共查询到20条相似文献，搜索用时 15 毫秒
1.
Zhi‐Qiao Wang Guan‐Suo Dui 《International journal for numerical methods in engineering》2008,75(12):1435-1456
This paper presents alternative forms of hyperelastic–plastic constitutive equations and their integration algorithms for isotropic‐hardening materials at large strain, which are established in two‐point tensor field, namely between the first Piola–Kirchhoff stress tensor and deformation gradient. The eigenvalue problems for symmetric and non‐symmetric tensors are applied to kinematics of multiplicative plasticity, which imply the transformation relationships of eigenvectors in current, intermediate and initial configurations. Based on the principle of plastic maximum dissipation, the two‐point hyperelastic stress–strain relationships and the evolution equations are achieved, in which it is considered that the plastic spin vanishes for isotropic plasticity. On the computational side, the exponential algorithm is used to integrate the plastic evolution equation. The return‐mapping procedure in principal axes, with respect to logarithmic elastic strain, possesses the same structure as infinitesimal deformation theory. Then, the theory of derivatives of non‐symmetric tensor functions is applied to derive the two‐point closed‐form consistent tangent modulus, which is useful for Newton's iterative solution of boundary value problem. Finally, the numerical simulation illustrates the application of the proposed formulations. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
2.
Erik Giesen Loo Frans P. van der Meer 《International journal for numerical methods in engineering》2020,121(19):4458-4470
The accuracy of multiscale modeling approaches for the analysis of heterogeneous materials hinges on the representativeness of the micromodel. One of the issues that affects this representativeness is the application of appropriate boundary conditions. Periodic boundary conditions are the most common choice. However, when localization takes place, periodic boundary conditions tend to overconstrain the microscopic problem. Weakly periodic boundary conditions have been proposed to overcome this effect. In this study, the effectiveness of weakly periodic boundary conditions in restoring transverse isotropy of representative volume elements (RVE) for a fiber-reinforced composite with elastoplastic matrix is investigated. The formulation of weakly periodic boundary conditions is extended to allow for force-controlled simulations where a uniaxial stress can be applied. A series of simulations is performed where the orientation of applied stress is gradually varied and the influence of this orientation on the averaged response is examined. An original method is presented to test the correlation between the ultimate principal stress and average localization angle of shear bands within an RVE. It is concluded that weakly periodic boundary conditions alleviate anisotropy in the RVE response but do not remove it. 相似文献
3.
Pauli Pedersen 《International journal for numerical methods in engineering》2005,62(3):334-352
Separating the dependence on material and stress/strain state from the dependence on initial geometry, we obtain analytical secant and tangent stiffness matrices. For the case of a linear displacement triangle with uniform thickness and uniform constitutive behaviour closed‐form results are listed, directly suited for coding in a finite element program. The nodal positions of an element and the displacement assumption give three basic matrices of order three. These matrices do not depend on material and stress/strain state, and thus are unchanged during the necessary iterations for obtaining a solution based on Green–Lagrange strain measure. The approach is especially useful in design optimization, because analytical sensitivity analysis then can be performed. The case of a three node triangular ring element for axisymmetric analysis involves small modifications and extension to four node tetrahedron elements should be straight forward. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
4.
Emma La Malfa Ribolla Giuseppe Giambanco Antonino Spada 《International journal for numerical methods in engineering》2020,121(16):3610-3635
The multiscale homogenization scheme is becoming a diffused tool for the analysis of heterogeneous materials as masonry since it allows dealing with the complexity of formulating closed-form constitutive laws by retrieving the material response from the solution of a unit cell (UC) boundary value problem (BVP). The robustness of multiscale simulations depends on the robustness of the nested macroscopic and mesoscopic models. In this study, specific attention is paid to the meshless solution of the UC BVP under plane stress conditions, comparing performances related to the application of linear displacement or periodic boundary conditions (BCs). The effect of the geometry of the UC is also investigated since the BVP is formulated for the two simpliest UCs, according to a displacement-based variational formulation assuming the block indefinitely elastic and the mortar joints as zero-thickness elasto-plastic interfaces. It will be showed that the meshless discretization allows obtaining some advantages with respect to a standard FE mesh. The influence of the UC morphology as well as the BCs on the linear and nonlinear UC macroscopic response is discussed for pure modes of failure. The results can be constructive in view of performing a general Fe·Meshless or Meshless2 analysis. 相似文献
5.
