饱和多孔介质中动力渗流耦合分析的Biot-Cosserat连续体模型与应变局部化有限元模拟

提出了适用于饱和多孔介质中应变局部化分析及动力渗流耦合分析的Biot-Cosserat连续体模型。基于饱和多孔介质动力渗流耦合分析的Biot理论,将固体骨架看作Cosserat连续体,并考虑旋转惯性,建立了饱和多孔介质动力渗流耦合分析的Biot-Cosserat连续体模型。基于Galerkin加权余量法,对所发展的模型推导了以固体骨架广义位移(包含旋转)及孔隙水压力为基本未知量的有限元公式。利用所发展的数值模型,对包含压力相关弹塑性固体骨架材料的饱和多孔介质进行了动力渗流耦合分析与应变局部化有限元模拟,结果表明,所发展的两相饱和多孔介质动力渗流耦合分析的Biot-Cosserat连续体模型能保持饱和两相介质应变局部化问题的适定性及模拟饱和多孔介质中由应变软化引起的应变局部化现象的有效性。     

一种考虑尺寸效应的颗粒材料流变模型及其验证

经典连续介质理论的粘塑性本构关系缺乏材料尺度的相关性,难以表征颗粒材料流变的尺寸效应,而Cosserat连续体中的内禀特征长度为刻画材料的尺寸效应提供了一种可能途径。该文旨在Cosserat连续体的理论框架下发展Perzyna粘塑性模型,以探讨颗粒材料流变的尺寸效应与影响机制。首先基于Drucker-Prager屈服准则导出了Cosserat连续体粘塑性模型的一致性算法,获得了过应力本构方程积分算法与一致切向模量的封闭形式,并在ABAQUS二次平台上采用用户自定义单元(UEL)予以程序实现。有限元数值算例模拟了软岩试样的三轴压缩蠕变和两种堆石料试样在常规三轴条件下的蠕变和应力松弛,数值预测结果与相应试验结果具有较好的一致性,表明该流变模型的适应性。同时,将颗粒的球型指数、圆度和平均粒径作为表征颗粒材料内禀特征长度的一种度量,以反映颗粒材料的试样尺寸及其颗粒粒径与形状对流变过程中的轴向应变、偏应变和偏应力的影响关系,表明所发展的流变模型可以捕捉颗粒材料流变行为的压力相关性和尺寸效应。     

基于Cosserat理论的应变梯度非协调数值研究

依据Cosserat连续介质理论下非协调离散体系的能量相容性,导出了非协调位移的一个合理约束条件。根据这个条件构造了一个应变梯度平面4节点非协调单元。计算结果表明,该单元对可压缩和不可压缩状态的Cosserat类型的应变梯度材料均给出合理的数值结果,再现了材料的应变梯度效应。     

连续—非连续结构应力分析现状与进展

对工程结构应力分析中采用的连续介质模型、非连续介质模型、连续——非连续介质力学模型作了系统介绍。三种模型物理数值模拟的各种理论及数值方法,代表了当今结构应力分析的主流及发展方向。随着工程建设中高、大、精、新结构的出现,表明这个古老而又崭新的命题仍有无限广泛的发展前景。从七个方面论述了它的现状及发展特征:从过时观到现代新观念;从连续到非连续;从精确到数值近似;从有限元到无单元;从单一到统一;从标量无网格到复变量无网格;从独立到耦合,全面介绍了其内容和方法。     

基于弹塑性损伤本构模型的复合材料层合板破坏荷载预测

在连续损伤力学和塑性力学框架内,建立一个同时考虑塑性效应和损伤累积导致材料属性退化的复合材料弹塑性损伤本构模型。基于最近点投影回映算法,开发本构模型的应变驱动隐式积分算法以更新应力及与解答相关的状态变量,并推导与所开发算法相应的数值一致性切线刚度矩阵,保证有限元分析采用NewtonRaphson迭代法解答非线性问题的计算效率。采用断裂带模型对已开发的本构模型软化段进行规则化,以减轻有限元分析结果的网格相关性问题。对损伤变量进行粘滞规则化,并推导出相应的粘滞规则化数值一致性切线刚度张量,解决了在有限元隐式计算程序中采用含应变软化段本构关系的数值分析由于计算困难而提前终止的问题。开发包含数值积分算法的用户材料子程序UMAT,并嵌于有限元程序Abaqus v6.14中。通过对力学行为展现显著塑性效应的AS4/3501-6V型开口复合材料层合板的渐进失效分析,验证本文提出的材料本构模型的有效性。结果显示,预测结果与已报道的试验结果吻合良好,并且预测精度高于其他已有弹性损伤模型。表明已建立的弹塑性损伤本构模型能够准确预测力学行为,展现显著塑性效应的复合材料层合板的破坏荷载,为其构件和结构设计提供一种有效的分析方法。     

