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1.
基于近场动力学理论的混凝土轴拉破坏过程模拟   总被引:2,自引:0,他引:2  
近场动力学PD(Peridynamics)是一种新兴的基于非局部模型描述材料特性的数值计算方法.该方法假定位于连续体内的粒子通过有限的距离与其他粒子相互作用,通过积分计算在一定近场范围(Horizon)内具有一定影响域的材料点之间的相互作用力,而不论位移场的连续与否,避免了传统的局部微分方程求解在面临不连续问题时的奇异性和现有多尺度算法的复杂性.本文概述了PD方法的基本思想、建模方法和计算体系,给出了用近场动力学方法模拟混凝土在轴向拉伸荷载作用下的计算格式.算例结果表明,PD方法可以很好地刻画和模拟混凝土在轴拉情形下的损伤累积与渐进破坏过程.最后讨论了PD方法在理论、计算和应用等方面有待进一步研究的问题.  相似文献
2.
近场动力学方法及其应用   总被引:2,自引:0,他引:2       下载免费PDF全文
黄丹  章青  乔丕忠  沈峰 《力学进展》2010,40(4):448-459
近场动力学(peridynamics, PD)是一种新兴的基于非局部作用思想建立模型并通过求解空间积分方程描述物质力学行为的方法. 它兼有分子动力学方法和无网格方法的优点, 避免了基于连续性假设建模和求解空间微分方程的传统宏观方法在面临不连续问题时的奇异性, 又突破了经典分子动力学方法在计算尺度上的局限, 在宏/微观不连续力学问题分析中均表现出很高的求解精度和效率. 首先概述了PD方法的理论基础、建模思路和计算体系; 进而介绍了PD方法在不同尺度不连续力学问题中的应用, 包括均匀与非均匀材料和结构的大变形、损伤、断裂、冲击、穿透和失稳问题, 结晶相变动力学问题以及纳米材料和结构的破坏问题; 最后讨论了PD方法在理论、计算和应用等方面值得进一步研究的问题.  相似文献
3.
Structural stability and failure analysis using peridynamic theory   总被引:2,自引:0,他引:2  
The peridynamic theory has been successfully utilized for damage prediction in many problems. However, the elastic stability of structures has not been studied using the peridynamic theory. Therefore, this paper investigates the elastic stability of simple structures to determine buckling characteristics of the peridynamic theory by considering two sets of problems. The first set of problems involves rectangular columns under compression to find the effects of the cross-sectional area and boundary conditions on buckling load. The second set involves rectangular plates under a uniform temperature load to establish the effects of plate dimensions and material properties on the critical buckling temperature. The predictions of the peridynamic theory agree with those published in the literature. The solution method is based on reducing the peridynamic equations of motion to discrete forms by using collocation points. These discrete equations are then solved using adaptive dynamic relaxation. Furthermore, perturbation method using geometrical imperfections is utilized to trigger lateral displacements in the numerical solutions.  相似文献
4.
基于近场动力学理论的层压板损伤分析方法   总被引:1,自引:0,他引:1  
提出了一种基于近场动力学理论的纤维增强复合材料层压板的渐进损伤分析方法.在弹性力学和复合材料力学的基础上,推导了适用于近场动力学建模的微模量和临界伸长率等基本参量,结合经典层压板理论中的偏轴模量,构建了适用于各向异性材料的对点力函数,可分析3种形式的损伤:纤维断裂,基体开裂和分层破坏.分析了含圆孔层压板在拉伸载荷作用下的破坏过程,预测结果与试验结果吻合良好.  相似文献
5.
Convergence of Peridynamics to Classical Elasticity Theory   总被引:1,自引:0,他引:1  
The peridynamic model of solid mechanics is a nonlocal theory containing a length scale. It is based on direct interactions between points in a continuum separated from each other by a finite distance. The maximum interaction distance provides a length scale for the material model. This paper addresses the question of whether the peridynamic model for an elastic material reproduces the classical local model as this length scale goes to zero. We show that if the motion, constitutive model, and any nonhomogeneities are sufficiently smooth, then the peridynamic stress tensor converges in this limit to a Piola-Kirchhoff stress tensor that is a function only of the local deformation gradient tensor, as in the classical theory. This limiting Piola-Kirchhoff stress tensor field is differentiable, and its divergence represents the force density due to internal forces. The limiting, or collapsed, stress-strain model satisfies the conditions in the classical theory for angular momentum balance, isotropy, objectivity, and hyperelasticity, provided the original peridynamic constitutive model satisfies the appropriate conditions.   相似文献
6.
