Law of damage accumulation and fracture criteria in highly filled polymer materials

We present the results of a large series of experiments aimed at the study of laws of damage accumulation and fracture in highly filled polymer materials under loading conditions of various types: monotone, repeated, low- and high-cycle, with varying type of stress state, dynamic (in general, more than 50 programs implemented on specimens from one lot of material). The data obtained in these test allow one to make conclusions about the constitutive role of the attained maximum of strain intensity when estimating the accumulated damage in the process of uniaxial tension by various programs (in particular, an additional cyclic deformation below the preliminary attained strain maximum does not affect the limit values of strain and stress in the subsequent active extension), about the strong influence of the stress state on the deformation and fracture, about the specific features of the nonlinear behavior of the material under the shock loading conditions and its influence on the repeated deformation. All tests are described (with an accuracy acceptable in practical calculations, both with respect to stresses and strains in the process of loading and at the moment of fracture) in the framework of the same model of nonlinear viscoelasticity with the same set of constants. The constants of the proposed model are calculated according to a relatively simple algorithm by using the results of standard uniaxial tension tests with constant values of the strain rate and hydrostatic pressure (each test for 2–3 levels of these parameters chosen from the ranges proposed in applications, each loading lasts until the fracture occurs, and one of the tests contains an intermediate interval of total loading and repeated loading) and one axial shock compression test if there are dynamic problems in the applications. The model is based on the use of the criterion fracture parameter which, in the class of proportional loading processes, is the sum of partial increments of the strain intensity on active segments of the process (where the strain intensity is at its historical maximum) with the form of the stress state and the intensity of strain rates taken into account.     

Simulation of damage evolution in ductile metals undergoing dynamic loading conditions

A set of constitutive equations for large rate-dependent elastic-plastic-damage materials at elevated temperatures is presented to be able to analyze adiabatic high strain rate deformation processes for a wide range of stress triaxialities. The model is based on the concepts of continuum damage mechanics. Since the material macroscopic thermo-mechanical response under large strain and high strain rate deformation loading is governed by different physical mechanisms, a multi-dissipative approach is proposed. It incorporates thermo-mechanical coupling effects as well as internal dissipative mechanisms through rate-dependent constitutive relations with a set of internal variables. In addition, the effect of stress triaxiality on the onset and evolution of plastic flow, damage and failure is discussed.Furthermore, the algorithm for numerical integration of the coupled constitutive rate equations is presented. It relies on operator split methodology resulting in an inelastic predictor-elastic corrector technique. The explicit finite element program LS-DYNA augmented by an user-defined material subroutine is used to approximate boundary-value problems under dynamic loading conditions. Numerical simulations of dynamic experiments with different specimens are performed and good correlation of numerical results and published experimental data is achieved. Based on numerical studies modified specimens geometries are proposed to be able to detect complex damage and failure mechanisms in Hopkinson-Bar experiments.     

复杂加载下混凝土的弹塑性本构模型

混凝土材料在不同应力路径下或复杂加载条件下会表现出差异性显著的应力应变关系,在小幅循环加载条件下,其应力应变关系会表现出类似于弹性变形的滞回曲线.在不同应力水平下,混凝土的应力应变关系以及破坏特性都具有静水压力相关特点,即随着静水压力增大,各向异性强度特性弱化.此外,混凝土受压及受拉破坏机理不同,因而对应于混凝土硬化损伤亦有不同,即可分为受压硬化损伤,受拉硬化损伤及两者的混合硬化损伤类型.基于Hsieh模型,对该模型进行了三点改进.（1）针对小幅循环加载下混凝土无塑性变形的试验规律,而模型中在应力水平较低的循环加载条件下始终存在塑性变形的预测问题,采用在边界面模型框架下,设置了应力空间的弹性域,初始屈服面与后续临界状态屈服面几何相似的假定.（2）基于广义非线性强度准则将原模型采用变换应力方法将其推广为三维弹塑性本构模型,采用变换后模型可合理的考虑不同应力路径对于子午面以及偏平面上静水压力效应形成的影响,并避免了边界面应力点奇异问题.（3）分别对拉压两种加载损伤模式建议了相应的硬化参数表达式,可分别用于描述上述加载中产生的应变软化及强度退化行为.基于多种加载路径模拟表明:所建立的三维弹塑性本构模型可合理地用于描述混凝土的一般应力应变关系特性.      

