Combination of fracture and damage mechanics for numerical failure analysis

A new approach for the analysis of crack propagation in brittle materials is proposed, which is based on a combination of fracture mechanics and continuum damage mechanics within the context of the finite element method. The approach combines the accuracy of singular crack-tip elements from fracture mechanics theories with the flexibility of crack representation by softening zones in damage mechanics formulations. A super element is constructed in which the typical elements are joined together. The crack propagation is decided on either of two fracture criteria; one criterion is based on the energy release rate or the J-integral, the other on the largest principal stress in the crack-tip region. Contrary to many damage mechanics methods, the combined fracture⧹damage approach is not sensitive to variations in the finite element division. Applications to situations of mixed-mode crack propagation in both two- and three-dimensional problems reveal that the calculated crack paths are independent of the element size and the element orientation and are accurate within one element from the theoretical (curvilinear) crack paths.     

A computational model of viscoplasticity and ductile damage for impact and penetration

A coupled constitutive model of viscoplasticity and ductile damage for penetration and impact related problems has been formulated and implemented in the explicit finite element code LS-DYNA. The model, which is based on the constitutive model and fracture strain model of Johnson and Cook, and on continuum damage mechanics as proposed by Lemaitre, includes linear thermoelasticity, the von Mises yield criterion, the associated flow rule, non-linear isotropic strain hardening, strain-rate hardening, temperature softening due to adiabatic heating, isotropic ductile damage and failure. For each of the physical phenomena included in the model, one or several material constants are required. However, all material constants can be identified from relatively simple uniaxial tensile tests without the use of numerical simulations. In this paper the constitutive model is described in detail. Then material tests for Weldox 460 E steel and the calibration procedure are presented and discussed. The calibrated model is finally verified and validated through numerical simulations of material and plate perforation tests investigated experimentally.     

一个新的普遍形式的局部损伤断裂准则

利用损伤函数概念，建立了一个普遍形式的局部断裂准则。该准则考虑了局掊应力，应变和损伤历史对断裂的影响，根据损伤力学理选取了一个新的连续损伤函数，从而导出一个新的连续损伤断裂准则。新的临界断裂参数ＷＤＣ，具有明显的物理意义，且易通过试验测得，是一个不依赖于应力状态的材料九。文中还从细观力学理论和有关的试验资料出发，选取了相应的损伤函数，再现了前人的细观力学准则和经验准则。     

Constitutive modeling of discontinuities by means of discrete and continuum approximations and damage models

In this paper the mathematical modeling of discontinuities using the discrete approximation and the continuum approximation with weak discontinuities is presented. First, the kinematics of discontinuities is discussed, then two constitutive models based on the continuum damage mechanics theory are developed. The first model is an isotropic damage model and is used in the discrete approximation. The second model is an anisotropic damage model and is used in the continuum approximation. These models are characterized for weighing the mode of failure in the failure criterion. An energy analysis is proposed to establish the equations that relate the parameters of both constitutive models; the fulfillment of the involved equations guarantee that both models are energetically equivalent. It is concluded that the proposed models are suitable to reproduce the constitutive behavior of discontinuities.     

纤维增强复合材料风机叶片宏细观一体化有限元分析An unified FEM for macroscopic and mesoscopic analysis of fiber reinforced composite fan blades

为了建立纤维增强复合材料风机叶片宏观性能和细观组分的直接关联,得到一般有限元分析时无法获得的细观参量值,利用FORTRAN程序把细观力学的失效／损伤分析模块,嵌入到有限元软件ABAQUS中的USD‐FLD 用户子程序中,建立了风机叶片宏细观一体化模型。该模型能够实现基于细观组分级损伤／失效判据的宏细观渐进损伤分析和强度预报功能。该模型计算结果与文献中的试验结果有较好的一致性。     

Three-dimensional analysis of reinforced concrete frames based on lumped damage mechanics

This paper presents a general formulation for the analysis of reinforced concrete frames. The model has been developed within the framework of lumped damage mechanics. This is a theory based on the methods of continuum damage mechanics, fracture mechanics and the concept of plastic hinge. The paper also describes the numerical implementation of the model in the finite element programs. The model is evaluated by the numerical simulation of three tests reported in the literature. Two of them deal with a column subjected to variable axial loads and biaxial flexure. The third is a two-story three-dimensional frame subjected to earthquake loadings outside the principal directions of the frame.     

