Initial planar deformation of dilatant granular materials

A theory for the initial planar deformation of dilatant granular materials based on a kinematic proposal of R. Butterfield and R.M. Harkness (1972) is presented. The theory introduces an additional parameter called the angle of dilatancy into the traditional structure of plasticity theories for granular materials and soils. When the angle of dilatancy is zero, the present theory reduces to the theory introduced by A.J.M. Spencer in 1964. When the angle of dilatancy is equal to the angle of internal friction, the present theory reduces to the planar form of the theory introduced by D. C. Drucker and W. Prager in 1952. The properties of the theory presented here include coincidence of the stress and velocity characteristics, realistic energy dissipation predictions, and, in general, non-coincidence of the principal axes of stress and strain-rate. However, the angle of dilatancy is assumed to be a constant in this analysis and it does not decrease to zero with increased monotonic shearing deformation as experiment requires that it should, the theory therefore being limited to the initial deformation of dilatant granular materials.     

Irreversible dilatancy or compressibility of viscoplastic rock-like materials and some applications

An elastic/viscoplastic constitutive equation for rock-like materials which is able to describe, besides creep, an irreversible compressibility and/or dilatancy of the volume is formulated. Mathematical definitions are used for the concepts of dilatancy, compressibility, compressibility/dilatancy boundary, and failure. Two examples of such constitutive equations are given for a hard rock and a softer rock.Two applications of this constitutive equation are presented. First the creep dilatancy and/or compressibility of the rocks surrounding an oil well or a pressure shaft are studied for various initial primary stresses. The location and the conditions under which the rock surrounding the well may become dilatant are then shown. The same problem is studied for the case of horizontal tunnels. Various depths and primary stresses are considered and it is shown where possible failure may occur. For both applications numerical examples are given.     

Continuum modeling of a porous solid with pressure-sensitive dilatant matrix

The pressure-sensitive plastic response of a material has been studied in terms of the intrinsic sensitivity of its yield stress to pressure and the presence and growth of cavities. This work focuses on the interplay between these two distinctly different mechanisms and the attendant material behavior. To this end, a constitutive model is proposed taking both mechanisms into account. Using Gurson's homogenization, an upper bound model is developed for a voided solid with a plastically dilatant matrix material. This model is built around a three-parameter axisymmetric velocity field for a unit sphere containing a spherical void. The void is also subjected to internal pressure; this can be relevant for polymeric adhesives permeated by moisture that vaporizes at elevated temperatures. The plastic response of the matrix material is described by Drucker–Prager's yield criterion and an associated flow rule. The resulting yield surface and porosity evolution law of the homogenized constitutive model are presented in parametric form. Using the solutions to special cases as building blocks, approximate models with explicit forms are proposed. The parametric form and an approximate explicit form are compared against full-field solutions obtained from finite element analysis. They are also studied for loading under generalized tension conditions. These computational simulations shed light on the interplay between the two mechanisms and its enhanced effect on yield strength and plastic flow. Among other things, the tensile yield strength of the porous solid is greatly reduced by the internal void pressure, particularly when a liquid/vapor phase is the source of the internal pressure.     

On micro-cracking,inelastic dilatancy,and the brittle-ductile transition in compact rocks: A micro-mechanical study

This work introduces a micro-mechanical grain-aggregate model and numerical simulation capability to study the combined effects of grain-boundary slip and separation, as well as grain-interior plasticity on the overall deformation of compact rocks. Two major conclusions can be drawn from our simulation study: (i) At sufficiently low confining pressures, the widely-observed inelastic dilatant response in compact rocks under compression is attributable to the geometrically-mismatched grain-boundary sliding and concomitant formation of triple-junction cracks which result in an increase in volume. Failure patterns change from splitting-fracture at low confining pressures, to distributed micro-cracking in macroscopic “shear”-bands as the confining pressure increases. (ii) When the confining pressure increases to an amount such that grain-boundary sliding is suppressed due to frictional effects, the inelastic dilatancy effects disappear, and isochoric grain-interior plasticity takes over to accommodate the imposed external deformation, and this is the major cause of the brittle-ductile transition in these materials.     

