On the deformation and fracture of porous materials

The constitutive behavior of porous materials (including the yield loci, the void growth rate, the macro stress-strain relation and the strain to localization instability) is examined based on the lower bound approach proposed by the present authors. These results are then compared with the experimental and the finite element results as well as those predicted by Gurson's equations. Emphasis is placed on approaching the real behavior from the upper and the lower bound analysis. Calculation is also made on the influence of void nucleation on the critical strain to instability and a modified strain-controlled nucleation criterion is proposed. Finally the instability and fracture of AISI4340 steel in plane strain tension is examined and comparison is made between theoretical and experimental results.     

An overview on nonlinear porous flow in low permeability porous media

This paper gives an overview on nonlinear porous flow in low permeability porous media, reveals the microscopic mechanisms of flows, and clarifies properties of porous flow fluids. It shows that, deviating from Darcy's linear law, the porous flow characteristics obey a nonlinear law in a low-permeability porous medium, and the viscosity of the porous flow fluid and the permeability values of water and oil are not constants. Based on these characters, a new porous flow model, which can better describe low permeability reservoir, is established. This model can describe various patterns of porous flow, as Darcy's linear law does. All the parameters involved in the model, having definite physical meanings, can be obtained directly from the experiments.     

A lower bound approach to the yield loci of porous materials

A lower bound approach is proposed for the first time to solve the macroscopic yield loci of porous materials. The results are then compared with Gurson's upper bound yield loci and those of the experiments. It is shown that the present analysis is much more in accordance with the experimental results than the Gurson's.     

A finite strain elastic-viscoplastic self-consistent model for polycrystalline materials

A large strain elastic-viscoplastic self-consistent (EVPSC) model for polycrystalline materials is developed. At single crystal level, both the rate sensitive slip and twinning are included as the plastic deformation mechanisms, while elastic anisotropy is accounted for in the elastic moduli. The transition from single crystal plasticity to polycrystal plasticity is based on a completely self-consistent approach. It is shown that the differences in the predicted stress-strain curves and texture evolutions based on the EVPSC and the viscoplastic self-consistent (VPSC) model proposed by Lebensohn and Tomé (1993) are negligible at large strains for monotonic loadings. For the deformations involving unloading and strain path changes, the EVPSC predicts a smooth elasto-plastic transition, while the VPSC model gives a discontinuous response due to lack of elastic deformation. It is also demonstrated that the EVPSC model can capture some important experimental features which cannot be simulated by using the VPSC model.     

Dual extremum principles for geometrically exact finite strain beams

Both necessary and sufficient conditions for the existence of two complementary-dual extremum principles for geometrically exact finite strain (one-dimensional) beam models are investigated by means of two different approaches. One is based on the results published by Gao and Strang, and the other relies on the approach proposed by Noble and Sewell. While the former is limited to beam models restricted to moderate large deformations, the latter is valid for arbitrarily large deformations (and strains). The numerical implementation of the complementary-dual extremum principles can lead to simple true global upper bounds of the error of the approximate solutions.     

Investigation of Donnan equilibrium in charged porous materials—a scale transition analysis

We propose a new theory describing how the macroscopic Donnan equilibrium potential can be derived from the microscale by a scale transition analysis. Knowledge of the location and magnitude of the charge density, together with the morphology of the pore space allows one to calculate the Donnan potential, characterizing ion exclusion in charged porous materials. Use of the electrochemical potential together with Gauss’ electrostatic theorem allows the computation of the ion and voltage distribution at the microscale. On the other hand, commonly used macroscopic counterparts of these equations allow the estimation of the Donnan potential and ion concentration on the macroscale. However, the classical macroscopic equations describing phase equilibrium do not account for the non-homogeneous distribution of ions and voltage at the microscale, leading to inconsistencies in determining the Donnan potential (at the macroscale). A new generalized macroscopic equilibrium equation is derived by means of volume averaging of the microscale electrochemical potential. These equations show that the macroscopic voltage is linked to so-called “effective ion concentrations”, which for ideal solutions are related to logarithmic volume averages of the ion concentration at the microscale. The effective ion concentrations must be linked to an effective fixed charge concentration by means of a generalized Poisson equation in order to deliver the correct Donnan potential. The theory is verified analytically and numerically for the case of two monovalent electrolytic solutions separated by a charged porous material. For the numerical analysis a hierarchical modeling approach is employed using a one-dimensional (1D)macroscale model and a two-dimensional (2D)microscale model. The influence of various parameters such as surface charge density and ion concentration on the Donnan potential are investigated.     

