Limitations in the Constitutive Modeling of Unsaturated Soils and Solutions

Over the past six decades, significant attention has been paid to the elastoplastic behavior of unsaturated soils. In the past two decades alone, elastoplastic theory for unsaturated soils has been established and experimental techniques for measuring the elastoplastic behavior of unsaturated soils have become more sophisticated. However, less effort has been directed at developing the best strategy for constitutive modeling of unsaturated soils. At present, there is no standard method for developing constitutive models for unsaturated soils from experimental data, and owing to the extreme complexity of unsaturated soil behavior, there are limitations in the existing modeling methods. If these limitations are not recognized, misleading results in the constitutive modeling of unsaturated soil behavior may occur. This paper discusses the origins of and possible solutions to these limitations. Experimental data from the recent literature are used to demonstrate the use of existing methods for the constitutive modeling of unsaturated soils and potential associated problems. A modified state-surface approach (MSSA), recently proposed to model the elastoplastic behavior of unsaturated soils under isotropic conditions, was applied to overcome the limitations and develop a constitutive model that can best represent the behavior of unsaturated soil. A comparison of the proposed method and existing methods is discussed, and from this discussion, the capability and effectiveness of the proposed method are evaluated.     

Relating Damping to Soil Permeability

Published comparisons of complex moduli in dry and saturated soils have shown that viscous behavior is only evident when a sufficiently massive viscous fluid (like water) is present. That is, the loss tangent is frequency dependent for water saturated specimens, but nearly frequency independent for dry samples. While the Kelvin–Voigt (KV) representation of a soil captures the general viscous behavior using a dashpot, it fails to account for the possibly separate motions of the fluid and frame (there is only a single mass element). An alternative representation which separates the two masses, water and frame, is presented here. This Kelvin–Voigt–Maxwell–Biot (KVMB) model draws on elements of the long standing linear viscoelastic models in a way that connects the viscous damping to permeability and inertial mass coupling. A mathematical mapping between the KV and KVMB representations is derived and permits continued use of the KV model, while retaining an understanding of the separate mass motions.     

Generalized Constitutive-Based Theoretical and Empirical Models for Hot Working Behavior of Functionally Graded Steels

Functionally graded steels with graded ferritic and austenitic regions including bainite and martensite intermediate layers produced by electroslag remelting have attracted much attention in recent years. In this article, an empirical model based on the Zener–Hollomon (Z-H) constitutive equation with generalized material constants is presented to investigate the effects of temperature and strain rate on the hot working behavior of functionally graded steels. Next, a theoretical model, generalized by strain compensation, is developed for the flow stress estimation of functionally graded steels under hot compression based on the phase mixture rule and boundary layer characteristics. The model is used for different strains and grading configurations. Specifically, the results for αβγMγ steels from empirical and theoretical models showed excellent agreement with those of experiments of other references within acceptable error.     

Rheological Foundations of Powder Consolidation Processes and the “Mean-Square” Concept

The past, present, and possible future development of basic models for engineering processes in powder metallurgy are examined. Special attention is devoted to the rheological concept of sintering and strain, as well as to the “mean-square” concept which together form the ideological basis for many existing models. Modern generalizations of sintering models to the cases of anisotropy and phase transitions in the matrix material are examined. Models of plastic and nonlinearly viscous flows that follow from the “mean-square concept” concept are correlated with other theories of flow in porous media. The relationship among these is established. The possible use of these ideas for solving current problems in materials science is discussed.     

Pressure-Dependent Elasticity and Energy Conservation in Elastoplastic Models for Soils

This paper presents a study on the consequences of combining energy conservative or non-conservative elasticity within a plasticity framework. Toward this end, a versatile energy potential function is first presented and examined. It is shown to cover a wide range of existing empirical relations for pressure-dependent stiffness of soils. Utilization of these functions within hyperplastic constitutive framework allows for the resulting models to satisfy the Law of Energy Conservation for both elastic and plastic components of soil behavior. Apart from the theoretical rigor, a very important result of this approach is that it automatically implies stress-induced cross-anisotropy of the elastic component of soil behavior and dilatancy term occurs due to shear modulus dependency on pressure. Proper modeling of these phenomena, normally neglected by conventional hypoelastic-plastic models, has been shown to have a significant effect on the accuracy of the model predictions of undrained behavior of overconsolidated clays both in laboratory tests and in tunnel excavation problem.     