闭孔泡沫铝的多轴唯象受压本构参数

基于显微计算机断层扫描影像信息, 逆向重建闭孔泡沫铝试件的三维细观有限元模型, 定量研究闭孔泡沫铝在多轴压缩载荷作用下的大变形力学行为. 讨论了泡沫金属唯象弹塑性本构参数的确定方法, 根据计算结果确定了3 个有代表性的泡沫材料本构模型的本构参数, 并验证了这些本构模型在描述多轴压缩应力状态下的精度. 研究表明, 对于单轴压缩, 3 个本构模型的屈服面均有很好的精度;对于静水压缩, 有限元软件"ABAQUS"的可压缩泡沫本构模型屈服面会发生严重偏离, 陈-卢本构模型"屈服面" 略微低估静水压缩的屈服应力, 而体积强化本构模型的屈服面有很好的精度.      

A viscoplastic model combined smedamage and smeared crack for softening of concrete

A viscoplastic model accounting for developing damage in concrete is proposed by assuming the rate of damage to be dependent on viscous strain and stress rates. The damage is measured by a scalar parameter affecting both the yield stress and the material viscosity. For a post-critical range of deformation, the localized mode occurs for which additional constitutive equations are specified. The model is applied to simulate uniaxial strain rate controlled and creep response for the concrete.     

Void coalescence within periodic clusters of particles

The effect of particle clustering on void damage rates in a ductile material under triaxial loading conditions is examined using three-dimensional finite element analysis. An infinite material containing a regular distribution of clustered particles is modelled using a unit cell approach. Three discrete particles are introduced into each unit cell while a secondary population of small particles within the surrounding matrix is represented using the Gurson-Tvergaard-Needleman (GTN) constitutive equations. Deformation strain states characteristic of sheet metal forming are considered; that is, deep drawing, plane strain and biaxial stretching. Uniaxial tensile stress states with varying levels of superimposed hydrostatic tension are also examined.The orientation of a particle cluster with respect to the direction of major principal loading is shown to significantly influence failure strains. Coalescence of voids within a first-order particle cluster (consisting of three particles) is a stable event while collapse of inter-cluster ligaments leads to imminent material collapse through void-sheeting.     

一个综合模糊裂纹和损伤的混凝土应变软化本构模型

本文研究就变软化材料的本构关系，提出了一个考虑损伤的粘塑性模型，损伤不仅影响材料的临界应力，而且影响材料的粘塑性，为模拟材料的应变软化行为，假设受损混凝土的破坏局部区域由模糊裂纹和损伤所统治，软化模量和局部区域尺度参量依赖于模糊裂纹扩展时释放的断裂能的参变量，用文中提出的模型计算了混凝土单轴压缩时不同应变速率下的瞬时应力应变响应以及等应力长期作用下的徐变，均得到很的结果。     

Micromechanics based second gradient continuum theory for shear band modeling in cohesive granular materials following damage elasticity

Gradient theories, as a regularized continuum mechanics approach, have found wide applications for modeling strain localization failure process. This paper presents a second gradient stress–strain damage elasticity theory based upon the method of virtual power. The theory considers the strain gradient and its conjugated double stresses. Instead of introducing an intrinsic material length scale into the constitutive law in an ad hoc fashion, a microstructural granular mechanics approach is applied to derive the higher-order constitutive coefficients such that the internal length scale parameter reflects the natural granularity of the underlying material microstructure. The derivations of the required damage constitutive relationships, the strong form governing equations as well as its weak form for the second gradient model are described. The recently popularized Element-Free Galerkin (EFG) method is then employed to discretize the weak form equilibrium equation for accommodating the resultant higher-order continuity requirements and further handling the mesh sensitivity problem. Numerical examples for shear band simulations show that the proposed second gradient continuum model can produce stable, accurate as well as mesh-size independent solutions without a priori assumption of the shear band path.     

