脆性固体损伤和局部软化的有限元分析

本文研究混凝土、岩石一类工程中常用的应变软化材料的有限元分析方法。在作者以往有关粘塑性损伤本构模型的工作基础上，给出了一组便于有限元计算的本构方程表达式。包括损伤弹性矩阵和局部损伤软化矩阵，分别运用于计算硬化和软化阶段的有限元刚度矩阵；对所提出的本构方程的实验验证计算和一些算例的有限元数值分析，表明文中给出的本构方程是可行的，相应的有限元算法能较好地对损伤固体的局部软化效应进行数值分析，并可成功地追踪应力应变响应的软化曲线     

冲击载荷下混凝土材料的动态本构关系

利用改装的杆径为 74mm的直锥变截面式大尺寸Hopkinson压杆对混凝土材料进行冲击压缩实验 ,系统研究了混凝土的应变率硬化效应 ,采用一种新的方法损伤冻结法对混凝土材料在冲击载荷下的损伤软化效应进行了系统研究 ,给出了冲击载荷下混凝土的损伤演化方程 ;在对数据进行合理分析的基础上 ,结合粘弹性本构理论 ,得到混凝土材料的损伤型线性粘弹性本构关系。     

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。     

A cohesive plastic and damage zone model for dynamic crack growth in rate-dependent materials

Mode I steady-state dynamic crack growth in rate-dependent viscoplastic solids containing damage, under small scale yielding conditions, is analyzed based on a modified cohesive zone model. A multi-scale approach is used to describe the entire non-linear zone consisting of a plastic region and a damage region, each of which has its own constitutive law. Traction in the damage region is characterized by a softening power-law, in terms of the ultimate strength, a softening index and a rate sensitivity factor. In the plastic region, the cohesive law is assumed to be both strain hardening and rate dependent. The critical crack opening displacement at the physical crack-tip controls crack growth. The governing integral equations are derived and solved by a collocation method combined with associated boundary conditions. Numerical results are presented for the traction and opening profiles along the cohesive zone, the fracture energy and lengths of the damage and non-linear zones at different crack speeds and for different material parameters. The importance of factors, such as material softening, plastic deformation, crack speed and viscosity, is identified by parametric studies. In addition, the competition of plastic flow and material damage, and its effect on crack growth, are discussed.     

饱和和非饱和介质的弹塑性损伤模型

针对饱和和非饱和工程材料变形和强度特点,给出了一个具体的弹塑性损伤本构方程,该本构方程可以描述材料性质的劣化过程（即损伤和软化）以及饱和程度对材料变形强度特性的影响。此外,还讨论了该弹塑性损伤本构方程的有限元实施方法,编制了专用的有限元程序。对常规三轴试伯进行了有限元分析,得出了一些具体的结果。     

Kevlar纤维增强复合材料动态压缩力学性能实验研究

通过实验较系统地研究了Kevlar纤维增强复合材料的动态压缩力学性能,实验结果表明,在冲击压缩载荷作用下Kevlar纤维增强复合材料有明显的损伤软化现象和应变率效应,针对Kevlar纤维增强复合材料动态应力应变实验曲线,提出了含损伤的率相关动态本构方程,由于所引入的损伤最反映了Kevlar纤维增强复合材料内部基体开裂、脱层、纤维断裂等多种破坏模式的总体效果,因此所提出的本构方程形式相对说来比较简便并易于嵌入目前有关冲击力学的有限元或有限差分程序,有一定的工程应用价值。     

Prediction of the softening and damage effects with permanent set in fibrous biological materials

Deformation induced softening is an inelastic phenomenon frequently accompanying mechanical response of soft biological tissues. Inelastic phenomena which occur in mechanical testing of biological tissues are very likely to be associated with alterations in the internal structure of these materials.In this study, a novel structural constitutive model is formulated to describe the inelastic effects in soft biological tissues such as Mullins type behavior, damage and permanent set as a result of residual strains after unloading. Anisotropic softening is considered by evolution of internal variables governing the anisotropic properties of the material. We consider two weight factors w_i (softening) and s_k (discontinuous damage) as internal variables characterizing the structural state of the material. Numerical simulations of several soft tissues are used to demonstrate the performance of the model in reproducing the inelastic behavior of soft biological tissues.     

