A damage constitutive model for sliding friction coupled to wear

Several new constitutive models are formulated for the planar interface of a soft body sliding on a rigid soil, describing stick-slip phenomena due to friction, and wear due to abrasion. Attention is focused on damage at the interface, by neglecting any interaction with damage of body and any propagation of damage inside the body. Models are formulated in the general framework of the Thermodynamics of the irreversible processes and account for suitable defined internal variables of phenomenological type, namely gap, isotropic friction hardening and wear. The main feature of the new presented models is that the formulation of the wear process at the interface is obtained in the contest of Damage Mechanics, and it is based on the formal analogy between abrasion of a soft body and ductile damage of an elastic-plastic material. By following this approach, a scalar wear field, an effective stress and appropriate state and dissipation potentials are defined, able to describe a tangential isotropic wear process due to stick-slip and to hardening mechanism. Both cases of linear and nonlinear friction hardening are formulated; moreover, wearable and no-wearable bodies are considered. Numerical results relevant to one-dimensional problems are illustrated for monotonic, forward-backward and cyclic displacement time-histories, showing evolution for stress, gap and wear. Results furnished by different models are compared and discussed.     

A model framework for anisotropic damage coupled to crystal (visco)plasticity

We develop a model framework for anisotropic damage coupled to crystal (visco)plasticity, which is based on the concept of a fictitious (undamaged) configuration. The theoretical setting is that of finite strains, which is natural when studying crystal inelasticity even in the case of actual small strains. It turns out that the evolution law for damage, which reflects degradation in the slip planes and which is the key new relation, bears strong resemblance with the inelastic flow rule. Some numerical results showing qualitatively the anisotropic development of damage concludes the paper.     

A new thermodynamically consistent continuum model for hardening plasticity coupled with damage

A phenomenological model for hardening–softening elasto-plasticity coupled with damage is presented. Specific kinematic internal variables are used to describe the mechanical state of the system. These, in the hypothesis of infinitesimal changes of configuration, are partitioned in the sum of a reversible and an irreversible part. The constitutive equations, developed in the framework of the Generalised Standard Material Model, are derived for reversible processes from an internal energy functional, postulated as the sum of the deformation energy and of the hardening energy both coupled with damage, while for irreversible phenomena from a dissipation functional.Performing duality transformations, the conjugated potentials of the complementary elastic energy and of the complementary dissipation are obtained. From the latter a generalised elastic domain in the extended space of stresses and thermodynamic forces is derived. The model, which is completely formulated in the space of actual stresses, is compared with other formulations based on the concept of effective stresses in the case of isotropic damage. It is observed that such models are consistent only for particular choices of the damage coupling. Finally, the predictions of the proposed model for some simple processes are analysed.     

A framework for multiplicative elastoplasticity with kinematic hardening coupled to anisotropic damage

The objective of this contribution is the formulation and algorithmic treatment of a phenomenological framework to capture anisotropic geometrically nonlinear inelasticity. We consider in particular the coupling of viscoplasticity with anisotropic continuum damage whereby both, proportional and kinematic hardening are taken into account. As a main advantage of the proposed formulation standard continuum damage models with respect to a fictitious isotropic configuration can be adopted and conveniently extended to anisotropic continuum damage. The key assumption is based on the introduction of a damage tangent map that acts as an affine pre-deformation. Conceptually speaking, we deal with an Euclidian space with respect to a non-constant metric. The evolution of this field is directly related to the degradation of the material and allows the modeling of specific classes of elastic anisotropy. In analogy to the damage mapping we introduce an internal variable that determines a back-stress tensor via a hyperelastic format and therefore enables the incorporation of plastic anisotropy. Several numerical examples underline the applicability of the proposed finite strain framework.     

Investigation on elasto-plastic constitutive model coupled with damage for localization phenomena

On the basis of existing plasticity-based damage model for plasticity coupled with damage for localization analysis, constitutive parameter identification was carried out through a series of numerical tests at local level. And then improvements were made on the expressions of the evolution laws of damage. Strain localization phenomena were simulated with a typical double-notched specimen under tensions. Numerical results indicate the validity of the proposed theory.     