An interacting micro-crack damage model for failure of brittle materials under compression

A model is developed for brittle failure under compressive loading with an explicit accounting of micro-crack interactions. The model incorporates a pre-existing flaw distribution in the material. The macroscopic inelastic deformation is assumed to be due to the nucleation and growth of tensile “wing” micro-cracks associated with frictional sliding on these flaws. Interactions among the cracks are modeled by means of a crack-matrix-effective-medium approach in which each crack experiences a stress field different from that acting on isolated cracks. This yields an effective stress intensity factor at the crack tips which is utilized in the formulation of the crack growth dynamics. Load-induced damage in the material is defined in terms of a scalar crack density parameter, the evolution of which is a function of the existing flaw distribution and the crack growth dynamics. This methodology is applied for the case of uniaxial compression under constant strain rate loading. The model provides a natural prediction of a peak stress (defined as the compressive strength of the material) and also of a transition strain rate, beyond which the compressive strength increases dramatically with the imposed strain rate. The influences of the crack growth dynamics, the initial flaw distribution, and the imposed strain rate on the constitutive response and the damage evolution are studied. It is shown that different characteristics of the flaw distribution are dominant at different imposed strain rates: at low rates the spread of the distribution is critical, while at high strain rates the total flaw density is critical.     

准脆性材料的弹塑性各向异性损伤耦合本构模型研究

针对准脆性材料的非线性特征：强度软化和刚度退化、单边效应、侧限强化和拉压软化、不可恢复变形、剪胀及非弹性体胀,在热动力学框架内,建立了准脆性材料的弹塑性与各向异性损伤耦合的本构关系。对准脆性材料的变形机理和损伤诱发的各向异性进行了诠释,并给出了损伤构形和有效构形中各物理量之间的关系。在有效应力空间内,建立了塑性屈服准则、拉压不同的塑性随动强化法则和各向同性强化法则。在损伤构形中,采用应变能释放率,建立了拉压损伤准则、拉压不同的损伤随动强化法则和各向同性强化法则。基于塑性屈服准则和损伤准则,构建了塑性势泛函和损伤势泛函,并由正交性法则,给出了塑性和损伤强化效应内变量的演化规律,同时,联立塑性屈服面和损伤加载面,给出了塑性流动和损伤演化内变量的演化法则。将损伤力学和塑性力学结合起来,建立了应变驱动的应力-应变增量本构关系,给出了本构数值积分的要点。以单轴加载-卸载往复试验识别和校准了本构材料常数,并对单轴单调试验、单轴加载-卸载往复试验、二轴受压、二轴拉压试验和三轴受压试验进行了预测,并与试验结果作了比较,结果表明,所建本构模型对准脆性材料的非线性材料性能有良好的预测能力。     

Modeling of fatigue life of materials and structures under low-cycle loading

A damaged medium model (DMM) consisting of three interconnected components (relations determining the cyclic elastoplastic behavior of the material, kinetic damage accumulation equations, and the strength criterion for the damaged material) was developed to estimate the stress strain state and the fatigue life of important engineering objects. The fatigue life of a strip with a cut under cyclic loading was estimated to obtain qualitative and quantitative estimates of the DMM constitutive relations under low-cycle loading. It was shown that the considered version of the constitutive relations reliably describes the main effects of elastoplastic deformation and the fatigue life processes of materials and structures.     

基于石膏材料的小结构重力坝损伤本构模型研究

大坝模型试验的模型材料力学性能是试验成功与否的关键影响因素。基于石膏模型材料基本力学性质和混凝土材料基本相似的实际情况,考虑石膏模型材料的孔隙率,在能量损伤理论模型的基础上,结合工程规范,建立了石膏模型材料的受拉损伤本构模型。同时,分析了模型材料应变率对材料峰值应力的影响,引入动应力提高系数,并给出了与应变率相关的模型材料受拉损伤本构模型。利用该本构模型模拟了动荷载下石膏模型重力坝的破坏过程,并与模型试验结果进行对比。结果表明：数值模拟得到的重力坝开裂破坏的位置、形式与模型试验结果较为接近。     

基于OTTOSEN准则的混凝土粘塑性力学模型

研究了混凝土的弹．粘塑性动态本构关系,提出一个应变率相关的非线性混凝土模型．模型改进Bicanic的混凝土塑性间断面变化规律和Ottosen的四参数屈服准则,建立冲击荷载下的混凝土本构方程,可以应用于地震和爆炸作用下混凝土材料响应的研究．根据混凝土动态实验结果对应变率和材料强度的关系提出合理假设,考虑以往被忽略的材料峰值应变和泊松比随应变率的变化．模型包含静水压力参数和动态塑性损伤因子,可以有效地反映混凝土的动态力学行为,为其动态问题的研究提供有益的思路和有效的工具．     