岩土软化行为的网格依赖性问题研究

岩土工程中常出现软化行为,传统的弹塑性有限元计算软化行为的剪切带问题会出现网格依赖性。该文引入偶应力弹塑性理论,详细推导了Drucker-Prager屈服准则下的偶应力增量有限元框架,采用可通过C0―1分片检验的RCT9+RT9单元,并通过UEL用户子程序将该单元加入到大型有限元软件ABAQUS中。算例表明:偶应力理论可以消除网格依赖性,为解决岩土软化问题提供了一条有效的途径。     

基于梯度塑性理论的动力软化问题分析

对于动力应变软化问题,采用梯度塑性模型进行分析,该模型能够有效地克服软化材料在有限元分析中的网格依赖性问题。对于动力非线性软化方程的求解则利用于基于参变量变分原理的参数二次规划方法。对于结构动力方程时域上的求解则采用传统的Newmark方法。本文的算法与传统方法相比在求解基于梯度塑性模型的非线性动力软化问题时保证了已有参数二次规划算法的优良特性,有实现简单与稳定性好等优点。给出的数值算例证实了本文的理论工作与所研制程序的正确性。     

Lemaitre等向硬化弹塑性损伤耦合本构模型积分算法及程序实现EI北大核心CSCD

涉及复杂材料弹塑性损伤问题数值计算研究时,不仅需要选择恰当预测损伤和破坏的本构模型,还需要有效和稳健的本构积分算法。首先,阐述了在热力学和连续介质力学框架下建立弹塑性损伤本构模型的基本步骤;其次,基于Lemaitre等向硬化弹塑性损伤耦合本构模型、相应的本构积分算法-完全隐式返回映射算法(Fully Return Mapping Algorithm)和一致切线模量,采用C++语言在Visual 6.0环境下编制有限元本构求解程序,在塑性损伤修正步中求解返回映射方程时,选取一种简单的形式,只需迭代求解一个标量非线性方程,计算效率较高。最后,通过缺口圆棒数值算例初步验证了程序的正确性,并编制接口程序对计算结果进行可视化。研究结果表明积分算法的有效性及程序的正确性,Lemaitre等向硬化弹塑性损伤耦合本构模型能够较好地模拟韧性材料的破坏发展过程,可以求解类似的有限元边界值问题,为考虑损伤特性的韧性材料结构研究和设计奠定基础。     

Lemaitre等向硬化弹塑性损伤耦合本构模型积分算法及程序实现

涉及复杂材料弹塑性损伤问题数值计算研究时,不仅需要选择恰当预测损伤和破坏的本构模型,还需要有效和稳健的本构积分算法。首先,阐述了在热力学和连续介质力学框架下建立弹塑性损伤本构模型的基本步骤;其次,基于Lemaitre等向硬化弹塑性损伤耦合本构模型、相应的本构积分算法-完全隐式返回映射算法(Fully Return Mapping Algorithm)和一致切线模量,采用C++语言在Visual 6.0 环境下编制有限元本构求解程序,在塑性损伤修正步中求解返回映射方程时,选取一种简单的形式,只需迭代求解一个标量非线性方程,计算效率较高。最后,通过缺口圆棒数值算例初步验证了程序的正确性,并编制接口程序对计算结果进行可视化。研究结果表明积分算法的有效性及程序的正确性,Lemaitre等向硬化弹塑性损伤耦合本构模型能够较好地模拟韧性材料的破坏发展过程,可以求解类似的有限元边界值问题,为考虑损伤特性的韧性材料结构研究和设计奠定基础。     

