Nonlinear Stress-strain Relationship Research Articles

전체변형률 영역에 대한 K0압밀시 풍화토의 변형특성 평가

본 연구에서는 미소변형 영역에서 파괴에 이르는 전체변형률 영역에서 지반의 변형거동 평가가 가능한 미소변형측정 삼축시험장비에 횡방향 변위측정시스템을 추가하여 시료의 포아송비 측정이 가능하도록 하였다. 구축한 횡방향 변위 측정시스템을 폴리우레탄시편을 이용하여 검증하였으며, 일정 구속압 재하 후 횡변위를 모니터링하며 축하중을 조정함으로써 <TEX>$K_0$</TEX> 압밀을 구현하였다. 구축된 시험시스템을 이용하여 화강풍화토 시료에 대하여 <TEX>$K_0$</TEX>압밀 및 등방압밀 상태에서 구속응력조건을 달리하며 시험을 수행하였고, 전체변형률 영역에서의 변형 및 강도거동을 비교, 평가하였다. <TEX>$K_0$</TEX>압밀 조건은 등방압밀 조건과 비교하여 동일한 평균유효구속응력 조건에서 포아송비, 탄성계수, 비선형 변형거동특성에 있어서 상이한 특성을 나타내었다. The small-to-large strain traixal testing apparatus has been adopted to evaluate the deformation characteristics of soils at full strain ranges (<TEX>$10^{-4}%{\sim}10%$</TEX>). In this study, a lateral deformation measurement system was additionally installed to the apparatus in order to measure Poisson's ratio. It was verified using polyurethane specimens and then used to set up <TEX>$K_0$</TEX>-consolidated state of soil specimens by monitoring the lateral deformation variation and adjusting axial stresses during a consolidation step. Test results show that Poisson's ratio, elastic modulus, and nonlinear stress-strain relations under <TEX>$K_0$</TEX> condition are significantly different from those under isotropic condition.

Biaxial loading of neo-classical liquid crystal elastomers: constitutive relations and soft behavior

The thermo-order-mechanical behaviors of liquid crystal elastomers (LCEs) under biaxial loading are studied in this paper. Inverse method for nonlinear elastic problems is utilized by imposing biaxial stretching to thin rectangular samples. Neo-classical elastic energy is used together with the Landau-de Gennes nematic free energy. Under plane stress assumptions, the constitutive equations are derived. Due to the possible reorientations of the liquid crystal molecules induced by the imposed biaxial loading, the in-plane nonlinear stress-strain relations can have different expressions depending on which loading axis will have the largest effective principal strain. And the free energy is a multi-well non-convex potential function. As shown by some typical loading paths, the LCE samples will exhibit an anisotropic nonlinear elastic behavior, as long as the loading has not induced a reorientation of the liquid crystal molecules. When this did occur, jumps of stresses could take place for dead loadings due to the losing of stability.

Experimental Detection of Damage Evolution in Concrete under Multiaxial Compression

The nonlinear inelastic stress-strain relationship of concrete is a result of changes to the fabric of the material caused by several damage mechanisms. Existing experimental research on concrete provides very little information on the evolution of these mechanisms. Instead, most experimental studies are limited to measuring the external loads and deformations of concrete specimens. The aim of the research presented here is to provide a direct link between macroscopically observed global stress-strain behavior and the development of damage mechanisms within the specimens. A novel experimental procedure is introduced to monitor the changes in the material during a conventional multiaxial compression test. This procedure, comprising small stress probes repeated at selected points of the stress-strain history, is designed to provide data on the tangent stiffness operator and the associated acoustic tensors. The acoustic tensor with the minimum value of its determinant provides information on both magnitude and orientation of the damage. The stress-probing methodology and some of the key practical aspects and limitations of the experimental procedure are illustrated by using five multiaxial compression tests as examples of different stress-strain histories. The results of the test methodology presented in this paper give an indication of the extent of damage and accurate information about its orientation. This paper therefore shows that the stress-probing procedure can be incorporated in multiaxial tests designed to monitor the relationship between damage evolution in the material and macroscopically observed stress-strain response of the specimen.

