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1.
It is well established that the use of inelastic constitutive equations accounting for induced softening, leads to pathological space (mesh) and time discretization dependency of the numerical solution of the associated Initial and Boundary Value Problem (IBVP). To avoid this drawback, many less or more approximate solutions have been proposed in the literature in order to regularize the IBVP and to obtain numerical solutions which are, at convergence, much less sensitive to the space and the time discretization. The basic idea behind these regularization techniques is the formulation of nonlocal constitutive equations by introducing some effects of characteristic lengths representing the materials microstructure. In this work, using the framework of generalized nonlocal continua, a thermodynamically-consistent micromorphic formulation using appropriate micromorphic state variables and their first gradients, is proposed in order to extend the classical local constitutive equations by incorporating appropriate characteristic internal lengths. The isotropic damage, the isotropic and the kinematic hardenings are supposed to carry the targeted micromorphic effects. First the theoretical aspects of this fully coupled micromorphic formulation is presented in details and the proposed generalized balance equations as well as the fully coupled micromorphic constitutive equations deduced. The associated numerical aspects in the framework of the classical Galerkin-based FE formulation are briefly discussed in the special case of micromorphic damage. Specifically, the formulation of 2D finite elements with additional degrees of freedom (d.o.f.), the dynamic explicit global resolution scheme as well as the local integration scheme, to compute the stress tensor and the state variables at each integration point of each element, are presented. Application is made to the typical uniaxial tension specimen under plane strain conditions in order to chow the predictive capabilities of the proposed micromorphic model, particularly against its ability to give (at convergence) a mesh independent solution even for high values of the ductile damage (i.e., the macroscopic cracks).  相似文献   

2.
杜成斌  黄文仓  江守燕 《力学学报》2022,54(4):1026-1039
混凝土是一种被广泛应用于土木和水利工程中的准脆性材料, 在各种内外部因素的作用下, 开裂是混凝土结构最为普遍的破坏形式, 准确模拟结构的开裂过程, 对于结构的安全评估至关重要. 将比例边界有限元与非局部宏微观损伤模型相结合提出一种准脆性材料开裂模拟新方法. 以比例边界有限元子域的比例中心作为物质点, 通过两比例中心(物质点对)之间的物质键的正伸长率来定义微细观损伤, 将某点影响域内物质键的微细观损伤加权平均得到该点的宏观拓扑损伤. 再引入能量退化函数, 将宏观拓扑损伤嵌入到比例边界有限元的基本框架中. 充分利用比例边界有限元网格允许存在悬挂节点的优势, 采用四叉树网格离散技术进行快速、高质量的多级网格划分与过渡. 通过一个I型开裂与一个混合型开裂的两个典型算例, 验证了该方法可捕获结构裂纹扩展路径与荷载变形曲线. 与现有的方法相比, 本文的损伤模型可得到更准确的局部开裂损伤带, 结果更为合理, 且具有更高的计算精度和计算效率. 当损伤过程区网格尺寸小于影响域半径的1/5时, 计算结果不存在网格敏感性问题.   相似文献   

3.
基于模态参数的结构损伤识别方法是振动损伤识别领域中应用最为广泛的方法。利用模态参数灵敏度构建结构损伤方程组,对其进行求解可以识别结构损伤位置和程度。由于实际工程中模态参数不完备性和噪声的影响,结构损伤方程易出现病态问题,直接求解可能产生错误的结果。为了解决这一问题,可以引入正则化方法进行求解。然而,各类正则化方法的基本原理、区别和联系及其在结构损伤识别中的应用没有系统的研究和对比。本文梳理了几类常用的正则化方法,对比分析其在基于模态参数灵敏度的损伤方程组求解中的适用性,讨论损伤程度、噪声水平和测点数目对几类方法识别结果的影响,为结构损伤识别中的正则化方法选择提供依据。通过连续梁和框架结构数值算例分析表明,在求解损伤方程的应用中,L1范数正则化方法鲁棒性较强,贝叶斯正则化方法次之,奇异值截断算法和L2范数正则化方法的鲁棒性较差;L1范数正则化方法能够产生更少的假阳性损伤单元,受噪声和测点数目影响较小,更适合损伤识别的应用。  相似文献   