Influence of axisymmetric dents in ribbed shells on minimum critical loads

The effect of axisymmetric dents in ribbed shells on the minimum critical loads is studied analytically. The upper and lower bounds for the critical stresses in imperfect cylindrical shells reinforced with stringers, rings, and both are estimated. The upper bounds are compared with those obtained from the known solutions for perfect ribbed momentless shells and with experimental data. The effect of the amplitude of initial dents and their number on the upper and lower bounds of critical stresses is examined. The procedure used is the most efficient to determine the load-bearing capacity of ring-reinforced and ribbed shells __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 73–79, May 2007.     

饱和多孔介质中的混合有限元法和有限应变下应变局部化分析

对基于Biot理论的饱和多孔介质中动力-渗流耦合分析提出了一个耦合场混合元．固相位移、应变和有效应力以及流相压力、压力梯度和Darcy速度在单元内均处理为独立变量分别插值．基于胡海昌-Washizu三变量广义变分原理给出的饱和多孔介质动力-渗流耦合问题控制方程的单元弱形式，导出了单元公式．进一步导出了考虑压力相关非关联塑性的非线性单元公式和发展了相应的一致性算法．对几何非线性分析，采用了共旋公式途径．数值结果例题显示所发展耦合场混合元模拟大应变下由应变软化引起以应变局部化为特征的渐进破坏现象的性能．     

ONSET CONDITION OF STRAIN LOCALIZATION IN MATRIX OF SATURATED POROUS MEDIA

Introduction Strainlocalizationofgeomaterialsisoneofmostpopularfailuretypesinnature,which canbeshowedaslandslidesandmudflowsinmountainousareasunderincessantorheavy raining,especiallythevegetationisseverelydamagedbywoodsharvest;pipingeffect,a typeoflocalfa…     

A NEW METHOD FOR THE UNCERTAIN RESPONSE ANALYSIS OF STRUCTURES WITH UNCERTAIN PARAMETERS

A computing method for estimating the upper and lower bounds of the response ofstructures with uncertainties is presented.The uncertain parameters are described by the convexmodel.A numerical example of the frame structure is given to illustrate the effectiveness of thismethod.     

THE UNCERTAIN EIGENVALUES ANALYSIS OF STRUCTURES WITH UNCERTAIN PARAMETERS

This paper presents a method for estimating the upper and lower bounds of eigenvalues of structures with uncertainties. The uncertain parameters are described by the convex model. A numerical example of the frame structure is given to illustrate the efficiency of the method. This work is supported by the National Natural Science Foundation of China(No. 19872028).     

Microscopic and macroscopic instabilities in finitely strained porous elastomers

The present work is an in-depth study of the connections between microstructural instabilities and their macroscopic manifestations—as captured through the effective properties—in finitely strained porous elastomers. The powerful second-order homogenization (SOH) technique initially developed for random media, is used for the first time here to study the onset of failure in periodic porous elastomers and the results are compared to more accurate finite element method (FEM) calculations. The influence of different microgeometries (random and periodic), initial porosity, matrix constitutive law and macroscopic load orientation on the microscopic buckling (for periodic microgeometries) and macroscopic loss of ellipticity (for all microgeometries) is investigated in detail. In addition to the above-described stability-based onset-of-failure mechanisms, constraints on the principal solution are also addressed, thus giving a complete picture of the different possible failure mechanisms present in finitely strained porous elastomers.     

Analysis of shear localization in porous materials

A set of constitutive equations are derived based on the authors' lower bound yield loci for porous materials. By using these equations, the conditions for shear localization in porous materials are then investigated and the results are compared with those of Gurson's equations and the finite element analysis. The advantages of the present constitutive equations are fully illustrated.     

An experimental study of thermal stress in porous materials by methods of holography and photoelasticity

In heat-loaded structures of energy equipment at the moment of crisis of heat exchange in working elements, the ultimate state of the material occurs. Thermal stresses were studied experimentally in a bulk porous material with a groove on the surface with a view to finding out the distribution of deformations and thermal stresses due to the location of the heat source. It appeared efficient to apply optical methods. Using holographic interferometry, a pattern of distribution of thermal deformations over the surface of the specimens was obtained. Using the photoelastic method to investigate a grooved porous structure, a physical pattern of the distribution of thermal stresses inside the block and in the groove was obtained. Ways are outlined for designing and reducing the probability of occurrence of destructive cracks. A similarity is observed in the distribution of strains and stresses that indicates the interrelatedness of surface and internal processes. The application of optical methods made it possible to discover a physical pattern of destruction. The results are expected to be used in the future to investigate other porous materials.     

