Unified sand modeling using associated or non-associated flow rule

A constitutive model for unified modeling of sand behavior was formulated in this study. The model is based on generalized plasticity and critical state mechanics. It incorporates a unique flow rule and a unique hardening modulus. The flow rule is a function of the void ratio and its deviation from an associated flow rule reduces with an increase in sand density. The hardening modulus allows the model to simulate a wide range of sand behavior even with an associated flow rule. With 13 material constants, most of which have definite physical meanings and are straightforward to calibrate using conventional element tests, the model can simulate the drained and undrained responses of sand over a large range of initial void ratios and confining pressures. In addition, the model can be readily degenerated to follow an associated flow rule. The associated-flow-model, which requires 11 material constants, can also reproduce the responses of medium-loose to dense sands when the confining pressure is modest. Although the associated-flow model is not capable of describing the bifurcation of sand responses before the failure surface is reached, it may have advantage in the numerical simulation of well-compacted earth structures like earthdams, embankments and retaining walls.     

Critical state shear behavior of the soil-structure interface determined by discrete element modeling

The interface between soil and structure can be referred to as a soil-structure system, and its behavior plays an important role in many geotechnical engineering practices. In this study, results are presented from a series of monotonic direct shear tests performed on a sand-structure interface under constant normal stiffness using the discrete element method (DEM). Strain localization and dilatancy behavior of the interface is carefully examined at both macroscopic and microscopic scales. The effects of soil initial relative density and normal stress on the interface shear behavior are also investigated. The results show that a shear band progressively develops along the structural surface as shear displacement increases. At large shear displacement a unique relationship between stress ratio and void ratio is reached in the shear band for a certain normal stress, indicating that a critical state exists in the shear band. It is also found that the thickness and void ratio of the shear band at the critical state decreases with increasing normal stress. Comparison of the DEM simulation results with experimental results provides insight into the shear behavior of a sand-structure interface and offers a means for quantitative modeling of such interfaces based on the critical state soil mechanics.     

关于土—结相互作用界面力学行为的数值模拟

根据土 -结 (桩 )相互作用典型的界面力学行为特点——两者相互作用直至剪切破坏的滑动面一般都是在土体一侧内部发生的 ,滑动层的厚薄与土性及结构物表面粗糙度等有关等 ,提出了把二者所谓相互作用的界面在概念上做广义化的处理 ,即泛化为一有限的区域 ,认为结构与土体相互作用的界面应是一个广义的相互作用影响范围而非绝对地仅只限于两者的相互接触界面 ,两者间相互作用的界面行为可近似地通过这有限薄层范围内土体材料的本构行为来模拟 ,从而形成了本文关于土 -结相互作用界面行为的模拟关键实质上可以归结为土体的非线性本构行为及其数值分析途径的研究等观点 ,仅供同行参考     

Exploring the relationship between critical state and particle shape for granular materials

The relationship between critical state and particle shape corresponds to the most fundamental aspect of the mechanics of granular materials. This paper presents an investigation into this relationship through macro-scale and micro-scale laboratory experiments in conjunction with interpretation and analysis in the framework of critical state soil mechanics. Spherical glass beads and crushed angular glass beads of different percentages were mixed with a uniform quartz sand (Fujian sand) to create a sequence of mixtures with varying particle shape. On the micro-scale, particle shape was accurately measured using a laser scanning technique, and was characterized by aspect ratio, sphericity and convexity; a new shape index, taken as the average of the three shape measures and referred to as overall regularity, was proposed to provide a collective characterization of particle shape. On the macro-scale, both undrained and drained triaxial tests were carried out to provide evidence that varying particle shape can alter the overall response as well as the critical states in both stress space and volumetric compression space. The mixtures of Fujian sand and spherical glass beads were found to be markedly more susceptible to liquefaction than the mixtures of Fujian sand and crushed angular glass beads. The change in liquefaction susceptibility was shown to be consistent with the change in the position of the critical state locus (CSL) in the compression space, manifested by a decrease in the intercept and gradient of the CSL due to the presence of spherical glass beads. Quantitative relationships have been established between each of the critical state parameters and each of the shape parameters, thereby providing a way to construct macro-scale constitutive models with intrinsic micro-scale properties built in.     