Analysis of the localization of deformation and the complete stress–strain relation for mesoscopic heterogeneous brittle rock under dynamic uniaxial tensile loading

Stress redistribution induced by excavation results in the tensile zone in parts of the surrounding rock mass. It is significant to analyze the localization of deformation and damage, and to study the complete stress–strain relation for mesoscopic heterogeneous rock under dynamic uniaxial tensile loading. On the basis of micromechanics, the complete stress–strain relation including linear elasticity, nonlinear hardening, rapid stress drop and strain softening is obtained. The behaviors of rapid stress drop and strain softening are due to localization of deformation and damage. The constitutive model, which analyze localization of deformation and damage, is distinct from the conventional model. Theoretical predictions have shown to consistent with the experimental results.     

A linked FEM-damage percolation model of aluminum alloy sheet forming

A so-called damage percolation model is linked with a finite element model of a sheet forming process to offer a comprehensive study of ductile damage evolution. In the current study, a damage percolation code is linked with LS-DYNA, an explicit dynamic FEM code used to introduce local strain gradients and compliance effects due to damage-induced softening. The linked model utilizes a Gurson-based yield surface to account for the softening effects of void damage, while the local damage development and void linkage events are modeled using the damage percolation code. The percolation code accepts detailed second phase particle fields from image analysis of a 2.0×1.6 mm optical micrograph of AA5182 aluminum alloy sheet. The model is applied to a stretch-flange stamping process which is known to be a damage-sensitive operation. The critical conditions for fracture are predicted for various initial stretch flange hole sizes.     

An invariant based damage model of stress-softening

A phenomenological model to predict the Mullins stress-softening effect in an isotropic, incompressible, hyperelastic rubber-like material is proposed which describes deformation induced microstructural damage and the same is characterised by a simple exponential softening function. The proposed isotropic damage function depends on the maximum previous value of the first invariant of the left Cauchy–Green deformation tensor. The proposed model of softening is illustrated with the theory of Gent material model and finally it is validated with experimental data provided in the literature. The model shows a simple functional form and brings out the interrelation between other models of this type.     

单轴压缩下2种PBX炸药的动态变形损伤及其温升效应

通过炸药单轴压缩实验,利用高速摄影和高速红外热像仪,对2种典型PBX炸药变形损伤过程和温升效应进行了实时观测。实验结果表明,2种典型PBX炸药的损伤以及温升效应表现出明显差别:低粘结剂含量的炸药表现出明显的脆性特征,材料应力应变曲线中的应变软化阶段是伴随着材料损伤的演化过程,最终的失稳破坏导致样品中贯穿裂纹的形成,非均匀的裂纹分布对应于局部高温带的出现; 高粘结剂含量的炸药表现出明显的韧性特征,材料应力应变曲线未出现应变软化现象,变形损伤分布较均匀,但剪切方向出现网络状的温升分布。     

冲击载荷下盐岩的力学性能和本构关系研究

利用直径75mm的大尺寸SHPB实验装置开展盐岩的动态压缩性能实验研究,得到了其动态应力应变曲线。分析表明,在冲击压缩载荷作用下,盐岩材料有明显的损伤软化现象和应变率效应。针对实验曲线,通过引入描述材料强度随应变率强化的应变率增强因子和随不可逆变形发展而弱化的损伤因子,提出了含损伤率的相关动态本构模型,拟合得到的本构方程形式比较简单,能够较好地反映盐岩动态实验加载过程的主要特征,具有一定的工程应用价值。     

Mullins effect and cyclic stress softening of filled elastomers by internal sliding and friction thermodynamics model

Elastomers are characterized by their ability to undergo large elastic deformation. Nevertheless, their behavior exhibits stress softening, hysteresis and cyclic softening. The first phenomenon, known as Mullins effect, is commonly assumed to be either the result of an evolution in the hard and soft domain microstructure whereby the effective volume fraction of the soft domain increases with stretch or the result of irreversible damage in the material or combination of both. Hysteresis and cyclic stress softening are often considered as the result of the effect of stress relaxation. Based on the physical structure of filled elastomers, the present study shows that the Mullins effect, hysteresis and cyclic softening can be modeled by dissipative friction phenomena due to internal sliding of the macromolecular chains and to sliding of the connecting chains on the reinforcing filler particles. This implies that the three effects are in fact related to one single deformation process. The proposed analysis allows to identify the state variables and to build a thermodynamic potential which accounts for the nonlinearity of the material behavior and for a time independent hysteresis. The constitutive model is 3D. Written in a rate form it applies to complex loadings: monotonic, cyclic, random fatigue, etc. Filled elastomers hysteresis loops and cyclic softening are represented with no need to introduce neither damage nor viscosity. The model was implemented in a Finite Element software to simulate a metal/elastomer lap joint. Good agreement with experiment was achieved.     