Modeling Permanent Deformation of Unbound Granular Materials under Repeated Loads

Finite-element analysis on a pavement structure under traffic loads has been a viable option for researchers and designers in highway pavement design and analysis. Most of the constitutive drivers used were nonlinear elastic models defined by empirical resilient modulus equations. Few isotropic/kinematic hardening elastoplastic models were used but applying thousands of repeated load cycles became computationally expensive. In this paper, a cyclic plasticity model based on fuzzy plasticity theory is presented to model the long-term behavior of unbound granular materials under repeated loads. The discussion focuses on the model parameters that control long-term behavior such as elastic shakedown. The performance of the constitutive model is presented by comparing modeled and measured permanent strain at various numbers of load cycles. Calculated resilient modulus from the complete stress-strain curve is also discussed.     

Constitutive Modeling for CdTe Single Crystals

To understand the role of thermal stresses in the generation, multiplication, and propagation of dislocations in CdTe single crystals produced by directional solidification, constitutive models which accurately reflect the elastic-viscoplastic behavior of CdTe over a wide range of temperatures are needed. In this article, the relevant reported mechanical behavior of CdTe is reviewed and discussed. Constitutive equations developed for single slip, isothermal behavior of elemental semiconductor crystals by Haasen and co-workers, which include dislocation density as the important internal variable, are then extended to include an additional dislocation arrangement internal variable as well as a high-temperature, time-dependent recovery behavior. The constitutive framework is incorporated in a continuum slip framework to include the possibility of multiple slip and to relate slip system shear strain rates to the macroscopic plastic strain rate. Comparison of the model with available experimental data for the small strain case over a wide range of temperatures is presented. Slip system interaction is included. These constitutive equations can then be used in computational analyses of thermal stress generation for comparison with characterized crystals grown in microgravity and ground-based experiments. This article is based on a presentation made in the symposium entitled “Microgravity Solidification, Theory and Experimental Results” as a part of the 1993 TMS Fall meeting, October 17-21, 1993, Pittsburgh, PA, under the auspices of the TMS Solidification Committee.     

Simulation of Semi-Solid Material Mechanical Behavior Using a Combined Discrete/Finite Element Method

As a necessary step toward the quantitative prediction of hot tearing defects, a three-dimensional stress–strain simulation based on a combined finite element (FE)/discrete element method (DEM) has been developed that is capable of predicting the mechanical behavior of semisolid metallic alloys during solidification. The solidification model used for generating the initial solid–liquid structure is based on a Voronoi tessellation of randomly distributed nucleation centers and a solute diffusion model for each element of this tessellation. At a given fraction of solid, the deformation is then simulated with the solid grains being modeled using an elastoviscoplastic constitutive law, whereas the remaining liquid layers at grain boundaries are approximated by flexible connectors, each consisting of a spring element and a damper element acting in parallel. The model predictions have been validated against Al-Cu alloy experimental data from the literature. The results show that a combined FE/DEM approach is able to express the overall mechanical behavior of semisolid alloys at the macroscale based on the morphology of the grain structure. For the first time, the localization of strain in the intergranular regions is taken into account. Thus, this approach constitutes an indispensible step towards the development of a comprehensive model of hot tearing.     

Analysis of Water Waves Passing Over a Submerged Rectangular Dike

The analytic solutions of inviscid and viscous water waves passing over a submerged rectangular dike are investigated. Owing to the fact that the orthogonality of eigenfunctions is invalid for viscous wave problem, two newly developed orthogonal inner products are applied to reduce the mathematical difficulty of viscous wave problem. Both inviscid and viscous water wave solutions are obtained under the assumption of linear water wave without separation. It shows that two solutions have no significant kinematic difference but the viscous contribution of dynamic effect is not negligible. Beside giving a better theoretical approach, which reduces the error of the conventional minimal squares method, the result of the present analytical solution can be used to quantitatively evaluate the correctness of experiments and also provides helpful information such as near wall boundary layer thickness and oscillating free surface for computational use.     