剪胀性砂土边界面模型的研究

剪胀性对于砂土,尤其是中密以及密实砂土,是一个非常显著的特性。相变线是剪胀性砂土的特征曲线,能够反映砂土的围压以及初时孔隙比对变形特性的影响。本文在边界面塑性理论的框架内,把相变状态参量引入到剪胀方程以及塑性硬化模量中,建立了一个能够描述砂土剪胀性以及循环特性的本构模型。本模型采用一套参量可以模拟不同初时孔隙比、不同围压、排水(或不排水)条件下单调(或循环)加载的应力-应变特性。验证表明本模型数值计算与试验结果相吻合。     

Effect of dilatancy on the strain localization of water-saturated elasto-viscoplastic soil

It is well known that geomaterials such as soils exhibit an increase in volume during shearing deformation, referred to as dilatancy. Dilatancy is a typical property of such granular materials as soils and is closely related to changes in the microstructure. Normally consolidated clay exhibits negative dilatancy or contractancy, namely, a decrease in volume during shearing. On the other hand, overconsolidated clay shows positive dilatancy, namely, an increase in volume during shearing. The aim of the present paper is to study the effects of the microstructure, such as dilatancy and permeability, on the strain localization of water-saturated clay using an elasto-viscoplastic constitutive model. Based on the non-linear kinematic hardening theory and a Chaboche type of viscoplasticity model, an elasto-viscoplastic model for both normally consolidated and overconsolidated clays is proposed; the model can address both negative and positive dilatancies. Firstly, the instability of the model under undrained creep conditions is analyzed in terms of the accelerating creep failure. The analysis shows that clay with positive dilatancy is more unstable than clay with negative dilatancy. Secondly, a finite element analysis of the deformation of water-saturated clay is presented with focus on the numerical results under plane strain conditions. From the present numerical analysis, it is found that both dilatancy and permeability prominently affect shear strain localization behavior.     

Equilibrium Paths of a Hyperelastic Body Under Progressive Damage

This paper deals with equilibrium problems in nonlinear dissipative inelasticity, where inelastic effects are produced by the damage of the material. The inelastic constitutive law is obtained by modifying the classical constitutive law for a hyperelastic isotropic material through a damage function. To define this damage function, which allows to measure the effective stress and the dissipated energy, it is first used the Clausius-Duhem inequality, to have the (rate-independent) flow law of the damaged state and then it has been imposed a damage criterion based on an energy approach. After making the constitutive modeling, the boundary-value problem of the Rivlin’s cube, now composed of damaged material, is formulated. The purpose is to analyze a three-dimensional body that, during the deformation process, experiences a progressively increasing damage. Equilibrium branches of symmetric and asymmetric solutions, together to bifurcation points, are computed. Emphasis is placed in investigating how the damage can alter these equilibrium paths with respect to the virgin undamaged case. In particular, the stress reductions caused by damage can give rise to transitions from hardening type to the softening one of the constitutive behavior. These changes can affect the quality of the equilibrium solutions. Accordingly, the analysis is completed by assessing the stability of the solutions. For this aim, the energetic method is extended to damaged materials.     

On the spatial localization of the laminar boundary layer in a non-Newtonian dilatant fluid

In dilatant fluids the shear perturbation propagation rate is finite, in contrast to Newtonian and pseudoplastic fluids in which it is infinite [1]. Therefore, in certain dilatant fluid flows, frontal surfaces separating regions with zero and nonzero shear perturbations may be formed. Since, in a sense, the boundary layer is a “time scan” of the nonstationary shear perturbation propagation process, in dilatant fluids the boundary layer should definitely be spatially localized. This was first mentioned in [2] where, however, it was mistakenly asserted that boundary layer spatial localization does not take place in all dilatant fluids and is absent in so-called “hardening” dilatant fluids. In [3], the solutions of the laminar boundary-layer equations for speudoplastic and “hardening” dilatant fluids were investigated qualitatively. The formation of frontal surfaces in dilatant fluid flows is usually mathematically related with the existence of singular solutions of the corresponding differential equations [4]. However, since the analysis performed in [3] was inaccurate, in that study singular solutions were not found and it was incorrectly concluded that in “hardening” dilatant fluids there is no spatial boundary layer localization. The investigation performed in [5] showed that in fact in “hardening” dilatant fluids boundary layers are spatially localized, since there exist singular solutions of the corresponding differential equations. Subsequently, this result was reproduced in [6], where an attempt was also made to carry out a qualitative investigation of the solutions of the laminar boundary-layer equations for other types of dilatant fluids. The author did not find singular solutions in this case and mistakenly concluded that in these fluids there is no spatial boundary layer localization. This misunderstanding was due to the fact that in [6] it was not understood that in dilatant fluid flows the formation of frontal surfaces can be mathematically described not only in relation to the existence of singular solutions.     

Coupled viscoplasticity damage constitutive model for concrete materials

A coupled viscoplasticity damage constitutive model for concrete materials is developed within the framework of irreversible thermodynamics.Simultaneously the Helmholtz free energy function and a non-associated flow potential function are given, which include the internal variables of kinematic hardening,isotropic hardening and dam- age.Results from the numerical simulation show that the model presented can describe the deformation properties of the concrete without the formal hypotheses of yield criterion and failure criteria,such as the volume dilatancy under the compression,strain-rate sen- sitivity,stiffness degradation and stress-softening behavior beyond the peak stress which are brought by damages and fractures.Moreover,we could benefit from the application of the finite element method based on this model under complex loading because of not having to choose different constitutive models based on the deformation level.     