4.
卢广达  陈建兵 《力学学报》2020,52(3):749-762
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.   相似文献   

5.
We present a damage model for softening materials with evolving nonlocal interactions. The thermodynamic implications and the material stability issue are addressed. The proposed nonlocal averaging scheme provides the obtained constitutive models with an evolving nonlocal interaction which is activated only when damage occurs. In the analysis of structures made of quasi-brittle materials, this feature helps not only to overcome some issues with the incorrect initiation of damage but also to better control the evolving size of the active fracture process zone. This is an essential feature that is usually not considered in depth in many existing nonlocal approaches to the continuum modelling of quasi-brittle fracture. Numerical examples are given to demonstrate features of the proposed modelling approach.  相似文献   

6.
In this paper, the problem of reconstructing numerical derivatives from noisy data is considered. A new framework of mollification methods based on the L generalized solution regularization methods is proposed. A specific algorithm for the first three derivatives is presented in the paper, in which a modification of TSVD, termed cTSVD is chosen as the regularization technique. Numerical examples given in the paper verify the theoretical results and show efficiency of the new method.  相似文献   

7.
本文对Oden等提出的非局部摩擦模型进行了修正,得到了修正后的非局部摩擦模型,并应用于岩土工程问题。文中利用Mindlin问题的位移解导出了岩体灌浆锚杆沿杆体表面所受的剪应力的弹性解,对岩体灌浆锚杆进行非局部摩擦分析,在简化的情况下,得到了在修正后的非局部摩擦模型下的岩体灌浆锚杆侧剪应力的积分形式,再用Maple程序求解,将其所得的结果与局部摩擦(库仑摩擦)模型下的侧剪应力进行比较,结果表明是合理有效的。  相似文献   

8.
Recent research studies on ductile fracture of metals have shown that the ductile fracture initiation is significantly affected by the stress state. In this study, the effects of the stress invariants as well as the effect of the reverse loading on ductile fracture are considered. To estimate the reduction of load carrying capacity and ductile fracture initiation, a scalar damage expression is proposed. This scalar damage is a function of the accumulated plastic strain, the first stress invariant and the Lode angle. To incorporate the effect of the reverse loading, the accumulated plastic strain is divided into the tension and compression components and each component has a different weight coefficient. For evaluating the plastic deformation until fracture initiation, the proposed damage function is coupled with the cyclic plasticity model which is affected by all of the stress invariants and pervious plastic deformation history.For verification and evaluation of this damage-plasticity constitutive equation a series of experimental tests are conducted on high-strength steel, DIN 1.6959. In addition finite element simulations are carried out including the integration of the constitutive equations using the modified return mapping algorithm. The modeling results show good agreement with experimental results.  相似文献   

9.
A new nonlocal, gradient based damage model is proposed for isotropic elastic damage using the phase field method in order to show the evolution of damage in brittle materials. The general framework of the phase field model (PFM) is discussed and the order parameter is related to the damage variable in continuum damage mechanics (CDM). The time dependent Ginzburg–Landau equation which is also termed the Allen–Cahn equation is used to describe the damage evolution process. Specific length scale which addresses the interface region in which the process of changing undamaged solid to fully damaged material (microcracks) occurs is defined in order to capture the effect of the damaged localization zone. A new implicit damage variable is proposed through the phase field theory. Details of the different aspects and regularization capabilities are illustrated by means of numerical examples and the validity and usefulness of the phase field modeling approach is demonstrated.  相似文献   