Liquefaction-Induced Lateral Spreading in Near-Fault Regions during the 1999 Chi-Chi, Taiwan Earthquake

We document and analyze incidents of liquefaction-induced lateral ground deformation at five sites located in the near-fault region of the 1999 Chi-Chi Taiwan earthquake. Each of the lateral spreads involved cyclic mobility of young alluvial soils towards a free face at creek channels. In each case, the lateral spreading produced relatively modest lateral displacements (approximately 10–200?cm) in parts of the spreads not immediately adjacent to channel slopes. For each site, we present displacement vectors across the spread features, which are based on mapping performed within three weeks of the earthquake. We review the results of detailed subsurface exploration conducted at each site, including cone penetration test soundings, borings with standard penetration testing, and laboratory index tests. We back-analyze the field displacements using recent empirical and semiempirical models and find that the models generally overestimate the observed ground displacements. Possible causes of the models’ overprediction bias include partial drainage of the liquefied soils during shaking, low but measurable plasticity of some of the soils’ fines fraction, and the absence of nonspread sites in the empirical databases used to develop existing empirical and semi-empirical lateral spread displacement prediction models.     

An Enhanced Herschel–Bulkley Model for Thixotropic Flow Behavior of Semisolid Steel Alloys

An enhanced model based on Herschel–Bulkley model has been proposed. Modifications are based on the attempts to overcome the limitations of the previously used models. The proposed model predicts thixotropic time-dependent flow behavior at medium shear rates, while reaching toward Newtonian viscosity at higher shear rates, which is a typical behavior of semisolid metal slurries. Rheology tests on M2 high-speed steel were then conducted using a self-developed high-temperature Searle-type rheometer for three different solid fractions. All of the tests were performed in an electric furnace with an argon-controlled atmosphere. Two series of experiments were performed to evaluate the rheological behavior of the material: steady-state flow stress experiments to determine the equilibrium flow curves, and step-change of shear-rate experiments to determine the time-dependent characteristics of the material. The model parameters were then derived using the experimental results and calibrated by curve fitting of experimental data. The model was then linked to a commercial CFD software, and simulation of the process was conducted to evaluate the model. The results show that the model fits well with the experimental data and is capable of simulating a wide range of shear rates compared with typical Herschel–Bulkley model.     

Nonlinear Model for Lead–Rubber Bearings Including Axial-Load Effects

Existing models for isolation bearings neglect certain aspects of their response behavior. For instance, rubber bearings have been observed to decrease in stiffness with increasing axial load, and soften in the vertical direction at large lateral deformations. The yield strength of lead–rubber bearings has also been observed to vary with axial load, such that a lightly loaded bearing may not achieve its theoretical strength. Models that include these axial-load effects in lead–rubber bearings are developed by extending an existing linear two-spring model to include nonlinear behavior. The nonlinearity includes an empirical equation for the experimentally observed variation of yield strength. For numerical implementation, the bearing forces are found by solving the nonlinear equilibrium and kinematic equations using Newton’s method, and the instantaneous bearing stiffness matrix is formed from the differentials of these equations. The response behavior of the models is confirmed by comparison with experimental data.     

Effect of rate sensitivity on slip system activity and lattice rotation

Viscoplastic constitutive models are used for crystals subjected to large strains and high strain-rates; they are based on the assumption that plastic strain occurs by viscous crystallographic slip. Rate-sensitivity and strain-rate effects on crystallographic shears and lattice rotations are investigated; it is shown that large strain-rate sensitivities such as those observed at very high strain rates and at high temperatures may increase the total number of significantly active slip systems and decrease the amount of plastic spin. This leads to contrasted texture evolutions in tension and simple shear which are described.     

Interactional analysis of suicidal behavior.