Constitutive modeling of Aluminum Alloy 7050 cyclic mean stress relaxation and ratcheting

The challenge of describing in a generalized mathematical pattern the inelastic behavior of metals has led to the development of several constitutive models, especially in the field of cyclic plasticity, where phenomena with particular importance to low-cycle fatigue appear. Significant research efforts have been undertaken in studying and simulating the cyclic elastoplastic response of steels, while light metals, like aluminum and titanium, have attracted less attention. This paper provides a preliminary examination on the capacity of the Multi-component Armstrong and Frederick Multiplicative (MAFM) model to simulate effectively the cyclic mean stress relaxation and ratcheting of Aluminum Alloy 7050. The derived results indicate that the model is capable to describe successfully the complex cyclic plasticity phenomena exhibited by this alloy.     

Historical review of internal state variable theory for inelasticity

A review of the development and the usages of internal state variable (ISV) theory are presented in this paper. The history of different developments leading up the formulation of the watershed paper by Coleman and Gurtin is discussed. Following the Coleman and Gurtin thermodynamics, different researchers have employed the ISV theory for dislocations, creep, continuum damage mechanics (CDM), unified-creep-plasticity (UCP), polymers, composites, biomaterials, particulate materials, multiphase and multiphysics materials, materials processing, multiscale modeling, integrating materials science (structure–property relations) into applied mechanics formulations, and design optimization under uncertainty for use in practical engineering applications.     

Constitutive modeling of orthotropic sheet metals by presenting hardening-induced anisotropy

An essential work on the constitutive modeling of rolled sheet metals is the consideration of hardening-induced anisotropy. In engineering applications, we often use testing results of four specified experiments, three uniaxial-tensions in rolling, transverse and diagonal directions and one equibiaxial-tension, to describe the anisotropic features of rolled sheet metals. In order to completely take all these experimental results, including stress-components and strain-ratios, into account in the constitutive modeling for presenting hardening-induced anisotropy, an appropriate yield model is developed. This yield model can be characterized experimentally from the offset of material yield to the end of material hardening. Since this adaptive yield model can directly represent any subsequent yielding state of rolled sheet metals without the need of an artificially defined “effective stress”, it makes the constitutive modeling simpler, clearer and more physics-based. This proposed yield model is convex from the initial yield state till the end of strain-hardening and is well-suited in implementation of finite element programs.     

用ABAQUS软件处理管土相互作用中的接触面问题

采用ABAQUS软件处理管土相互作用中的接触面问题，利用ABAQUS软件中的主控-从属接触算法，使管道和海床形成一个接触对；并且建立了管土系统有限单元模型．海床土体分别采用非线性弹性模型、多孔弹性模型、Ramberg-Osgood塑性模型对管土系统进行计算通过分析计算，得到了管道沉降量与管重间的关系，以及由于管道沉陷而形成的土体楔形，土体楔形的存在，增加了管道的稳定性．计算结果和有关试验结果相符合，说明采用该软件进行管土相互作用问题分析是可行的．     

弹性力学混合状态方程的小波解法

应用小波理论求解弹性力学混合状态方程，讨论了解的收敛性。从文中的数值算例不难看出，该方法不失为混合状态方程一种新的求解途径。     

Modelling of the interface between a thin film and a substrate within a strain gradient plasticity framework

Interfaces play an important role for the plastic deformation at the micron scale. In this paper, two types of interface models for isotropic materials are developed and applied in a thin film analysis. The first type, which can also be motivated from dislocation theory, assumes that the plastic work at the interface is stored as a surface energy that is linear in plastic strain. In the second model, the plastic work is completely dissipated and there is no build-up of a surface energy. Both formulations introduce one length scale parameter for the bulk material and one for the interface, which together control the film behaviour. It is demonstrated that the two interface models give equivalent results for a monotonous, increasing load. The combined influence of bulk and interface is numerically studied and it is shown that size effects are obtained, which are controlled by the length scale parameters of bulk and interface.     