A self-consistent analysis for coupled elastoplastic damage problems

Based on irreversible thermodynamics and internal state variable theory, the volume-averaged Clausius-Duhem inequality is presented. In contrast to former investigations on damage-elastoplasticity, our evalustions are founded on the volume-averaged field equations of the analyzed elements and the self-consistent method. Hence, our results not only include the influence of void shapes but also consider the interaction among voids. Further, previous work about coupled elastoplastic damage problems only takes into account small initial void volume fractions. Our work, however, will be able to deal with elastoplastic damage problems with larger initial void volume fractions. Project supported by the National Natural Science Foundation of China (19762002) and Natural Science Foundation of Jiangxi in China     

气泡在液体中运动过程的数值模拟

本文用数值方法预测气泡在液体中的百定常运动。运用位标函数进行界面的隐含跟踪并且与有限体积法相结合构成一种可行的计算方法。本文方法允许在界面处存在很大的物性差，而且较容易将表面张力引入控制方程。我们对气液两相流中单个气泡的运动进行了计算，得到了与实验结果符合很好的数值结果。     

A block particle coupled model and its application to landslides

To simulate the progressive failure of slope, a block particle coupled model is introduced. Particle oriented cell mapping(POCM) algorithm is used to enhance the search efficiency, and particlepoint, particle-edge, particle-face contact detecting method is adopted to establish contact pair between particles and blocks precisely. Strain softening Mohr Coulomb model with tensile cutoff is adopted for blocks, and brittle Mohr Coulomb model is used for particles. The particle-block replacement approach is used to describe the fracture and fragmentation process of continuum media. Once the cohesion or tensile strength of one block reaches zero, the block will be deleted,and particles are generated at the same place with all information inherited from the deleted block. Some numerical cases related to landslides demonstrate the precision and rationality of the coupled model.     

An isotropic unilateral damage model coupled with frictional sliding for quasi-brittle materials

In this paper, we present an original extension of an isotropic damage model for quasi-brittle materials and assess its predictive capabilities. The proposed model accounts not only for unilateral behavior related to the opening and closure of microcracks but also for inelastic strains reflecting the frictional sliding along closed microcracks. More importantly, owing to its careful mathematical formulation with a particular attention paid to the continuous differentiability of the underlined thermodynamic potential, the model ensures the continuity of the inelastic stress–strain response. First applications show that it is able to predict the asymmetric behavior and hysteretic response of microcracked materials such as concrete and some rocks     

基于微态方法的耦合韧性损伤的弹塑性本构模型

基于广义连续介质力学提出了一个热力学一致性的耦合微态韧性损伤的弹塑性本构模型。该模型遵循Forest的微态方法,在有限变形中提出引入额外的微态损伤因子及其一阶梯度以考虑材料的内部特征尺度。通过广义虚功原理得到了微态损伤的补充控制方程,对亥姆霍兹自由能进行扩展,得到了新的包含微态损伤变量的损伤能量释放率,在微态损伤的正则化作用下,采用隐式迭代更新局部损伤和应力等状态变量。基于Galerkin加权余量法,推导了以传统位移和微态损伤为基本未知量的有限元列式。利用该数值模型,对DP1000材料的单向拉伸实验和十字形零件的冲压实验进行了应变局部化与材料断裂的有限元分析。结果表明,该微态弹塑性损伤模型可以得到一致的有限元模拟响应曲线并收敛到实验曲线,从而避免发生网格依赖性问题。     

A simplified model of coupled relaxation oscillators

In this paper we analyze a simplified model of a pair of coupled relaxation oscillators. The simplified model employs a two-dimensional phase space with jump conditions to approximate the behavior in the full four-dimensional phase space. The stability of the phase-locked modes of oscillation for the simplified system is obtained using phase plane techniques and compared to that previously obtained for the full system using asymptotic and numerical methods. It is shown that these results differ qualitatively over a region of the parameter space, and Lyapunov's direct stability method is used to explain this shortcoming of the model.     