10.
以非局部塑性理论为基础,应用状态空间理论,通过局部和非局部两个状态空间的塑性能量耗散率等效原理,提出了一种求解应变局部化问题的新方法,以得到与网格无关的数值解.针对二维问题的屈服函数和流动法则导出了求解非局部内变量的一般方程,并提出了在有限元环境中求解应变局部化问题的应力更新算法.为了验证所提出的方法,对1个一维拉杆和3个二维平面应变加载试件进行了有限元分析.数值结果表明,塑性应变的分布和载荷-位移曲线都随着网格的变小而稳定地收敛,应变局部化区域的尺寸只与材料内尺度有关,而对有限元网格的大小不敏感.对于一维问题,当有限元网格尺寸减小时,数值解收敛于解析解.对于二维剪切带局部化问题,数值解随着网格尺寸的减小而稳定地向唯一解收敛.当网格尺寸减小时,剪切带的宽度和方向基本上没有变化.而且得到的塑性应变分布和网格变形是平滑的.这说明,所提方法可以克服经典连续介质力学模型导致的网格相关性问题,从而获得具有物理意义的客观解.此模型只需要单元之间的位移插值函数具有C~0连续性,因而容易在现有的有限元程序中实现而无需对程序作大的修改.  相似文献   

11.
12.
13.
The dynamic meshless methods for local and nonlocal field theories are formulated in this paper. Application to two crack problems is presented. The meshless method of local theory gives solution that is in good agreement with the classical analytical crack tip solution, while the nonlocal theory yields a solution without stress singularity at the crack tip. The numerical results also show the embedded nonlocal nature of meshless methods.  相似文献   

14.
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.  相似文献   

15.
A mesh-free approximation of large deformations of flexible membrane structures within the tension field theory is considered in this paper. A modification of the wrinkling theory, originally proposed by Roddeman et al. (1987) [Roddeman, D.G., Drukker, J., Oomens, C.W.J., Janssen, J.D., 1987, The wrinkling of thin membranes: Part I—theory; Part II—numerical analysis. ASME J. Appl. Mech. 54, 884–892.], is proposed to study the behaviour of an isotropic membrane under the mixed state of stress (taut, wrinkled and slack). Using the facts that the state of stress is not uniform across an element and that the deformation gradient is a spatially continuous (and possibly non-differentiable) tensor, the proposed model uses a continuously modified deformation gradient to capture the location and orientation of wrinkles more precisely. While the deformation gradient need not be everywhere-differentiable in a wrinkled membrane, it is argued that the fictive non-wrinkled (non-slack) surface may be looked upon as an everywhere-taut surface in the limit as the minor (and major) principal tensile stresses over the wrinkled (slack) portions go to zero. Accordingly, the modified deformation gradient is thought of as the limit of a sequence of everywhere-differentiable tensors. The weighted residual from the governing equations are presently solved via a mesh-free method, where the entire domain is discretized only by a set of grid points. A non-uniform-rational-B-spline (NURBS) based error reproducing kernel method (ERKM) has been used to approximate the field variable over the domain. The first step in the method is to approximate a function and its derivatives through NURBS basis functions. However, since NURBS functions neither reproduce any polynomial nor interpolate the grid points (also referred to as control or nodal points), the approximated functions result in uncontrolled errors over the domain including the grid points. Accordingly the error functions in the NURBS approximation and its derivatives are reproduced via a family of non-NURBS basis functions. The non-NURBS basis functions are constructed using a polynomial reproduction condition and added to the NURBS approximation of the function obtained in the first step. Several numerical examples on wrinkled and/or slack membranes are also provided.  相似文献   

16.
黄丹 《固体力学学报》2017,38(6):483-491
采用近场动力学方法对巴西圆盘劈裂破坏问题进行建模分析.在非局部键型近场动力学(Peridynamics,PD)理论基础上,通过引入物质点对的转动自由度构建双参数微观弹脆性近场动力学本构模型以突破常规模型的应用范围限制,并考虑岩石混凝土类固体材料的宏观拉压异性和断裂特征.引入动态松弛、粒子系统力边界条件和平衡收敛准则等算法,构建了完备的PD求解体系.实现了含不同倾角中心裂纹巴西圆盘受压劈裂破坏全过程的近场动力学数值模拟,裂纹扩展路径及破坏形式均与试验结果高度吻合.进一步分析了初始中心裂纹倾角及其相对长度对巴西圆盘破坏荷载的影响.  相似文献   