岩土工程开挖模拟的非局部软化模型

基于非线性几何场论，建立了含有天然缺陷的岩土材料非局部连续模型、变分方程及相应的实时更新拖带系大变形有限元数值模型，设计了这一模型的数值卷积算法。对工程材料特别是岩土工程的地下开挖进行的数值结果表明，非局部连续模型描述变形局部化问题是适当的，物性方程包含材料特征尺度对于带缺陷体材料应变软化和损伤的分析是必要的。     

On error estimates and adaptivity in elastoplastic solids: Applications to the numerical simulation of strain localization in classical and Cosserat continua

The a posteriori error estimates based on the post-processing approach are introduced for elastoplastic solids. The standard energy norm error estimate established for linear elliptic problems is generalized here to account for the presence of internal variables through the norm associated with the complementary free energy. This is known to represent a natural metric for the class of elastoplastic problems of evolution. In addition, the intrinsic dissipation functional is utilized as a basis for a complementary a posteriori error estimates. A posteriori error estimates and adaptive refinement techniques are applied to the finite element analysis of a strain localization problem. As a model problem, the constitutive equations describing a generalization of standard J₂-elastoplasticity within the Cosserat continuum are used to overcome serious limitations exhibited by classical continuum models in the post-instability region. The proposed a posteriori error estimates are appropriately modified to account for the Cosserat continuum model and linked with adaptive techniques in order to simulate strain localization problems. Superior behaviour of the Cosserat continuum model in comparison to the classical continuum model is demonstrated through the finite element simulation of the localization in a plane strain tensile test for an elastopiastic softening material, resulting in convergent solutions with an h-refinement and almost uniform error distribution in all considered error norms.     

Application of the Cosserat continua to numerical studies on the properties of the materials

The finite element models of Cosserat continuum in two- and three-dimensions are presented. The size effects of a cantilever beam and a micro-rod, the well-posedness, the mesh-independent solutions of the boundary value problems with non-associated elastoplastic and strain softening constitutive behavior, and the progressive failure of the two- and three-dimensional vertical excavations are studied. Numerical results illustrate that the proposed Cosserat continuum models are capable of reflecting the size effects of micro-structures, preserving the well-posedness of the boundary value problem characterized by the strain localization, ensuring mesh-independent solutions, and simulating the entire progressive failure process occurring in engineering structures.     

3D modelling of strong discontinuities in elastoplastic solids: fixed and rotating localization formulations

This paper is concerned with the incorporation of displacement discontinuities into a continuum theory of elastoplasticity for the modelling of localization processes such as cracking in brittle materials. Based on the strong discontinuity approach (SDA) (Computational Mechanics 1993; 12: 277–296) mesh objective 2D and 3D finite element formulations are developed using linear and quadratic 2D elements as well as 8‐noded 3D elements. In the formulation of the finite‐element model proposed in the paper, the analogy with standard formulations is emphasized. The parameter defining the amplitude of the displacement jump within the finite element is condensed out at the material level without employing the standard static condensation technique. This approach results in linearized constitutive equations formally identical to continuum models. Therefore, the standard return mapping algorithm is used to solve the non‐linear equations. In analogy to concepts used in continuum smeared crack models, a rotating formulation of the SDA is proposed in addition to the standard concept of fixed discontinuities. It is shown that the rotating localization approach reduces locking effects observed in analyses based on fixed localization directions. The applicability of the proposed SDA finite‐element model as well as its numerical performance is investigated by means of a three‐dimensional ultimate load analysis of a steel anchor embedded in a concrete block subjected to a shear force. Copyright © 2003 John Wiley & Sons, Ltd.     

Finite element analysis of 3D elastic–plastic frictional contact problem for Cosserat materials

The objective of this paper is to develop a finite element model for 3D elastic–plastic frictional contact problem of Cosserat materials. Because 3D elastic–plastic frictional contact problems belong to the unspecified boundary problems with nonlinearities in both material and geometric forms, a large number of calculations are needed to obtain numerical results with high accuracy. Based on the parametric variational principle and the corresponding quadratic programming method for numerical simulation of frictional contact problems, a finite element model is developed for 3D elastic–plastic frictional contact analysis of Cosserat materials. The problems are finally reduced to linear complementarity problems (LCP). Numerical examples show the feasibility and importance of the developed model for analyzing the contact problems of structures with materials which have micro-polar characteristics.     