压力敏感材料中的空洞长大研究及其在页岩及高分子材料中的应用

主要研究压力敏感材料中含内压的空洞长大,如页岩或者高分子材料。采用数值方法研究含内压空洞的对称和非对称球形和柱形胞元的宏观力学行为。结果表明,压力敏感性及其空洞内压将极大影响空洞的形核与长大。在球形胞元情形中未出现柱形胞元的单轴拉伸现象。将胞元有限变形的数值计算结果与基于近期提出的考虑压力敏感材料中空洞长大的塑形力学模型的分析结果进行了对比。     

Micromechanics, macromechanics and constitutive modeling of the elasto-viscoplastic deformation of rubber-toughened glassy polymers

Under certain conditions, such as sufficiently low temperatures, high loading rates and/or highly triaxial stress states, glassy polymers display an unfavorable characteristic—brittleness. A technique used for reducing the brittleness (increasing the fracture toughness) of these materials is rubber toughening. While there is significant qualitative understanding of the mechanical behavior of rubber-toughened polymers, quantitative modeling tools for the large-strain deformation of rubber-toughened glassy polymers are largely lacking.In this paper, we develop a suite of numerical tools to investigate the mechanical behavior of rubber-toughened glassy polymers, with emphasis on rubber-toughened polycarbonate. The rubber particles are modeled as voids in view of their deformation-induced cavitation early during deformation. A three-dimensional micromechanical model of the heterogeneous microstructure is developed to study the effects of initial rubber particle (void) volume fraction on the underlying elasto-viscoplastic deformation mechanisms in the material, and how these mechanisms influence the macroscopic response of the material. A continuum-level constitutive model is developed for the large-strain elasto-viscoplastic deformation of porous glassy polymers, and it is calibrated against micromechanical modeling results for porous polycarbonate. The constitutive model can be used to study various boundary value problems involving rubber-toughened (porous) glassy polymers. As an example, the case of an axisymmetric notched bar is simulated for the case of polycarbonate with varying levels of initial porosity. The quality of the constitutive model calibration is assessed using a multi-scale modeling approach.     

Corotational rates in constitutive modeling of elastic-plastic deformation

The principal axes technique is used to develop a new hypoelastic constitutive model for an isotropic elastic solid in finite deformation. The new model is shown to produce solutions that are independent of the choice of objective stress rate. In addition, the new model is found to be equivalent to the isotropic finite elastic model; this is essential if both models describe the same material.

The new hypoelastic model is combined with an isotropic flow rule to form an elastic-plastic rate constitutive equation. Use of the principal axes technique ensures that the stress tensor is coaxial with the elastic stretch tensor and that solutions do not depend on the choice of objective stress rate. The flow rule of von Mises and a parabolic hardening law are used to provide an example of application of the new theory. A solution is obtained for the prescribed deformation of simple rectilinear shear of an isotropic elastic and isotropic elastic-plastic material.     

Unified elastoplastic finite difference and its application

Two elastoplastic constitutive models based on the unified strength theory (UST) are established and implemented in an explicit finite difference code, fast Lagrangian analysis of continua (FLAC/FLAC3D), which includes an associated/non-associated flow rule, strain-hardening/softening, and solutions of singularities. Those two constitutive models are appropriate for metallic and strength-different (SD) materials, respectively. Two verification examples are used to compare the computation results and test data using the two-dimensional finite difference code FLAC and the finite element code ANSYS, and the two constitutive models proposed in this paper are verified. Two application examples, the large deformation of a prismatic bar and the strain-softening behavior of soft rock under a complex stress state, are analyzed using the three-dimensional code FLAC3D. The two new elastoplastic constitutive models proposed in this paper can be used in bearing capacity evaluation or stability analysis of structures built of metallic or SD materials. The effect of the intermediate principal stress on metallic or SD material structures under complex stress states, including large deformation, three-dimensional and non-association problems, can be analyzed easily using the two constitutive models proposed in this paper.     

Fluctuations in flow produced by competition between apparent wall slip and dilatancy

Dense suspensions can exhibit a dramatic stress-induced transition from liquid-like to solid-like behavior. In many materials, the solid-like flow state is characterized by large flow fluctuations and instabilities. Although various experiments have been performed to characterize flow fluctuations, the mechanisms that govern the flow instabilities remain poorly understood. To elucidate these mechanisms, we characterize a system that rapidly fluctuates between two flow states. One of the flow states is dominated by apparent wall slip, and the other is dominated by dilatancy. The dilatant regime occurs at elevated stresses and is associated with reduced wall slip, whereas the wall slip-dominated regime occurs at lower stresses. At stresses that are intermediate between these two regimes, the material fluctuates between the two regimes in a semi-regular fashion. Our analysis of the fluctuations at millisecond timescales shows that fluctuations occur because neither regime is capable of supporting a constant stress in a stable manner. We rationalize our results in terms of the differences in the shear-induced particle pressure between regions that are particle-rich and regions of slip that are particle-depleted.     