A generalization of the original peridynamic framework for solid mechanics is proposed. This generalization permits the response of a material at a point to depend collectively on the deformation of all bonds connected to the point. This extends the types of material response that can be reproduced by peridynamic theory to include an explicit dependence on such collectively determined quantities as volume change or shear angle. To accomplish this generalization, a mathematical object called a deformation state is defined, a function that maps any bond onto its image under the deformation. A similar object called a force state is defined, which contains the forces within bonds of all lengths and orientation. The relation between the deformation state and force state is the constitutive model for the material. In addition to providing a more general capability for reproducing material response, the new framework provides a means to incorporate a constitutive model from the conventional theory of solid mechanics directly into a peridynamic model. It also allows the condition of plastic incompressibility to be enforced in a peridynamic material model for permanent deformation analogous to conventional plasticity theory.   相似文献
7.
We study the kinetics of phase transformations in solids using the peridynamic formulation of continuum mechanics. The peridynamic theory is a nonlocal formulation that does not involve spatial derivatives, and is a powerful tool to study defects such as cracks and interfaces.We apply the peridynamic formulation to the motion of phase boundaries in one dimension. We show that unlike the classical continuum theory, the peridynamic formulation does not require any extraneous constitutive laws such as the kinetic relation (the relation between the velocity of the interface and the thermodynamic driving force acting across it) or the nucleation criterion (the criterion that determines whether a new phase arises from a single phase). Instead this information is obtained from inside the theory simply by specifying the inter-particle interaction. We derive a nucleation criterion by examining nucleation as a dynamic instability. We find the induced kinetic relation by analyzing the solutions of impact and release problems, and also directly by viewing phase boundaries as traveling waves.We also study the interaction of a phase boundary with an elastic non-transforming inclusion in two dimensions. We find that phase boundaries remain essentially planar with little bowing. Further, we find a new mechanism whereby acoustic waves ahead of the phase boundary nucleate new phase boundaries at the edges of the inclusion while the original phase boundary slows down or stops. Transformation proceeds as the freshly nucleated phase boundaries propagate leaving behind some untransformed martensite around the inclusion.  相似文献
8.
The one-dimensional dynamic response of an infinite bar composed of a linear “microelastic material” is examined. The principal physical characteristic of this constitutive model is that it accounts for the effects of long-range forces. The general theory that describes our setting, including the accompanying equation of motion, was developed independently by Kunin (Elastic Media with Microstructure I, 1982), Rogula (Nonlocal Theory of Material Media, 1982) and Silling (J. Mech. Phys. Solids 48 (2000) 175), and is called the peridynamic theory. The general initial-value problem is solved and the motion is found to be dispersive as a consequence of the long-range forces. The result converges, in the limit of short-range forces, to the classical result for a linearly elastic medium. Explicit solutions in elementary form are given in a broad class of special cases. The most striking observations arise in the Riemann-like problem corresponding to a constant initial displacement field and a piecewise constant initial velocity field. Even though, initially, the displacement field is continuous, it involves a jump discontinuity for all later times, the Lagrangian location of which remains stationary. For some materials the magnitude of the discontinuity-jump oscillates about an average value, while for others it grows monotonically, presumably fracturing the material when it exceeds some critical level.  相似文献
9.
10.
This paper develops a new peridynamic state based model to represent the bending of an Euler–Bernoulli beam. This model is non-ordinary and derived from the concept of a rotational spring between bonds. While multiple peridynamic material models capture the behavior of solid materials, this is the first 1D state based peridynamic model to resist bending. For sufficiently homogeneous and differentiable displacements, the model is shown to be equivalent to Eringen’s nonlocal elasticity. As the peridynamic horizon approaches 0, it reduces to the classical Euler–Bernoulli beam equations. Simple test cases demonstrate the model’s performance.  相似文献
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