Buckling of steel columns in fire: non‐linear behaviour and design proposal

AbstractIn a fire the buckling strength of steel columns is heavily influenced by the distinctly non‐linear material behaviour of steel at elevated temperatures. A general analytical model that explicitly includes the non‐linear material behaviour is presented here and verified with full‐scale tests at elevated temperature. Based on test results and this general model, a new model for flexural buckling is developed which can be used to design slender columns and allows non‐linear stress–strain relationships, geometrical imperfections and load eccentricities to be considered. In addition, the model can be easily extended to include local cross‐section instabilities describing the interaction between local and global buckling phenomena.

Global stability of thin-walled ferritic stainless steel members

As more metallic alloys are introduced in engineering structures, the demand for the proper utilisation of their nonlinear stress–strain relationship is increasing. This paper discusses the inelastic buckling of members from such materials with a special focus on ferritic stainless steels. Here we introduce an alternative approach for the overall stability of members that considers material nonlinearity, namely the strain hardening parameter n. The suitability of the new model is verified by regression analysis in comparison with the commonly used standard calculations. The analysis results show that the present approach could be applied successfully in flexural, flexural–torsional and lateral–torsional buckling.

Oscillatory instability in slow crack propagation in rubber under large deformation

We performed experiments to investigate slow fracture in thin rubber films under uniaxial tension using high-viscosity oils. In this system we observed an oscillating instability in slowly propagating cracks for small applied strains. The transition between oscillatory and straight patterns occurred near the characteristic strain at which rubber exhibits a nonlinear stress-strain relation. This suggests that nonlinear elasticity plays an important role in the formation of the observed pattern. This was confirmed by numerical simulation for neo-Hookean and linear elasticity models.

Finite element analysis of rigid pavement on a nonlinear two parameter foundation model

A numerical iterative procedure based on finite element method has been presented for analyzing the dynamic response of pavement to moving load resting on a nonlinear subgrade. The pavement is descretized by finite and infinite beam elements. The foundation is modeled by Pasternak's two parameter soil medium. The nonlinear stress-strain relationship in the soil is considered. The dynamic vehicle-pavement interaction (VPI) effects are incorporated in the analysis. The effect of the material nonlinearity of the supporting soil medium on the pavement response is investigated by conducting a parametric study.

Comparative analysis of pelvic ligaments: a biomechanics study

Pelvic organ prolapse (POP) affects one third of women of all ages and is a major concern for gynecological surgeons. In pelvic reconstructive surgery, native ligaments are widely used as a corrective support, while their biomechanical properties are unknown. We hypothesized differences in the strength of various pelvic ligaments and therefore, aimed to evaluate and compare their biomechanical properties. Samples from the left and right broad, round, and uterosacral ligaments from 13 fresh female cadavers without pelvic organ prolapse were collected. Uniaxial tension tests at a constant rate of deformation were performed and stress-strain curves were obtained. We observed a non-linear stress-strain relationship and a hyperelastic mechanical behavior of the tissues. The uterosacral ligaments were the most rigid whether at low or high deformation, while the round ligament was more rigid than the broad ligament. Pelvic ligaments differ in their biomechanical properties and there is fairly good evidence that the uterosacral ligaments play an important role in the maintenance of pelvic support from a biomechanical point of view.

Existence result of an effective stress for an isotropic visco-plastic composite

We define and present some theoretical characterizations of associated constitutive equations for a visco-plastic deformation of a composite. Introducing of an adequate topological framework for some visco-plastic state parameters, when considered a nonlinear stress–strain relations of Prandtl–Reuss type, we obtain the existence and uniqueness results of a steady state for a composite reinforced with other inclusions. The time-dependent plastic strains of these Al based composites reinforced with SiC inclusions are then calculated as a function of inclusion volume concentration, effective stress and effective visco-plastic strain, following an dynamical yield function of power type. Viewed as a Drucker–Prager material, a selection criterion for visco-plastic strain rate, permit us a formulation as an isotropic hardening problem and their reduction to a sweeping process problem for an elastic component of the strain. In this paper a family of models for the composite deformation, defined by Halphen and Nguyen Quoc Son, enlarges the classical class of generalized standard materials, ant they are characterized by monotone-gradient flow function. These models improve the tensile process of Al based composite, in order to allow new practical solutions in civil engineering.