Constitutive modeling and the trousers test for fracture of rubber-like materials

The classical constitutive modeling of incompressible hyperelastic materials such as vulcanized rubber involves strain-energy densities that depend on the first two invariants of the strain tensor. The most well-known of these is the Mooney-Rivlin model and its specialization to the neo-Hookean form. While each of these models accurately predicts the mechanical behavior of rubber at moderate stretches, they fail to reflect the severe strain-stiffening and effects of limiting chain extensibility observed in experiments at large stretch. In recent years, several constitutive models that capture the effects of limiting chain extensibility have been proposed. Here we confine attention to two such phenomenological models. The first, proposed by Gent in 1996, depends only on the first invariant and involves just two material parameters. Its mathematical simplicity has facilitated the analytic solution of a wide variety of basic boundary-value problems. A modification of this model that reflects dependence on the second invariant has been proposed recently by Horgan and Saccomandi. Here we discuss the stress response of the Gent and HS models for some homogeneous deformations and apply the results to the fracture of rubber-like materials. Attention is focused on a particular fracture test, namely the trousers test where two legs of a cut specimen are pulled horizontally apart. It is shown that the cut position plays a key role in the fracture analysis, and that the effect of the cut position depends crucially on the constitutive model employed. For stiff rubber-like or biological materials, it is shown that the influence of the cut position is diminished. In fact, for linearly elastic materials, the critical driving force for fracture is independent of the cut position. It is also shown that the limiting chain extensibility models predict finite fracture toughness as the cut position approaches the edge of the specimen whereas classical hyperelastic models predict unbounded toughness in this limit. The results are relevant to the structural integrity of rubber components such as vibration isolators, vehicle tires, earthquake bearings, seals and flexible joints.     

The rational mechanics and thermodynamics of polymeric fluids based upon the concept of a variable relaxed state

The conceptual framework of polymer continuum mechanics based upon Eckart's idea of a variable relaxed state is developed. No constitutive models are explicitly used. The theory admits four constitutive functions only, the scalar specific internal energy, the vectorial heat flux, and two tensorial fluxes representing non-elastic stress and flow (slippage). The non-linearity of the constitutive relations includes self-induced anisotropy (Leonov) with Reiner-Rivlin's equation representing a special example for this. — The effectiveness of this non-linear theory is demonstrated by treating elongational flows of polymer melts.     

Micromechanical modeling of the elasto-viscoplastic behavior of semi-crystalline polymers

A micromechanically based constitutive model for the elasto-viscoplastic deformation and texture evolution of semi-crystalline polymers is developed. The model idealizes the microstructure to consist of an aggregate of two-phase layered composite inclusions. A new framework for the composite inclusion model is formulated to facilitate the use of finite deformation elasto-viscoplastic constitutive models for each constituent phase. The crystalline lamellae are modeled as anisotropic elastic with plastic flow occurring via crystallographic slip. The amorphous phase is modeled as isotropic elastic with plastic flow being a rate-dependent process with strain hardening resulting from molecular orientation. The volume-averaged deformation and stress within the inclusions are related to the macroscopic fields by a hybrid interaction model. The uniaxial compression of initially isotropic high density polyethylene (HDPE) is taken as a case study. The ability of the model to capture the elasto-plastic stress-strain behavior of HDPE during monotonic and cyclic loading, the evolution of anisotropy, and the effect of crystallinity on initial modulus, yield stress, post-yield behavior and unloading-reloading cycles are presented.     