基于近场动力学的梁结构振动特性分析方法研究

基于欧拉梁理论推导了两自由度梁的常规态型近场动力学（Peridynamics,PD）模型,并提出一种新的自由边界条件施加方法,对不同边界条件的PD梁进行了模态分析,与局部梁的有限元结果进行了对比,验证了模型的收敛性,分析了PD非局部参数对固有频率的影响。结果表明,当近场作用域内物质点密度较小时,PD梁模型非局部性较弱,与局部梁的有限元结果接近,随着物质点密度逐渐增大,非局部作用增强,PD梁的固有频率逐渐降低;当尺度参数趋于零时,PD梁的固有频率收敛到局部梁的有限元解,PD梁退化为局部梁。研究表明,本文提出的PD梁模型和自由边界施加方法适用于分析梁的振动特性,为采用PD方法分析梁结构的动力特性提供了参考。     

Anisotropic damage–plasticity model for concrete

A material model for concrete is proposed here within the framework of a thermodynamically consistent elasto-plasticity–damage theory. Two anisotropic damage tensors and two damage criteria are adopted to describe the distinctive degradation of the mechanical properties of concrete under tensile and compressive loadings. The total stress tensor is decomposed into tensile and compressive components in order to accommodate the need for the above mentioned damage tensors. The plasticity yield criterion presented in this work accounts for the spectral decomposition of the stress tensor and allows multiple hardening rules to be used. This plastic yield criterion is used simultaneously with the damage criteria to simulate the physical behavior of concrete. Non-associative flow rule for the plastic strains is used to account for the dilatancy of concrete as a frictional material. The thermodynamic Helmholtz free energy concept is used to consistently derive dissipation potentials for damage and plasticity and to allow evolution laws for different hardening parameters. The evolution of the two damage tensors is accounted for through the use of fracture-energy-based continuum damage mechanics. An expression is derived for the damage–elasto-plastic tangent operator. The theoretical framework of the model is described here while the implementation of this model will be discussed in a subsequent paper.     

各向异性损伤力学中的弹塑性分析

提出了一套分析损伤力学问题的各向异性弹塑性理论公式及其相应的有限元分析,通过对各向同性及各向异性损伤力学的数值算例的分析说明该理论公式的适用性。     

弹体贯穿钢筋混凝土数值模拟

详细描述了依据损伤原理建立的连续损伤模型,并对该模型进行了改进。在LS DYNA程序用户自定义材料模型中加入改进的连续损伤模型,并对弹体侵彻钢筋混凝土的穿孔过程进行了数值模拟,其结果与实验结果相吻合,模型可以用于钢筋混凝土的动态破坏预报。     

Elasto-plastic postbuckling of damaged orthotropic plates

Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion related to spherical tensor of stress is proposed to describe the mixed hardening of damaged orthotropic materials. Its dimensionless form is isomorphic with the Mises criterion for isotropic materials. Furthermore, the incremental elasto-plastic damage constitutive equations and damage evolution equations are established. Based on the classical nonlinear plate theory, the incremental nonlinear equilibrium equations of orthotropic thin plates considering damage effect are obtained, and solved with the finite difference and iteration methods. In the numerical examples, the effects of damage evolution and initial deflection on the elasto-plastic postbuckling of orthotropic plates are discussed in detail.     

An optimization of a multi-layered plate under ballistic impact

This paper may be the first trial regarding the optimal design of a multi-layered plate under ballistic impact. An optimal design of a multi-layered plate to endure ballistic impact is suggested by using size optimization based on numerical simulations. The NET2D, a Lagrangian explicit time-integration finite element code for impact analyses, is used to find the optimal parameter values. Three different materials such as mild steel and aluminum for a multi-layered plate structure and die steel for the pellet are assumed. In order to consider the effects of strain rate hardening, strain hardening and thermal softening, the Johnson–Cook model is used as the constitutive models for the simulation. Several mesh types of different size and aspect ratio are tried to check the effect of mesh on the solution and to obtain the appropriate mesh density. The measuring domain is selected to reduce the analyzing time without affecting the sensitivity.The response surface method based on the design of experiments is used to obtain the optimal design. The average temperature or the equivalent plastic strain is introduced as a response for the optimization of the impact problem. Furthermore, the perforation criteria with the equivalent plastic strain to determine whether the plate structure is perforated or not is suggested. The optimized thickness of each layer in which perforation does not occur and the strength of multi-layer is maximized is obtained at a constant velocity of a pellet with a designated total thickness.     

损伤统计演化方程的性质和数值模拟

通过对一种含成核尺寸效应的损伤统计演化方程性质的分析和数值模拟,揭示了损伤率主要是由微损伤在二维相空间中的前沿的运动所决定的这也就是Kachanov提出的损伤率演化方程的物理基础数值结果进一步显示了含成核尺寸效应模型在损伤发展上与-维模型的区别而且,由几种形式的细观动力学算出的损伤率与损伤的关系简单,可近似拟合为宏观上封闭的形式     

冲击波-破片群联合作用下舰船复合材料结构近场动力学损伤模拟

采用一种新兴的无网格法——近场动力学理论,模拟复合材料结构在冲击波-破片群联合作用下的损伤情况。根据复合材料结构承受的载荷特性,分析冲击波-破片群联合作用下层合板及加筋板结构的损伤模式,考虑载荷作用次序等因素对于联合作用毁伤能力的影响规律。结果表明:联合作用对复合材料结构的损伤程度主要与冲击波强度、破片群侵彻能力、作用次序有关,主要损伤模式为分层失效、基体损伤、剪切损伤以及结构大变形;对于层合板而言,在冲击波先作用的工况下,结构损伤程度更高,损伤范围更大;对于加筋板而言,由于加筋板的筋条能显著降低冲击波作用,进而降低冲击波对破片群侵彻能力的增强效应,最终影响联合作用的毁伤能力,因而在破片群先作用的工况下反而损伤更严重。     

