elastic behavior of rigid and elastic plastic foams are used and compared. The results of structural simulation of anisotropic auxetic (i.e., having a negative Poisson ratio) foams with concave cells are presented. For cyclic uniaxial compression of rigid foams and volumetric deformation of elastic foams, the stress-strain curves are obtained. The general shape of the curves agrees well with the nonlinearly elastic behavior of plastic foams observed in experiments.     

Elastic constants of monotropic plastic foams. 1. Deformation parallel to foam rise direction. A mathematical model

A mathematical model of the deformative properties and structure of lightweight, monotropic (or isotropic in the limiting case) plastic foams with a pronounced strut-like structure has been elaborated in the linear theory of deformation. A selection of five independent elastic constants is described. For the integral characterization of the deformative properties of plastic foams as micrononhomogeneous composite materials, the elastic constants are introduced as the effective constants. In order to describe the plastic foam structure, a local model consisting of two parts is proposed, i.e., a model of a continuous medium for the calculation of stresses and a local structure model. Considering deformation parallel to the foam rise direction when the semiaxes hypothesis is assumed, the Young modulus and Poisson's ratio are determined.Institute of Polymer Mechanics. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 6, pp. 719–733, November–December, 1997.     

Microstructural Model of a Closed-Cell Foam on the Basis of Image Analysis

The focus of this work is the identification of a unit cell that is able to represent the microstructure of a closed-cell solid foam to predict the effective behaviour of the foam numerically. For the investigation, a finite element model consisting of a repeating unit cell with periodical boundary conditions is implemented. A tetrakaidecahedral foam microstructure is considered as simplified cell geometry, and a strain-energy based homogenisation concept is utilized. On the basis of image analysis imperfections are applied to the cell. The obtained model is used as a representative volume element (RVE) for further investigations of the postbuckling behaviour of the foams. Different analyses are performed and the results are compared to literature and experimental data. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Collapse criteria of foam cells under various loading

Recently porous materials are widely used in civil and mechanical engineering. In particular, such porous materials as metal and polymer foams have applications in lightweight structures. From mechanics point of view foams can demonstrate unusual behavior such as strain localization related to foam cells buckling under certain loads. The aim of this work is the elaboration of the model of foam material taking into account the cell collapse. We consider the cell collapse initiation during the elastic instability and its further evolution under loading. The geometrical structure of foam is generated with the use of the Voronoi algorithm. Based on stochastic distributions of cells we create various geometrical models of foams. The influence of the cell volume, wall thicknesses and material properties of the foam material on critical loads is obtained. The calculations are performed with the use of Abaqus CAD/CAE system. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of cellular structure on the mechanical properties of plastic foams

A generalized equation for the compressive stress-strain diagrams of plastic foams is derived on the basis of a 14-faced model of the cell. The results obtained make it possible to predict the polymer base and type of cellular structure required to obtain a foam with predetermined mechanical properties in compression. The calculated values are shown to be in satisfactory agreement with the experimental data.Vladimir Scientific-Research Institute of Synthetic Resins. Translated from Mekhanika Polimerov, No. 4, pp. 594–602, July–August, 1970.     

Comparison of hyperelastic 2‐D and 3‐D model foams at large deformations

The influence of the modeling dimension on the determination of effective properties for hyperelastic foams is investigated by means of regular 2‐D and 3‐D model foams. For calculating the effective stress‐strain relationships of both microstructures, a strain energy based homogenization procedure is employed. The results from numerical analyses show that with a 2‐D model foam the basic deformation mechanisms of the 3‐D model can be captured. Nevertheless, due to the distinct quantitative deviations found from the homogenization analyses, 3‐D modeling approaches should be used if quantitative predictions for the effective material properties are required. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of the cellular structure on thermal conductivity of rigid closed-cell foam polymers during long-term aging

The thermal conductivity of rigid closed-cell polyurethane foams during long-term aging has been studied. The similarity between the kinetics of changes in the physical and mechanical characteristics of PU foams on progressive aging is established, which is attributed to the effect of matrix destruction. It is found that rigid foams have cell walls of various strength, whose impact on the kinetics of changes in the physical characteristics of the foams during long-term aging is ascertained. The results of predicting the thermal conductivity of PU foams by the method of temperature-time analogy and establishing the limits of its application are discussed. The research presented is of interest both in determining the foam durability and in replacing freons by alternative, ecologically less harmful blowing agents.     

