Calculation of Dependent Elastic Constants of Plastic Foams with a Pronounced Strut-Like Structure

Seven dependent elastic constants of monotropic plastic foams with an expressed strut-like structure are calculated. For this purpose, the basic results of the previously elaborated mathematical model for light-weight plastic foams is used. The model includes a model cell of local structure for monotropic/isotropic plastic foams and an ensemble of structural elements, which allows one to calculate the seven dependent elastic constants, taking into account the pronounced polydispersity of the structure of plastic foams. The numerical values of the constants are compared with the available experimental data, and a satisfactory agreement is found to exist. As a final result, a full set of general expressions and numerical values are obtained for all 12 elastic constants of monotropic plastic foams.     

Model of Deformation of Monotropic Plastic Foams Parallel to the Foam Rise Direction Based on the Volume-Deformation Hypothesis

The deformation properties of monotropic plastic foams under uniaxial deformation (compression or tension) parallel to the foam rise direction is considered. The theoretical results are obtained in the case where the volume-deformation hypothesis is assumed. The validity of neglecting the fluctuation component in calculations of the effective volume strains of foams is substantiated. A tie condition permitting the sought-for semiaxes to vary not obligatorily equally is derived. The values of Young's modulus and Poisson coefficients are obtained for a wide range of model cell stretch ratios and foam space-filling coefficients. A comparison of the theoretical results with the experimental data available is performed.     

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.     

Elastic constants of monotropic plastic foams. 2. Deformation parallel to foam rise direction. Numerical calculations

In order to perform numerical calculations of the elastic constants of monotropic plastic foams with a pronounced strut-like structure, a package of computing programs has been developed. Numerical values of the elastic constants were determined using the Simpson method for the calculation of triple averaging integrals and stepwise unconditional minimization of the one-argument potential energy function. The parameters of the numerical calculation process providing acceptable accuracy of the results were evaluated. Dimensions of the structural elements in the model of isotropic plastic foams were determined and analyzed.Institute of Polymer Mechanics, Riga, LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 2, pp. 163–172, March–April, 1998.     

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.     

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.     

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.     

简单剪切有限塑性内时理论分析

在有限塑性内时理论中引入Jaumann率、广义Jaumann率、扶率及Wu率,并以此分析了简单剪切大变形问题．结果验证了简单剪切变形中,采用次弹性或内时刚塑性材料的Jaumann率客观模型,随单调递增的剪切变形剪切应力和法向应力都会出现振荡现象．这说明振荡现象的出现不取决于弹塑性模型,而与选取不同的客观率有很大的关系．同时指出在简单剪切大变形时,法向应力并不为零．     

Deformability and strengh of expanded polystyrene (EPS) under short-term shear loading

Data obtained in investigating the ultimate strength and deformability of expanded polystyrene under short-term shear loading according to EN 12090 are discussed. Linear regression equations are used for describing the ultimate shear strength and modulus in relation to the density of EPS. A correlation is found to exist between the ultimate strength of EPS and its density and specimen thickness. An empirical dependence between the shear modulus and density of EPS is established. The strains corresponding to the conditional limit of proportionality and to the ultimate shear strength of EPS in short-term loading are determined. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 121–134, January–February, 2007.     

Effect of material properties on the stability of transversely isotropic shells with an elastic filler subjected to the action of mechanical loads and temperature

The effect of the low shear strength of the material (glass-reinforced plastic) on the stability of cylindrical shells with an elastic filler is investigated in relation to axial compression, external pressure, and heating. The equations of the thermoelastic problem of the theory of monotropic shells, constructed with allowance for the effect of tangential shearing stresses, are used in the calculations.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. L'vov Polytechnic Institute. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 903–907, September–October, 1970.     

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.     

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)     

简单剪切振荡现象及弹塑性本构的限制条件

基于在真应力空间刻划弹塑性物质的强化、软化和理想塑性特性,本文以刚塑性随动强化模型为例说明产生简单剪切振荡现象,是与模型在简单剪切变形下,其强化和软化特性发生交替变化的现象有关。为使弹塑性本构模型更符合实际,要求它们必须满足如下条件:即对任意弹塑性加载变形过程,本构模型所给出的应力应该是非振荡的,所描述的强化和软化特性,不存在从软化阶段至强化阶段的过渡。     

Finite element analysis of arches undergoing large rotations - I: Theoretical comparison

In this two part paper, the first part deals with five different nonlinear theories applicable to the analysis of arches in the context of solving the large displacement and the large rotation problem. These theories include, classical theory, first-order shear deformation theory, third-order shear deformation theory, modified classical theory and the Donnell-type theory. All the theories are developed using the Total Lagrangian approach. Simplifications and assumptions used in each of the theory are discussed. Explicit strain displacement gradient relations and element independent equilibrium equations in terms of displacement gradients are given for all the theories. Limitations of each of theory are discussed. In the second part of this paper, application of these theories for the classification of arch geometries is considered.     