Restrictions on nonlinear constitutive equations for elastic rods

Constitutive equations for the resultant forces and moments applied to a rod-like body necessarily couple the influences of the rod geometry and the constitutive nature of the three-dimensional material from which the rod was constructed. Consequently, even when the nonlinear constitutive equation of the three-dimensional material is known, the influence of the rod geometry on the constitutive response of the rod is not known. The main objective of this paper is to develop restrictions on the constitutive equations of nonlinear elastic rods which ensure that exact solutions of the rod equations are consistent with exact nonlinear solutions of the three-dimensional equations for all homogeneous deformations. Since these restrictions are nonlinear in nature they provide valuable general theoretical guidance for specific constitutive assumptions about the coupling of material and geometric properties of rods. Also, an example of a straight beam clamped at one end and subjected to a shear force at the other end is used to examine the validity of the proposed value for the transverse shear deformation coefficient.     

超弹性材料本构关系的最新研究进展

超弹性材料是工程实际中的常用材料, 具有在外力作用下经历非常大变形、在外力撤去后完全恢复至初始状态的特征. 超弹性材料是典型的非线性弹性材料, 其性能可通过材料的应变能函数予以表征. 近几十年来, 围绕应变能函数形式的构造, 已提出许多超弹性材料本构关系研究的数学模型和物理模型, 但适用于多种变形模式和全变形范围的完全本构关系仍是该领域期待解决的重要问题. 本文从3个不同角度, 对超弹性材料本构关系研究的最新进展进行了总结和分析: (1)不同体积变化模式, 包含不可压与可压两种; (2)多变形模式, 包含单轴拉伸、剪切、等双轴以及复合拉剪等多个种类; (3)全范围变形程度, 包含小变形、中等变形到较大变形范围. 超弹性材料本构关系研究的最新进展表明, 为了全面描述具体材料的实验数据并在实际问题中应用超弹性材料, 需要建立适合于多种变形模式和全变形范围的可压超弹性材料的完全本构关系. 对实际超弹性材料完全本构关系的建立及可压超弹性材料应变能函数的构造, 笔者还提出了相应的实施步骤和研究方法.      

STATE OF THE ART OF CONSTITUTIVE RELATIONS OF HYPERELASTIC MATERIALS 1)

超弹性材料是工程实际中的常用材料, 具有在外力作用下经历非常大变形、在外力撤去后完全恢复至初始状态的特征. 超弹性材料是典型的非线性弹性材料, 其性能可通过材料的应变能函数予以表征. 近几十年来, 围绕应变能函数形式的构造, 已提出许多超弹性材料本构关系研究的数学模型和物理模型, 但适用于多种变形模式和全变形范围的完全本构关系仍是该领域期待解决的重要问题. 本文从3个不同角度, 对超弹性材料本构关系研究的最新进展进行了总结和分析: (1)不同体积变化模式, 包含不可压与可压两种; (2)多变形模式, 包含单轴拉伸、剪切、等双轴以及复合拉剪等多个种类; (3)全范围变形程度, 包含小变形、中等变形到较大变形范围. 超弹性材料本构关系研究的最新进展表明, 为了全面描述具体材料的实验数据并在实际问题中应用超弹性材料, 需要建立适合于多种变形模式和全变形范围的可压超弹性材料的完全本构关系. 对实际超弹性材料完全本构关系的建立及可压超弹性材料应变能函数的构造, 笔者还提出了相应的实施步骤和研究方法.     

Determination of the Constitutive Relation Parameters of a Metallic Material by Measurement of Temperature Increment in Compressive Dynamic Tests

The mechanical behaviour of a material can be established by an analytic expression called the constitutive relation that shows stress as a function of plastic strain, strain rate, temperature, and possibly other thermo-mechanical variables. The constitutive relation usually includes such parameters as coefficients or exponents that must be determined. At a high strain rate, the heat generated during the deformation process is directly related to the plastic deformation energy of the material. This energy can be calculated from the plastic work, resulting in an expression that includes the constitutive relation parameters as variables. The heat generated can also be estimated by measuring the temperature surface of the specimen during compressive tests using the technique of infrared thermography. The objective of this paper is to present a procedure for determining the constitutive relation parameters by measuring the temperature increase associated with plastic strain in compressive Hopkinson tests. The procedure was applied to estimate the parameters of the Johnson–Cook constitutive relation of an aluminium alloy (Al6082).