Modeling of Concrete for Nonlinear Analysis using Finite Element Code ABAQUS

ABSTRACT Concrete is the main constituent material in many structures. The behavior of concrete is nonlinear and complex. Increasing use of computer based methods for designing and simulation have also increased the urge for the exact solution of the problems. This leads to difficulties in simulation and modeling of concrete structures. A good approach is to use the general purpose finite element software ABAQUS. In this paper a 3D model of a concrete cube is prepared using smeared crack model and concrete damage plasticity approach. The validation of the model to the desired behavior under monotonic loading is then discussed. Keywords Finite element, ABAQUS, smeared cracking, concrete damage plasticity, tension stiffening. 1. ultimate INTRODUCTION Since 1970, analyses of reinforced concrete structures using finite element method, have witnessed a remarkable advancement. Many researchers have made valuable contributions in understanding the behavior of concrete and have developed sophisticated methods of analysis. These achievements are well documented and available in various reports and technical papers but still there are many areas in which much remains to be understood and researched. The past decade with the advancement in computing techniques and the computational capabilities of the high end computers has led to a better study of the behavior of concrete. However the complex behavior of concrete sets some limitations in implementing FEM. The complexity is mainly due to non-linear stress-strain relation of the concrete under multi-axial stress conditions, strain softening and anisotropic stiffness reduction, progressive cracking caused by tensile stresses and strains, bond between concrete and reinforcement, aggregation interlocks and dowel action of reinforcement, time dependant behavior as creep and shrinkage [1]. Several researchers have documented about nonlinear analysis of reinforced concrete and prestressed concrete structures. For nonlinear analysis many commercial software are available, such as ANSYS, ABAQUS, NASTARAN, and ADINA. All these softwares are not tailor made applications which can work automatically on just feeding few data and the requirements. An acceptable analysis of any structure as a whole or a part there in, using Finite element software, and the correctness of it totally depends on the input values, especially the material properties used. However when one is working with concrete a sound technical background is required to use them in a proper manner and get the desired results. Concrete used in common engineering structures, basically is a composite material, produced using cement, aggregate and water. Sometimes, as per need some chemicals and mineral admixtures are also added. Experimental tests show that concrete behaves in a highly nonlinear manner in uniaxial compression. Figure.1 shows a typical stress-strain relationship subjected to uniaxial compression. This stress-strain curve is linearly elastic up to 30% of the maximum compressive strength. Above this point tie curve increases gradually up to about 70-90% of the maximum compressive strength. Eventually it reaches the pick value which is the maximum compressive strength

Introduction to the mechanics and design of undamageable materials

In this work proposed damage variables that are examined in the framework of continuum damage mechanics are used to illustrate the new concept of an undamageable material. This type of material is derived theoretically in this work with exact nonlinear stress–strain relationships. Such a material may undergo deformation with zero damage, i.e. maintain a zero value for the damage variable in the context of continuum damage mechanics. The theoretical formulation is presented in the hope that in the future, the manufacturing of such a material may be realized. The proposed undamageable material is a type of hyperelastic material similar to the Mooney–Rivlin material. It is hoped that this work will open the way for new areas of research in materials science.