Macroscopic modelling of transport phenomena in porous media. 1: The continuum approach

This is the first of two papers presenting a systematic development of a continuum model of a porous medium and of transport processes occurring in it. The concept of a Representative Elementary Volume (REV) as opposed to any arbitrary volume of averaging quantities at the micro-scale, is quantified. A universal criterion for selecting the size of an REV as a function of measurable characteristics of a porous medium and selected tolerance levels of estimation errors, is developed. The rules of spatial averaging are extended by including the effects of both the configuration of the solid matrix and of interphase transfer phenomena within an REV.     

Numerical limit analysis bounds for ductile porous media with oblate voids

The paper is devoted to a numerical limit analysis of a hollow spheroidal model with a von Mises solid matrix. To this purpose, existing kinematic and static 3D-FEM codes for the case of spherical cavities have been modified and improved to account for the model of a spheroidal cavity confocal with the external spheroidal boundary. The optimized conic programming formulations and the resulting codes appear to be very efficient. This framework is then applied to the derivation of numerical upper and lower anisotropic bounds in the case of an oblate void. The numerical results obtained from a series of tests are presented and allow to assess the accuracy of closed-form expressions of the macroscopic criteria proposed by [Gologanu et al., 1994] and [Gologanu et al., 1997] for porous media with oblate voids.     

梯度多孔金属材料梁的屈曲和屈曲基础上的振动

为研究梯度多孔金属材料梁的屈曲以及屈曲附近的振动特性,首先建立了随从分布压力下梯度多孔材料梁的动力学控制方程,得到了描述后屈曲的静态控制微分方程和描述屈曲前后振动响应的控制方程。通过打靶法数值求解两组强非线性方程,获得了简支-固支梯度多孔梁的屈曲临界载荷以及屈曲前后振动频率与载荷之间的关系曲线。分析了孔隙率系数和孔隙分布方式对屈曲临界载荷和屈曲前后振动频率的影响。结果表明,随着孔隙率系数e₀的增加,发生屈曲时的临界载荷减小;各阶固有频率也减小。屈曲前,各阶振动频率随载荷增大而减小,屈曲后,除三阶频率外,一阶和二阶频率随载荷增大而增大。     

AN INTERVAL FINITE ELEMENT METHOD BASED ON THE NEUMANN SERIES EXPANSION 1)

实际工程问题中通常存在大量的不确定参数, 区间有限元方法是一种结合有限元数值计算工具对结构进行不确定性分析的区间方法. 区间有限元的目的是获得在含有区间不确定性参数条件下的结构响应上下边界, 其关键问题在于区间平衡方程组的求解, 而这属于一类往往很难求解的NP-hard问题. 本文归纳了一类工程实际中常见的结构不确定性问题, 即可线性分解式区间有限元问题, 并针对此提出一种基于Neumann级数的区间有限元方法. 在区间有限元分析中, 当区间不确定参数表示为一组独立区间变量线性叠加时, 若结构的刚度矩阵也可表示为这些独立区间变量的线性叠加形式, 则称此类区间有限元问题为可线性分解式区间有限元问题. 对于此类问题, 采用Neumann级数对其刚度矩阵的逆矩阵进行表示, 可获得结构响应关于区间变量的显式表达式, 从而可高效求解结构响应的上下边界. 最后通过两个算例验证了本文所提方法的有效性.     

应变损伤材料I型动态扩展裂纹尖端场的渐近分析

研究了应变损伤材料Ｉ型动态扩展的裂纹尖端场。假定材料服从Ｊ２流动理论，且损伤规律以幂律应变软化的规律给出。对于塑性区引进了应力函数φ，ψ０借助于动力学方程的分析，给出了渐近方程及数值解。结果表明，对于可压缩材料Ｉ型平面应变尖端场是完全由塑性区组成，没有弹性卸载区。在裂纹尖端附近，应力和应变分别具有如下的奇异性：σ￣（ｌｎＲ／ｒ）＾－ｎ／ｎ＋１，ε￣（ｌｎＲ／ｒ）＾１／ｎ＋１。