A nonlocal model with strain-based damage

A thermodynamically consistent formulation of nonlocal damage in the framework of the internal variable theories of inelastic behaviours of associative type is presented. The damage behaviour is defined in the strain space and the effective stress turns out to be additively splitted in the actual stress and in the nonlocal counterpart of the relaxation stress related to damage phenomena. An important advantage of models with strain-based loading functions and explicit damage evolution laws is that the stress corresponding to a given strain can be evaluated directly without any need for solving a nonlinear system of equations. A mixed nonlocal variational formulation in the complete set of state variables is presented and is specialized to a mixed two-field variational formulation. Hence a finite element procedure for the analysis of the elastic model with nonlocal damage is established on the basis of the proposed two-field variational formulation. Two examples concerning a one-dimensional bar in simple tension and a two-dimensional notched plate are addressed. No mesh dependence or boundary effects are apparent.     

含损伤演化的TM耦合数值模型及其应用研究

从岩石材料的细观结构层次出发，应用损伤力学和热弹性理论，对热力耦合作用下岩石破裂 过程中热－应力相互作用关系进行了分析. 初步建立了细观岩石热－力(TM)耦合数值模型， 探讨了TM耦合作用下岩石材料的细观结构损伤及其诱发的材料力学性能演化机制，把岩石 热固耦合问题的研究从应力状态分析深入到损伤、破坏过程分析之中. 运用该数值模型对某 硬岩实验室开展的原位尺度实验中的废料处理井间柱稳定性进行了模拟分析，其应力场、岩 石剥离破坏形态及破坏诱发的AE特性等均与实验监测结果表现出了较好的一致性，证 明了该数值模型的合理性和有效性.     

A model of imperfect interface with damage

In this paper two models of damaged materials are presented. The first one describes a structure composed by two adherents and an adhesive which is micro-cracked and subject to two different regimes, one in traction and one in compression. The second model is a model of interface derived from the first one through an asymptotic analysis, and it can be interpreted as a model for contact with adhesion and unilateral constraint. Simple numerical examples are presented.     

A model to predict the coupled axial torsion properties of ACSR electrical conductors

The modeling of ACSR (aluminum-conductor steel-reinforced) electrical conductors for dynamic analysis requires some knowledge of the mechanical properties of the conductor. It was found both experimentally and theoretically, using a simple strength of materials approach, that the axial-torsional behavior of ACSR conductors is highly coupled; i.e., axial motion causes torsional motion and vice versa. Although wind-induced oscillation of ACSR power lines has been observed for years, the importance of axial-torsional coupling has not been generally recognized, nor studied. A simplified mathematical model correlated well with experimental measurements for this type of coupled mechanical behavior. It is hoped that being able to control the amount of coupling through cable design may lead to better control of wind-induced oscillations.     

A coupled micro-mechanical based model for saturated soils

It is generally accepted that the apparent behavior of geo-materials is the representation of the average micro-mechanical behavior of its constituents. Constitutive models that do not incorporate these micro-mechanical features in calibrating the material parameters cannot address various material localization features in large strain problems such as shear bands and slope failures, etc. In the absence of such micro-mechanical features the calibration of such models may be incorrect.A rigorous formulation that incorporates these micro-mechanical based mechanisms into the general behavior of the saturated soils is presented here. The plastic rotation of particles, the interaction of particles, the rate dependency, the damage, and the coupling of particles with pore fluid pressure are incorporated through the plastic spin, the gradient theory, the visco-plasticity, the damage theory, and the coupled theory of mixtures, respectively. The link between the micro-mechanical mechanisms and the macro-mechanical behavior is made through the use of RVE (representative volume element). As a result, a full formulation for the micro-mechanics implemented continuum plasticity for saturated soils is presented here.     

A coupled Timoshenko model for smart slender structures

In this paper, a generalized Timoshenko model has been developed for prismatic, beam-like slender structures with embedded or surface mounted piezoelectric type smart materials. Starting from a geometrically exact formulation of the original, three-dimensional electromechanical problem, we apply the variational asymptotic method to carry out a systematic dimensional reduction. In the process, the three-dimensional electromechanical enthalpy functional is approximated asymptotically using the slenderness as the small parameter to find out an equivalent one-dimensional electromechanical enthalpy functional. For Timoshenko-like refinement over the Euler–Bernoulli beam model, terms up to the second order of the slenderness are kept in the enthalpy expression. As an unified analysis tool, the present model can analyze embedded or surface mounted active layer with arbitrary cross-sectional geometry as two cases of a general one, no special assumptions or modifications need to be made for these two separate types of active inclusions.