Analysis of the localization of damage and the complete stress-strain relation for mesoscopic heterogeneous brittle rock subjected to compressive loads

A micromechanics-based model is established. The model takes the interaction among sliding cracks into account, and it is able to quantify the effect of various parameters on the localization condition of damage and deformation for brittle rock subjected to compressive loads. The closed-form explicit expression for the complete stress-strain relation of rock containing microcracks subjected to compressive loads was obtained. It is showed that the complete stress-strain relation includes linear elasticity, nonlinear hardening, rapid stress drop and strain softening. The behavior of rapid stress drop and strain softening is due to localization of deformation and damage. Theoretical predictions have shown to be consistent with the exoerimental results.     

A symmetric nonlocal damage theory

The paper presents a thermodynamically consistent formulation for nonlocal damage models. Nonlocal models have been recognized as a theoretically clean and computationally efficient approach to overcome the shortcomings arising in continuum media with softening. The main features of the presented formulation are: (i) relations derived by the free energy potential fully complying with nonlocal thermodynamic principles; (ii) nonlocal integral operator which is self-adjoint at every point of the solid, including zones near to the solid’s boundary; (iii) capacity of regularizing the softening ill-posed continuum problem, restoring a meaningful nonlocal boundary value problem. In the present approach the nonlocal integral operator is applied consistently to the damage variable and to its thermodynamic conjugate force, i.e. nonlocality is restricted to internal variables only. The present model, when associative nonlocal damage flow rules are assumed, allows the derivation of the continuum tangent moduli tensor and the consistent tangent stiffness matrix which are symmetric. The formulation has been compared with other available nonlocal damage theories.Finally, the theory has been implemented in a finite element program and the numerical results obtained for 1-D and 2-D problems show its capability to reproduce in every circumstance a physical meaningful solution and fully mesh independent results.     

Damage precursor detection for structures subjected to rotational base vibration

This paper presents a nonlinear dynamic methodology for monitoring precursors of fatigue damage in metallic structures under variable rotational base excitation. The methodology accounts for important nonlinearities due to the complex loading generated by variable rotation and structural degradation. The sources of the nonlinearities include: structural stiffening due to gyroscopic motion and high-response amplitude at the fundamental mode, softening due to inertial forces and gyroscopic loads, and localized microscopic material damage and micro-plasticity. The loading intensity and number of vibration cycles increase the influence of these effects. The change in the dynamic response due to fatigue damage accumulation is experimentally investigated by exciting a cantilever beam at variable rotational base motions. The observed fatigue evolution in the material microstructure at regions of large stresses (and the resulting progressive structural softening) is tracked by quantifying the growth in the tip response, the change in the fundamental natural frequency of the beam and the skewedness of the stepped-sine response curve. Previous understanding of the structural dynamic behavior is necessary to ascertain the damage precursor location and evolution. Nanoindentation studies near the beam clamped boundary are conducted to confirm the gradual progression in the local mechanical properties as a function of loading cycles, and microstructural studies are conducted to obtain qualitative preliminary insights into the microstructure evolution. This study demonstrates that careful monitoring of the nonlinearities in the structural dynamic response can be a sensitive parameter for detection of damage precursors.     

Micro-cracks informed damage models for brittle solids

A class of micro-cracks informed damage models for describing the softening behavior of brittle solids is proposed, in which damage evolution is treated as a consequence of micro-crack propagation. The homogenized stress–strain relation in the cracked microscopic cell defines the degradation tensor, which can be obtained by the equivalence between the averaged strain energy of the microscopic cell and the strain energy density of the homogenized material. This energy equivalence relationship serves as an energy bridging vehicle between the damaged continuum and the cracked microstructure. Several damage evolution equations are obtained by this energy bridging method. The size effect of the micro-cracks informed damage law is characterized through the microscopic cell analysis, and the proper scaling of the characterized damage evolution functions to eliminate mesh dependency in the continuum solution is introduced.     

岩体—界面系统剪切不稳定性分析

基于界面的刚塑性应变软化假设，分析了岩体－界面系统在端部剪力和岩体中分布剪切载荷共同作用下的变形、应力和损伤演化。利用位能原理和稳定性的能量准则，得到了岩体界面系统的不稳定性条件。分析结果表明，损伤区达到边界之前，系统可能是稳定的或者是不稳定的。依赖于分布剪切载荷和界面摩擦力的比较，若均布剪切载荷大于界面摩擦力，则系统不稳定，否则系统稳定；当损伤区达到边界之后，系统的不稳定性决定于载荷及界面材料性质，界面软化刚度系数和界面强度对于不稳定性有明显影响。