Analyzes the limitations inherent in 5 empirical research models (pure environmental, pure individual differences, discrete parallel, nonparallel typological, and parallel typological models) that have been used to study suicidal behavior. These extant models are shown to have specific limitations in terms of their ability to reflect an interactional perspective on suicidal behavior. A more adequate research model was then developed and used to test 2 hypotheses derived from a general interactional thesis; approximately 510,400 Ss were studied. Findings support both hypotheses, thus providing considerable support for the general thesis, i.e., that such real-life behaviors cannot adequately be understood by recourse to either individual difference variables alone or environmental variables alone. The implications of these findings and the empirical research model that revealed them are discussed in terms of heuristic value and relevance to students of other forms of human behavior. (76 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Improved Approach to Construct Constitutive Surfaces for Stable-Structured Soils Covering Both Saturated and Unsaturated Conditions

Constitutive surfaces are indispensable for investigation of the behavior of soils. Saturated and unsaturated soils coexist in most engineering problems and it is meaningful to develop constitutive surfaces covering both saturated and unsaturated conditions which help to investigate the behavior for both saturated and unsaturated soils in a unified way. At present, the methodologies used for saturated and unsaturated soils are different and few researchers consider the constitutive surfaces for saturated soils. For unsaturated soils, the suction-controlled triaxial tests are usually laborious, time consuming, costly, and may not justify routine engineering projects. This paper discusses the role of constitutive surfaces in soil mechanics and presents an improved approach over existing interpolation methods to construct the constitutive surfaces for saturated and unsaturated conditions for a stable-structured soil using simple laboratory tests.     

Buckling of Delaminated Composite Beams with Shear Deformation Effect

A general 1D model of composite delaminated beams with shear deformation effect is derived for buckling behavior. The constitutive models of composite laminated beams are derived from the classical 2D laminate theory. The present cylindrical bending models can be used—with much greater accuracy than their well-known plane-strain and plane-stress counterparts—as upper and lower bounds toward one of which the behavior tends, depending on the width-to-length ratio. The analysis is based on the first-order Timoshenko-Mindlin kinematic approach. The differential equations are solved with the aid of a specially developed, very efficient interlaced finite-difference scheme eliminating the “shear locking” phenomenon. A parametric study of the shear deformation effect associated with various constitutive models is carried out for angle-ply delaminated laminate. It was found that the most significant difference between the models is associated with the mix of local and global modes.     

07MnNiMoDR板轧制热变形本构方程

摘要：利用 Gleeble-3500 热模拟实验机完成了07MnNiMoDR钢热等温平面应变压缩实验,获得了温度 900～1100℃、应变速率 0.01～1s-1、变形率45%等条件的高温流变行为,其中温度和应变速率对流变应力的影响明显。基于对Arrhenius 方程和 Zener Hollomon 参数的解析,获得了热变形激活能Q,确定了峰值应力本构模型;通过分析应力应变与位错的关系,获得了硬化率及Z参数等与应力之间的内在关联性,建立了加工硬化 动态回复过程的流变应力模型;基于动态再结晶理论,采用Avrami模型计算了动态再结晶体积分数,获得Z参数计算方法,建立了动态再结晶过程的流变应力模型。利用所建立的本构模型完成了预测及对比分析,相关系数r为0.99,所建立的本构关系模型精度很高。     

Laminar and Turbulent Bottom Boundary Layer Induced by Nonlinear Water Waves

Results of a numerical study to investigate wave-induced boundary layer flows are reported. In this study, the writers consider a coupled viscous-inviscid approach, in which the fully nonlinear free surface boundary conditions are satisfied in the inviscid flow calculation, while the viscous flow near the seabed is solved via the Reynolds-averaged Navier-Stokes equations, instead of the thin boundary layer equation. To simulate the turbulent flow, a two-layer k-ε model is applied. Coupling of the viscous and inviscid computations is accomplished by the direct matching of the velocity and pressure distributions on the matching boundaries. Validation of the numerical model is carried out separately for the inviscid and viscous models, and the coupling approach as a whole. The numerical results are compared with theoretical solutions and available experimental data. A parametric study of the laminar and turbulent boundary layers for highly and weakly nonlinear waves is performed using the coupled viscous-inviscid approach. The results are compared with corresponding U-tube simulations, and the discrepancy is highlighted and discussed.