Large Elastic Strains of Plastic Foams

The elastic deformation of plastic foams with a low (< 6%) volume fraction of solid phase is described based on a 4-rod equivalent element. A criterion is proposed which allows one to determine the parameter of structure of this element. Based on an analysis of the equivalent element, a procedure is developed for constructing the compression diagram of plastic foams in the region of large (> 70%) strains. The calculation results are compared with data found in the literature and experimental results for polyurethane foams obtained by the present authors. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 5, pp. 619–632, September–October, 2005.     

Experimental and numerical investigation of metal foams undergoing large deformations

Open cell aluminum metal foams are a new kind of material that are used in composite structures to reduce their weight, to increase their sound or energy absorption capability or to decrease their thermal conductivity. The design and analysis of such structures requires a macroscopic constitutive model of the foam that has to be determined by various experiments under different loading conditions. We support this procedure by analyzing the microstructure of the metal foam numerically under large deformations. To this end, we employ the finite cell method that can deal with large deformations and allows for an automatic and efficient discretization of the CT-image of the foam. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study of Heat Flow through Highly Porous Heat Insulators

A comprehensive study is done to model flow of heat through heat insulators based on materials with high gas content such as solidified foams (e.g., eXtruded PolyStyrene foams, Expanded PolyStyrene foam), cellular glass, etc. The actual internal cell-like structure of such an insulator is replicated by regularly shaped gas pockets, which are separated from each other by thin rims of solid materials. The first model focuses on heat flow across the insulator caused by conduction and convection. Subsequently, the effect of radiation is also studied. Several numerical results are presented and computational results are compared with experimentally measured data.     

On the stabilization mechanisms in liquid metallic foams

Metal foams are porous structures made up of conventional metals such as aluminium. Their advantageous density to stiffness ratio leads to a variety of applications especially in automotive industry, where they have gained interest as material used in shock absorbers and light weight construction parts. Solid metal foams are usually produced by solidification of a liquid metallic foam. The latter is generated by the introduction of gas into a melt analogous to aqueous foams. Depending on the parameters of the production process, porous structures with relative densities down to 10% of the original metal can be achieved. However, while the mechanisms leading to stable aqueous foams are quite well understood, this is not the case for metallic foams. In contrast for example to soap foams, no surface active or polar substances are present in liquid metals. It is merely known empirically that solid particles have a major influence on the stability of a liquid metallic foam. In this paper we present experimental observations showing that the stability and structure of metallic foams produced via a melt route are predominantly governed by interface rather than drainage effects. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of the cellular structure on thermal conductivity of rigid closed-cell foam polymers during long-term aging

The thermal conductivity of rigid closed-cell polyurethane foams during long-term aging has been studied. The similarity between the kinetics of changes in the physical and mechanical characteristics of PU foams on progressive aging is established, which is attributed to the effect of matrix destruction. It is found that rigid foams have cell walls of various strength, whose impact on the kinetics of changes in the physical characteristics of the foams during long-term aging is ascertained. The results of predicting the thermal conductivity of PU foams by the method of temperature-time analogy and establishing the limits of its application are discussed. The research presented is of interest both in determining the foam durability and in replacing freons by alternative, ecologically less harmful blowing agents.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 2, pp. 187–198, March–April, 1999.     