A constitutive model for the formation of martensite in austenitic steels under large strain plasticity

A constitutive model for diffusionless phase transitions in elastoplastic materials undergoing large deformations is developed. The model takes basic thermodynamic relations as its starting point and the phase transition is treated through an internal variable (the phase fractions) approach. The usual yield potential is used together with a transformation potential to describe the evolution of the new phase. A numerical implementation of the model is presented, along with the derivation of a consistent algorithmic tangent modulus. Simulations based on the presented model are shown to agree well with experimental findings. The proposed model provides a robust tool suitable for large-scale simulations of phase transformations in austenitic steels undergoing extensive deformations, as is demonstrated in simulations of the necking of a bar under tensile loading and also in simulations of a cup deep-drawing process.     

基于物理界面的双重介质有限裂隙渗流模型

基于连续介质或者离散裂隙假设,含裂隙的多孔介质渗流问题有多种数学力学模型。受物理界面的启发,提出一种新的有限裂隙连续介质力学模型,可以为宏观裂隙-多孔介质内的流体输运问题等提供近似计算方案。该模型属于一类双重介质模型,将曲面上低维度的流场转化为三维空间的流场,并且与连续的多孔介质的流场耦合,在数学上表示为统一的输运控制方程和初始边界条件。这个近似模型为不方便实施高维度-低维度耦合求解的数值计算方法提供新的模拟思路,如光滑粒子流体动力学等无网格粒子类方法。     

ANALYSIS OF INTERPHASE MECHANICAL BEHAVIOR WITH INTERFACE ELEMENT IN THE COMPOSITE MATERIALS

ＡＮＡＬＹＳＩＳＯＦＩＮＴＥＲＰＨＡＳＥＭＥＣＨＡＮＩＣＡＬＢＥＨＡＶＩＯＲＷＩＴＨＩＮＴＥＲＦＡＣＥＥＬＥＭＥＮＴＩＮＴＨＥＣＯＭＰＯＳＩＴＥＭＡＴＥＲＩＡＬＳＡＮＡＬＹＳＩＳＯＦＩＮＴＥＲＰＨＡＳＥＭＥＣＨＡＮＩＣＡＬＢＥＨＡＶＩＯＲＷＩＴＨＩＮ...     

爆炸焊接界面波的数值模拟

借助动力学分析软件ANSYS/LS-DYNA 11.0,运用光滑粒子流体动力学方法(SPH方法),建立以Johnson-Cook材料模型和Grüneisen状态方程为基础的热塑性流体力学模型,对同种钢板爆炸焊接界面波进行了数值模拟.结果表明,运用SPH方法可以得到清晰的爆炸焊接界面波形貌.与实验结果的比较表明:模拟误...     

On the definitions of failure and critical states in hypoplasticity

A granular body is said to be at failure or in a critical state if the stress state does not change while the body is continuously deformed. Within the framework of hypoplasticity, such states, generally called stationary states,are conventionally defined by the condition that an objective (the Jaumann) stress rate vanishes. However, not all stationary states attained under monotonic deformation lie within the scope of this definition. Simple shear is an example. In fact, stationary states are characterized by zero material time derivative of the stress tensor rather than zero Jaumann rate. In the present paper, we give a generalized definition of stationarity by the condition of zero material time derivative of the stress tensor. The new definition extends the set of possible stationary states and includes those which are not covered by the previous definition. Stationary states are analysed quantitatively using calibrated hypoplastic equations. It is shown numerically that, if the norm of the spin tensor is of the same order as, or smaller than, the norm of the stretching tensor, the old definition approximates all possible sationary states with sufficient accuracy.      

Modelling long-term deformation of granular soils incorporating the concept of fractional calculus

Many constitutive models exist to characterise the cyclic behaviour of granular soils but can only simulate deformations for very limited cycles. Fractional derivatives have been regarded as one potential instrument for modelling memory-dependent phenomena. In this paper, the physical connection between the fractional derivative order and the fractal dimension of granular soils is investigated in detail.Then a modified elasto-plastic constitutive model is proposed for evaluating the long-term deformation of granular soils under cyclic loading by incorporating the concept of factional calculus. To describe the flow direction of granular soils under cyclic loading, a cyclic flow potential considering particle breakage is used. Test results of several types of granular soils are used to validate the model performance.