A novel deformation method for fast simulation of biological tissue formed by fibers and fluid

This paper presents a new approach to the simulation of soft tissues deformation suitable for real time computation, particularly intriguing for medical applications. The approach implements a quasi-static solution for elastic global deformations of objects filled with fluid and fibers, which can be a good approximation for biological tissues. It is based on the Pascal's principle and the conservation of volume. Large deformations that quickly change the whole shape of the object can be stably simulated in a small number of time steps. In our approach each pair of surface vertices is connected and defines an elastic fiber. The set of all the elastic fibers defines a mesh of an order of magnitude smaller than the volumetric meshes, allowing the simulation of complex objects with less computational effort. The proposed method was applied to study the effects of forces for deformation and displacement of soft geometrical objects (rod, sphere, etc.) in order to analyze the results on simple forms. Then a compression similar to the deformation obtained during a mammographic examination procedure is applied to a breast. A preliminary validation is done by comparing deformation result between our new method and real ex vivo bovine liver. The results of this comparison show a high degree of similarities between the experimental results and deformations calculated by our method. This new method is suited to isotropic or anisotropic elasticity and linear or nonlinear stress-strain relationship. Finally, the results of the deformations were shown to be independent of the mesh discretization for our method.

A New Class of Damage Variables in Continuum Damage Mechanics

In this work various new proposed damage variables are introduced, examined and compared. Only the scalar case pertaining to isotropic damage is investigated here. Several types of new damage variables are proposed as follows: (1) damage variables that are defined in terms of cross-sectional area, (2) damage variables that are defined in terms of the elastic modulus or stiffness, and (3) composite damage variables that are defined in terms of two parameters relating to both cross-sectional area and stiffness. However, the generalization to tensors and general states of deformation and damage may be a straightforward process but is beyond the scope of this work. The damage variables introduced in this work can be applied to elastic materials including homogeneous materials like metals and heterogeneous materials like composite laminates. In the second part of this work, higher-order strain energy forms are proposed. It is seen that a specific nonlinear stress-strain relationship is associated with each higher-order strain energy form. These higher order strain energy forms along with some of the proposed damage variables are used in trying to lay the theoretical groundwork for the design of undamageable materials, i.e., materials that cannot be damaged where the value of the damage variable remains zero throughout the deformation process.

Assessment of the fire resistance of a nuclear power plant subjected to a large commercial aircraft crash

Abstract The safety assessment of infrastructures, such as a nuclear power plant, for the crash of a large commercial aircraft has been performed worldwide after the terrorism that occurred in the U.S. on September 11, 2001. The assessment, however, has mainly focused on the techniques of impact analysis. In this study, a systematic procedure to assess the fire resistance of containment and auxiliary buildings subjected to such an aircraft crash is proposed. The intensity, duration and distribution of the fire are determined based on aircraft crash analyses and characteristics of jet fuel. A three-dimensional detailed finite element model of the containment and auxiliary buildings is established and used for heat transfer and thermal stress analyses, taking into account the material properties at an elevated temperature. Section forces can then be obtained that are based on a nonlinear stress–strain relationship. The fire resistance of the structure is assessed by comparing the fire-induced section forces with the section resistance which is evaluated using the load–moment strength interaction diagram. The study addresses the problem whereby the conventional assessment that only considers the flexural behaviour is less accurate. The assessment results support the general conclusion that the nuclear power plant structures can maintain structural integrity against external fire due to their relatively thick sections. The proposed procedure can be extensively applied to evaluate the fire endurance time of any type of structure subjected to an arbitrary fire.

Effect of ambient temperature on stress, deformation and temperature of dump truck tire

The influence of the ambient temperature on the stress, deformation and temperature of a dump truck tire has been predicted with the virtual tire model established in this work by employing the finite element method (FEM) and Algor software. The nonlinear stress–strain relationship of tire rubber material has been given by Mooney–Rivlin material model. The hysteresis and loss strain energy density have been related to give the heat generation rate. A two-dimensional (2D) FE model of rolling radial tire has been built in Algor environment according to the actual construction of bridgestone 24.00R35 tire adopted for Caterpillar Earth Mover 775E Model. The model consists of the tread, belt, carcass, air filled volume and tire–rim interface. The material properties of the components and boundary conditions from tire–rim contact and tire–road contact are considered. The mechanical event simulation (MES) with nonlinear material model and the steady-state heat transfer analysis have been performed. The analysis results of the tire stress, deformation and temperature are presented under the ambient temperatures ranging from −40 to 40°C conditions at the Syncrude mine in Canada. The results show that the effect of the ambient temperature on the tire deformation is larger than on the tire stress. The increase of ambient temperature will cause the tire temperature rise. This study provides a comprehensive modeling and analysis that provide key to avoid tire temperature related failure.