Analysis of adiabatic shear bands in thermo-elasto-viscoplastic materials by using piece-wise discontinuous basis functions

An adiabatic shear band (ASB) is a narrow region of intense plastic deformation that forms when some metallic alloys and some polymers are deformed at high strain rates and there is not enough time for the heat generated by plastic deformations to diffuse away. The study of ASBs is important because an ASB is a precursor to shear/ductile fractures. Initial-boundary-value problems simulating the initiation and propagation of an ASB have been analyzed usually using the finite element method (FEM). Because of the large plastic strains involved, the FE mesh needs to be refined several times to delineate the ASB width. Each refinement requires, in turn, interpolation of data from the previous mesh to the new one which causes a smoothening of the sharp gradients of the deformation fields, and affects characteristics of the ASB. In this paper, we propose the application of the finite element method with piecewise discontinuous basis functions for studying the occurrence of ASBs in simple shearing deformations of a body composed of an isotropic and homogeneous thermo-elastoviscoplastic material. The mathematical model of the problem is defined by a system of coupled nonlinear partial differential equations and an inequality constraint associated with the plastic strain rates admissibility.     

An analysis of the joint operation of a CFRP concrete in flexural elements

The strength and fracture mechanism of the contact zone between a carbon-fiber-reinforced plastic (CFRP) and concrete in flexural structural elements is investigated. Two methods for calculating the shear force in the contact zone are considered, one of which takes into account the compliance of the zone and gives results agreeing rather well with experimental data for beams, regardless of the way the CFRP is fastened to concrete. The method of shear stresses is good for beams with in significant shear strains between CFRP and concrete. A method allowing for hardening of the contact zone is suggested. It is shown that the fracture mechanism of the zone depends on the way of fastening the CFRP and the depth the adhesive penetrates into concrete. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 687–700, September–October, 2007.     

Theoretical-experimental method for determining the averaged elastic and strength characteristics of a honeycomb core of sandwich designs

Analytic formulas for the averaged elastic and strength characteristics of a honeycomb core with a hexahedral structure are derived by introducing the hypothesis about the momentless work of its elements (walls) in the course of loading and during their stepwise exclusion from operation after their buckling in compression-compression or pure shear. The dimensionless coefficients appearing in the structural formulas when solving the problems formulated are to be determined from experimental data on tension, compression, and pure shear in two planes. It is shown that, in tension-compression, honeycomb must be considered as a heteromodular material with averaged elastoplastic properties, for which the relations between averaged stresses and averaged strains in compression and shear change stepwise on some sections (conditional plastic flow).     

Post-bucking of angle-ply laminated plates under thermal loading

Notionsa. b, h Plate dimensionsL', [-. [1- mid-plane displacement componentsu- v- Ic dboensionless mid-plane displacement componentsVy., ac'~ slOPeS in xo and gi plane, ropectivelyJll, N number of terms in Cheby-shev series in x and y directions, respectivelyCCCC all edges clampedSSSS all edges simply supportedCCCS three edges (x = fi and y = 1) clamped and one (y = --1) simply supportedCCSS two edges (x = 11) clamped and two (y = fi) simply supportedCSSS one edge (x = --1) clamped …     

Determination of arterial wall shear stress

The arteries can remodel their structure and function to adapt themselves to the mechanical environment. In various factors that lead to vascular remodeling, the shear stress on the arterial wall induced by the blood flow is of great importance. However, there are many technique difficulties in measuring the wall shear stress directly at present. In this paper, through analyzing the pulsatile blood flow in arteries, a method has been proposed that can determine the wall shear stress quantitatively by measuring the velocity on the arterial axis, and that provides a necessary means to discuss the influence of arterial wall shear stress on vascular remodeling.     

韧性金属大变形拟流动角点理论及应用

本文提出韧性金属弹塑性大变形拟流动角点理论（ｑｕａｓｉ－ｆｌｏｗｃｏｒｎｅｒｔｈｅｏｒｙ）．该理论从塑性变形正交法则出发，将”模量衰减函数”及屈服面的尖点效应引入本构模型，从而实现了由正交法则本构模型向非正交法则本构模型以及从塑性加载向物理弹性却载的光滑过渡，使一般无角点各向异性硬化屈服函数与有角点硬化情形相结合成为可能．用于数值模拟各向异性金属薄板单向拉伸失稳与剪切带分析并与实验结果作比较，表明本文理论的有效性．