A highly efficient membrane finite element with drilling degrees of freedom

In this paper, the development of a new quadrilateral membrane finite element with drilling degrees of freedom is discussed. A variational principle employing an independent rotation field around the normal of a plane continuum element is derived. This potential is based on the Cosserat continuum theory where skew symmetric stress and strain tensors are introduced in connection with the rotation of a point. From this higher continuum theory a formulation that incorporates rotational degrees of freedom is extracted, while the stress tensor is symmetric in a weak form. The resulting potential is found to be similar to that obtained by the procedure of Hughes and Brezzi. However, Hughes and Brezzi derived their potential in terms of pure mathematical investigations of Reissner’s potential, while the present procedure is based on physical considerations. This framework can be enhanced in terms of assumed stress and strain interpolations, if the numerical model is based on a modified Hu-Washizu functional with symmetric and asymmetric terms. The resulting variational statement enables the development of a new finite element that is very efficient since all parts of the stiffness matrix can be obtained analytically even in terms of arbitrary element distortions. Without the addition of any internal degrees of freedom the element shows excellent performance in bending dominated problems for rectangular element configurations.     

A mixed finite element for the nonlinear analysis of in-plane loaded masonry walls

A mixed membrane eight-node quadrilateral finite element for the analysis of masonry walls is presented. Assuming that a nonlinear and history-dependent 2D stress-strain constitutive law is used to model masonry material, the element derivation is based on a Hu-Washizu variational statement, involving displacement, strain, and stress fields as primary variables. As the behavior of masonry structures is often characterized by strain localization phenomena, due to strain softening at material level, a discontinuous, piecewise constant interpolation of the strain field is considered at element level, to capture highly nonlinear strain spatial distributions also within finite elements. Newton's method of solution is adopted for the element state determination problem. For avoiding pathological sensitivity to the finite element mesh, a novel algorithm is proposed to perform an integral-type nonlocal regularization of the constitutive equations in the present mixed formulation. By the comparison with competing serendipity displacement-based formulation, numerical simulations prove high performances of the proposed finite element, especially when coarse meshes are adopted.     

A new finite element based on the theory of a Cosserat point—extension to initially distorted elements for 2D plane strain

This paper describes an improvement of the Cosserat point element formulation for initially distorted, non-rectangular shaped elements in 2D. The original finite element formulation for 3D large deformations shows excellent behaviour for sensitive geometries, large deformations, coarse meshes, bending dominated and stability problems without showing undesired effects such as locking or hourglassing, as long as the initial element shape resembles that of a rectangular parallelepiped. In the following, an extension of this element formulation for 2D plane strain is presented which has the same good properties also for the case of non-rectangular initial element shapes. Results of numerical tests are presented, that clearly show the advantages of the improved Cosserat point element compared to the standard displacement elements and the original version of the Cosserat point element. Copyright © 2007 John Wiley & Sons, Ltd.     

A nonlocal multiscale discrete‐continuum model for predicting mechanical behavior of granular materials

A three‐dimensional nonlocal multiscale discrete‐continuum model has been developed for modeling mechanical behavior of granular materials. In the proposed multiscale scheme, we establish an information‐passing coupling between the discrete element method, which explicitly replicates granular motion of individual particles, and a finite element continuum model, which captures nonlocal overall responses of the granular assemblies. The resulting multiscale discrete‐continuum coupling method retains the simplicity and efficiency of a continuum‐based finite element model, while circumventing mesh pathology in the post‐bifurcation regime by means of staggered nonlocal operator. We demonstrate that the multiscale coupling scheme is able to capture the plastic dilatancy and pressure‐sensitive frictional responses commonly observed inside dilatant shear bands, without employing a phenomenological plasticity model at a macroscopic level. In addition, internal variables, such as plastic dilatancy and plastic flow direction, are now inferred directly from granular physics, without introducing unnecessary empirical relations and phenomenology. The simple shear and the biaxial compression tests are used to analyze the onset and evolution of shear bands in granular materials and sensitivity to mesh density. The robustness and the accuracy of the proposed multiscale model are verified in comparisons with single‐scale benchmark discrete element method simulations. Copyright © 2015 John Wiley & Sons, Ltd.