Numerical Analysis and Comparative Study of the Cross-Sectional Capacity of Structural Steel Members in Fire

The cross-sectional capacity of steel sections subjected to fire is strongly affected by the decreasing stiffness during heating and the nonlinear stress-strain relationship of steel at elevated temperatures. This paper analyses the cross-sectional capacity of common steel sections subjected to combined axial compression and biaxial bending moments at both ambient and elevated temperatures considering section yielding and local buckling effects. The results of a parametric study using the finite element approach are presented as temperature-dependent normalized N-M interaction curves and are compared to results using elastic and plastic interaction formulae. A comparative study shows that European fire design models may lead to conservative results for semi-compact and slender cross sections (class 3 and 4 sections) due to the partial plastic capacity of these sections. However, for steel members predominately subjected to axial compression the design models may lead to unconservative results due to local buckling deflections that occur even for plastic and compact sections (class 1 and 2).

Prediction of Nonlinear Stress-Strain Relationship of Lightly Stabilized Granular Materials from Unconfined Compression Testing

AbstractThis paper examines the nonlinear stress-strain behavior of lightly stabilized granular base materials and presents a method to predict them based on modified and extended Ramberg-Osgood expression from unconfined compression (UC) testing. A typical granular material was lightly stabilized with 0.5–3.0% cement-flyash (CF) as well as with 1.5–3.0% slag-lime (SL) and tested in UC with internal deformation measurement setup. This study indicates that the proposed mathematical model can accurately predict the nonlinear stress-strain relationships of the lightly stabilized materials obtained from the experiments. The parameters involved with the proposed model were initial elastic modulus E0, 0.2% proof stress σ0.2, ultimate strain eu, and the exponents for quantifying the nonlinearity of the curves n and m. Values of all the parameters were determined from the experimental stress-strain responses and reliable regression relationships were developed between these parameters and unconfined compressive s...

Study on Pore Water Pressure Model of Soft Clay

Based on the consolidated undrained triaxial test of soft clay, a formula for computing pore water pressure is developed, by using of the critical state theory of volume strain and the characteristic normalization of soft clay. It is shown that the new proposed formula is reasonable to reveal the nonlinear stress-strain relationship and the dilatancy characteristics of soft clay. With the comparison between the pore water pressure simulation results by the new formula and the experimental data, it is shown that the simulation values agree well with the experimental data. Meanwhile, based on the failure criterion, a formula for the critical pore water pressure is proposed. It is shown that the new formula is reasonable to simulate the critical pore water pressure. It is very useful to predict the foundation stability.

Normal Section Bearing Capacity of Light Weight Aggregate Concrete Member with Circular Section under Eccentric Compression

According to the nonlinear stress-strain relationship of LAC (lightweight aggregate concrete), in this paper whole process theoretical analysis on normal section bearing capacity has been done on lightweight aggregate reinforced concrete member with circular section under eccentric compressive loading. Fundamental equation of numerical iteration is established for normal section bearing capacity of LAC member with circular section under eccentric compressive loading, which provides theoretical basis for concerned calculation simplification.

Study on Pore Water Pressure Model of Soft Clay

Based on the consolidated undrained triaxial test of soft clay, a formula for computing pore water pressure is developed, by using of the critical state theory of volume strain and the characteristic normalization of soft clay. It is shown that the new proposed formula is reasonable to reveal the nonlinear stress-strain relationship and the dilatancy characteristics of soft clay. With the comparison between the pore water pressure simulation results by the new formula and the experimental data, it is shown that the simulation values agree well with the experimental data. Meanwhile, based on the failure criterion, a formula for the critical pore water pressure is proposed. It is shown that the new formula is reasonable to simulate the critical pore water pressure. It is very useful to predict the foundation stability.