Damage model for metal–matrix composite under high intensity loading

A damage model for a composite structure under high intensity dynamic loading is presented. The model is based on a thermodynamic micromechanic approach, which is formulated using the conservation laws and the energy balance equations (the first and second laws of thermodynamics). A homogenization or averaging technique is implemented in the development to simplify the representation of the non-homogeneous material. The metal–matrix composite's inelastic response is modeled using elastic–plastic constitutive relations considering finite plastic strain and damage effect. The damage model is validated with experimental data available in the literatures, and it shows fairly good agreement. A parametric study demonstrating the characteristics of the damage model is also presented.     

Load-induced oriented damage and anisotropy of rock-like materials

Theoretical model for deformability of brittle rock-like materials in the presence of an oriented damage of their internal structure is formulated and verified experimentally. This model is based on the assumption that non-linearity of the stress–strain curves of these materials is a result of irreversible process of oriented damage growth. It was also assumed that a material response, represented by the strain tensor, is a function of two tensorial variables: the stress tensor and the damage effect tensor that is responsible for the current state of the internal structure of the material. The explicit form of the respective non-linear stress–strain relations that account for the appropriate damage evolution equation was obtained by employing the theory of tensor function representations and by using the results of own experiments on damage growth. Such an oriented damage that grows in the material, described by the second order symmetric damage effect tensor, results in gradual development of the material anisotropy. The validity of the constitutive equations proposed was verified by using the available experimental results for concrete subjected to the plane state of stress. The relevant experimental data for sandstone and concrete subjected to tri-axial state of stress were also used.     

Magnetic field-induced martensitic phase transformation in magnetic shape memory alloys: Modeling and experiments

In this work, a continuum based model of the magnetic field induced phase transformation (FIPT) for magnetic shape memory alloys (MSMA) is developed. Hysteretic material behaviors are considered through the introduction of internal state variables. A Gibbs free energy is proposed using group invariant theory and the coupled constitutive equations are derived in a thermodynamically consistent way. An experimental procedure of FIPT in NiMnCoIn MSMA single crystals, which can operate under high blocking stress, is described. The model is then reduced to a 1-D form and the material parameter identification from the experimental results is discussed. Model predictions of magneto-thermo-mechanical loading conditions are presented and compared to experiments.     

A 3D mechanistic model for brittle materials containing evolving flaw distributions under dynamic multiaxial loading

We present a validated fully 3D mechanism-based micromechanical constitutive model for brittle solids under dynamic multiaxial loading conditions. Flaw statistics are explicitly incorporated through a defect density, and evolving flaw distributions in both orientation and size. Interactions among cracks are modeled by means of a crack-matrix-effective-medium approach. A tensorial damage parameter is defined based upon the crack length and orientation development under local effective stress fields. At low confining stresses, the wing-cracking mechanism dominates, leading to the degradation of the modulus and peak strength of the material, whereas at high enough confining stresses, the cracking mechanism is completely shut-down and dislocation mechanisms become dominant. The model handles general multiaxial stress states, accounts for evolving internal variables in the form of evolving flaw size and orientation distributions, includes evolving anisotropic damage and irreversible damage strains in a thermodynamically consistent fashion, incorporates rate-dependence through the micromechanics, and includes dynamic bulking based on independent experimental data. Simulation results are discussed and compared with experimental results on one specific structural ceramic, aluminum nitride. We demonstrate that this 3D constitutive model is capable of capturing the general constitutive response of structural ceramics.     

Complex loading of heterogeneous materials with redistribution of internal mass

The problem of inhomogeneous material with internal friction subjected to complex loading is solved in this paper. Different complex loadings are considered by continuously rotating the principal axes of the strain tensor. A hypoplastic model with internal variables is used to describe the internal structure of the material. The model can describe loading and unloading states. It accounts for essential non-linearity of constitutive equations. The finite element algorithm reduces the problem to a system of nonlinear algebraic equations of high order which are solved by the Newton's method. The results show a good qualitative and quantitative assessment of calculated parameters when compared with data obtained from experiments. Redistribution of internal mass takes place under loading such that a fractal structure is developed in time reflecting the material discontinuities.