17.
The nonlocal peridynamic theory has been proven to be a promising method for the material failure and damage analyses in solid mechanics.Based upon the integrodifferential equations,peridynamics enables predicting the complex fracture phenomena such as spontaneous crack nucleation and crack branching,curving,and arrest.In this paper,the bond-based peridynamic approach is used to study the impact damage in a beam with an offset notch,which is widely used to investigate the mixed I-II crack propagation in brittle materials.The predictions from the peridynamic analysis agree well with available experimental observations.The numerical results show that the dynamic fracture behaviors of the beam under the impact load,such as crack initiation,curving,and branching,rely on the location of the offset notch and the impact speed of the drop hammer.  相似文献   

18.
Ⅱ型载荷作用下裂纹变形模式也为Ⅱ型的破坏问题称为真Ⅱ型破坏.准确定量地把握真Ⅱ型破坏的全过程是具有挑战性的问题.本文采用结构化变形驱动的非局部宏-微观损伤模型对真Ⅱ型破坏问题进行了模拟.根据结构化变形理论将点偶的非局部应变分解为弹性应变与结构化应变两部分,进而利用Cauchy-Born准则与结构化应变计算点偶的结构化正伸长量.在本文中,结构化应变取为非局部应变的偏量部分.当点偶的结构化正伸长量超过临界伸长量时,微细观损伤开始在点偶层次发展.将微细观损伤在作用域中进行加权求和得到拓扑损伤,并通过能量退化函数将其嵌入到连续介质-损伤力学框架中进行数值求解.进一步地,本文采用Gauss-Lobatto积分格式计算点偶的非局部应变,将积分点数目降低到4个,显著降低了前处理和非线性分析的计算成本.通过对Ⅱ型加载下裂尖应变场的分析揭示了采用偏应变作为结构化应变的原因.对两个典型真Ⅱ型破坏问题的模拟结果表明,本文方法不仅可以把握Ⅱ型加载下的真Ⅱ型裂纹扩展模式,同时可以定量刻画加载过程中的载荷-变形曲线,且不具有网格敏感性.最后指出了需要进一步研究的问题.  相似文献   

19.
Kernels for non-local elasticity are in general obtained from phonon dispersion relations. However, non-local elastic kernels are in the form of three-dimensional (3D) functions, whereas the dispersion relations are always in the form of one-dimensional (1D) frequency versus wave number curves corresponding to a particular wave direction. In this paper, an approach to build 2D and 3D kernels from 1D phonon dispersion data is presented. Our particular focus is on isotropic media where we show that kernels can be obtained using Fourier–Bessel transform, yielding axisymmetric kernel profiles in reciprocal and real spaces. These kernel functions are designed to satisfy the necessary requirements for stable wave propagation, uniformity of nonlocal stress and stress regularization. The proposed concept is demonstrated by developing some physically meaningful 2D and 3D kernels that will find useful applications in nonlocal mechanics. Relative merits of the kernels obtained via proposed methods are explored by fitting 1D kernels to dispersion data for Argon and using the kernel to understand the size effect in non local energy as seen from molecular simulations. A comparison of proposed kernels is made based on their predictions of stress field around a crack tip singularity.  相似文献   

20.
本文采用了一种基于不连续场修正权函数的无网格方法来处理二维平面问题中的有限长裂纹。相较于目前常用的无网格裂纹不连续性处理方案,采用修正权函数处理裂纹附近不连续场时只需要对原权函数进行修正,算法简便易实现。本文采用基于不连续场修正权函数的无单元Galerkin方法(EFGM),对在边界上施加I-II混合型裂纹位移场的斜裂纹板进行了数值分析。并与可视性准则、衍射法和透射法等不连续准则对比了裂尖位移场、应力场和应力强度因子解的数值精度。另外,本文还对这四种不连续准则形函数的计算效率进行了分析和比较。  相似文献   

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