Elastic constants of monotropic plastic foams. 3. Deformation parallel to foam rise direction. Analysis of the results

Based on an elaborate mathematical model shaped like an ellipsoidal cell, the Poisson's ratio v ₃₁ ^* and Young's modulusE ₃ ^* are calculated for monotropic (isotropic in the limiting case) plastic foams when loading parallel to the foam rise direction is considered and the hypothesis of half-axis is assumed. The effect of the state of the strut system on the calculation results is studied. The dependence of the calculated elastic constants on the characteristics of plastic foams such as the space filling coefficient, degree of anisotropy and knot parameter is analyzed. The theoretical results are compared with the experimental results as well as the results of other authors.Institute of Polymer Mechanics, University of Latvia, 23 Aizkraukles St., Riga, LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 6, pp. 823–838, November–December, 1998.     

Experimental Investigations on Polymeric Foams

The knowledge of the material behaviour of polymeric foams and their experimental investigation is the starting point for the structure of the chosen constitutive equations and for the following identification of the material constants therein. Especially for the parameter identification, it is necessary to make an adequate set of experimental data available. In this regard, it is important that the experiments make the different kinds of material behaviour visible like elastic, plastic or viscous material properties. For this reason, the foam is observed under uniaxial tension and compression and under simple shear tests combined with different deformation states in axial direction. Unfortunately, due to different reasons, e.g., the foam must be sticked on the fastener to realize the tests mentioned above, it is very difficult to initialize a homogenous deformation state in the specimen. Therefore, the experiments are recorded with a standard digital camcorder to get local information of the deformation state by tracking single points with algorithms of the digital image processing. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Physicomechanical Characteristics of Spray-On Rigid Polyurethane Foams at Normal and Low Temperatures

The effect of processing factors on the inhomogeneity and physicomechanical characteristics of spray-on polyurethane foams is studied. The dependences of the basic characteristics of foam plastics on the apparent density and cell-shape factor are determined. A method is offered for evaluating the effect of the technological surface skin on the tensile characteristics of foam plastics under normal and low temperatures.     

Numerical analysis of Ni/Al hybrid metal foams using the finite cell method

Aluminium metal foams are a new type of material that can be used in many lightweight applications. One method to improve their mechanical properties is to coat them with a thin layer of nickel by electrodeposition. A voxel representation of this hybrid foam can be obtained in a straightforward way using a CT scanner. The voxel-based geometry can then be processed and modified with respect to the thickness of the nickel layer in order to investigate its influence on the effective properties. By employing the finite cell method (FCM) we are able to automatically convert the voxel-based geometry into a finite cell grid and to directly perform a homogenization procedure. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental and numerical investigation of PUR foam under dynamic loading

Various factors may subject buildings to shock which continues in their structure and is perceived by the people living in them as noticeable vibrations or noise. In this context, polyurethane (PUR) foams, which have been developed to isolate vibrations, have shown to be very effective in practical use. However, whereas static properties of open-cell structures have already been determined numerically in good agreement to experimental results, cf. [1], there are hardly any investigations on the dynamical properties characterizing acoustic damping. In order to validate experimental measurements of eigenfrequencies for different PUR foam specimen we present here a strategy to reproduce the foam behavior numerically. In doing so, PUR foams are modeled using a three dimensional Voronoi-tessellation technique. The resulting Voronoi cells correspond to open pores and are scaled in such a way that the volume ratio between the pores and material matches the given PUR foam. For finite element analysis the connections between the cells are modeled as beam elements, the beam shape follows Bezièr curves. The generated model is analyzed with a finite element software and the dynamical parameters are determined. The numerical results are compared to our experimental data. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical modeling of large strain behavior of polymeric crushable foams

This paper describes a constitutive law modeling isotropic polymeric foam materials. Focus has been placed on modeling the relative density dependency effect on polymeric foams subjected to large deformations using uniaxial and hydrostatic compressive hardening laws. The constitutive model is written in terms of the rotated Kirchhoff stress and of its conjugate logarithmic, or Hencky, strain measure. A numerical scheme for solving the constitutive model is described and implemented using both the finite element and the element-free Galerkin methods, in a Total Lagrangian finite strain framework. The imposition of the unilateral contact with friction and the essential boundary conditions are obtained by applying the Augmented Lagrangian method. Numerical examples are presented in order to attest the performance of the proposed constitutive model.