基于应变梯度有限元的单层石墨烯振动研究

建立了单层石墨烯等效非局部薄板的一种新的有限元模型,并运用有限元法分析不同边界条件下单层石墨烯振动的小尺度效应。给出了基于弹性应变梯度理论下Kirchhoff板的振动方程。发展了一种4节点24自由度的板单元,用于离散化求解考虑微纳结构尺度效应的高阶微分方程。在研究四边简支板振动时,考虑应变梯度的非局部弹性有限元数值计算结果与理论分析结果相一致。用有限元方法研究了不同尺寸、振动波长、振动模态阶数、边界条件类型以及非局部参数的单层石墨烯振动。     

纤维增强陶瓷基复合材料的D失效判据

经典唯象强度理论适用于正交各向异性线弹性体。对于非线性纤维增强复合材料,通过加卸载试验和损伤力学的分析方法,可以得到一种虚拟的线性化应力-应变关系;依据损伤等效假设,针对线性损伤和非线性损伤,对基于应力的经典二次失效准则进行变换,建立了一种基于损伤的强度理论,即“D失效判据”,这一强度理论可以作为经典判据的补充和扩展。针对平纹编织C/SiC复合材料的拉/剪组合试验,进行了实例计算,结果表明：利用D失效判据预测的失效包络线比蔡-希尔准则的预测曲线低,而且,失效曲线的形式与材料的损伤演化规律相关。     

A model of fracture in reinforced concrete arches based on lumped damage mechanics

A simplified model of cracking and damage in RC circular elements is proposed. The model can be used for the structural assessment of arches and rings. The constitutive equations are based on lumped damage mechanics which is an adaptation of fracture and continuum damage mechanics to the theory of frames with plastic hinges. An arch element is assumed to be the assemblage of an elastic circular component and two inelastic hinges where the main inelastic effects, plastic yielding of the longitudinal reinforcement and concrete cracking, are concentrated. Deformations in the elastic part are assumed to be small but the model may include some geometrically nonlinear effects due to large displacements or rotations of the hinges. The numerical examples presented in the paper show that the model describes correctly the global behavior of two structures including the softening phase.     

基于一类非局部宏-微观损伤模型的裂纹模拟

结合近场动力学和统一相场理论的基本思想, 最近提出了一类非局部宏-微观损伤模型, 为固体裂纹扩展模拟提供了新途径. 本文在此基础上改进了微观损伤准则, 并给出损伤的$\bar{\lambda}-\ell$语言以刻画固体破坏过程中位移场的不连续程度. 在改进模型中, 首先根据两物质点(即物质点对)之间的变形量, 基于相对临界伸长量的历史最大超越程度, 给出表征物质键性能退化的微细观损伤. 进而, 对影响域内的物质键损伤进行空间局部加权平均, 获得宏观拓扑损伤. 通过引入能量退化函数, 建立基于能量的损伤与宏观拓扑损伤之间的关系, 由此将其嵌入连续损伤力学基本框架, 形成了问题求解的基本方程. 该模型是一类非局部化模型, 可采用有限单元法进行离散求解, 避免了经典局部损伤力学所面临的网格敏感性问题. 文中, 进一步将其应用于具有强非线性回弹特性的裂纹扩展模拟问题. 实例分析表明, 本文方法不仅可以把握裂纹扩展模式, 而且能够定量刻画裂纹扩展过程中的载荷-变形关系. 最后指出了需要进一步研究的问题.      

桁架板等效刚度分析

桁架材料的连续介质等效模型的研究已有相当基础,而工程中桁架材料往往以类板结构形式出现,其变形表现出明显的弯曲特征。将类板桁架材料采用弯曲板模型模拟,研究合理的方法确定等效板模型的刚度具有重要意义。本文在基于Kirchhoff假定的小挠度薄板弹性理论框架下,研究了类板桁架材料的等效弯曲薄板模型,提出了确定薄板模型等效刚度的基于Dirichlet位移边界条件的代表体元法,给出了确定各刚度系数所对应的代表体元的边界位移形式。具体计算了几种典型形式桁架板的等效刚度,并采用有限元离散模型和实验技术分析了桁架板在一定的边界约束和荷载作用下的响应,并与等效板模型的分析结果进行了对比。结果表明,在响应分析中,具有等效刚度的薄板模型可准确模拟类板桁架材料;连续介质板等效刚度计算的积分法不能给出准确的桁架板等效刚度,而基于Dirichlet位移边界条件的代表体元法获得的等效板的刚度具有很高的精度。