Erik Svenning Martin Fagerström Fredrik Larsson 《International journal for numerical methods in engineering》2017,111(5):493-500
When computing the homogenized response of a representative volume element (RVE), a popular choice is to impose periodic boundary conditions on the RVE. Despite their popularity, it is well known that standard periodic boundary conditions lead to inaccurate results if cracks or localization bands in the RVE are not aligned with the periodicity directions. A previously proposed remedy is to use modified strong periodic boundary conditions that are aligned with the dominating localization direction in the RVE. In the present work, we show that alignment of periodic boundary conditions can also conveniently be performed on weak form. Starting from a previously proposed format for weak micro‐periodicity that does not require a periodic mesh, we show that aligned weakly periodic boundary conditions may be constructed by only modifying the mapping (mirror function) between the associated parts of the RVE boundary. In particular, we propose a modified mirror function that allows alignment with an identified localization direction. This modified mirror function corresponds to a shifted stacking of RVEs, and thereby ensures compatibility of the dominating discontinuity over the RVE boundaries. The proposed method leads to more accurate results compared to using unaligned periodic boundary conditions, as demonstrated by the numerical examples. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
6.
FRANCISCO PADILLA YVES SECRETAN MICHEL LECLERC 《International journal for numerical methods in engineering》1997,40(13):2493-2516
A steady-state and transient finite element model has been developed to approximate, with simple triangular elements, the two-dimensional advection–diffusion equation for practical river surface flow simulations. Essentially, the space–time Crank–Nicolson–Galerkin formulation scheme was used to solve for a given conservative flow-field. Several kinds of point sources and boundary conditions, namely Cauchy and Open, were theoretically and numerically analysed. Steady-state and transient numerical tests investigated the accuracy of boundary conditions on inflow, noflow and outflow boundaries where diffusion is important (diffusive boundaries). With the proper choice of boundary conditions, the steady-state Galerkin and the transient Crank–Nicolson–Galerkin finite element schemes gave stable and precise results for advection-dominated transport problems. Comparisons indicated that the present approach can give equivalent or more precise results than other streamline upwind and high-order time-stepping schemes. Diffusive boundaries can be treated with Cauchy conditions when the flow enters the domain (inflow), and with Open conditions when the flow leaves the domain (outflow), or when it is parallel to the boundary (noflow). Although systems with mainly diffusive noflow boundaries may still be solved precisely with Open conditions, they are more susceptible to be influenced by other numerical sources of error. Moreover, the treatment of open boundaries greatly increases the possibilities of correctly modelling restricted domains of actual and numerical interest. © 1997 by John Wiley & Sons, Ltd. 相似文献
7.
8.
S. Lucarini J. Segurado 《International journal for numerical methods in engineering》2019,119(8):797-805
A new algorithm is proposed to impose a macroscopic stress or mixed stress/deformation gradient history in the context of nonlinear Galerkin-based fast Fourier transform homogenization. The method proposed is based on the definition of a modified projection operator in which the null frequencies enforce the type of control (stress or strain) for each component of either the macroscopic first Piola stress or the deformation gradient. The resulting problem is solved exactly as the original variational method, and it does not require additional iterations compared to the strain control version, neither in the linear iterative solver nor in the Newton scheme. The efficiency of the proposed method is demonstrated with a series of numerical examples, including a polycrystal and a particle-reinforced hyperelastic material. 相似文献
9.
Abstract Light scattering by long finite cylinders is applied for particle characterization, investigation of scattering and absorption properties of interstellar dust, ice crystals and many other fields. In recent years many methods have been used to solve this problem, but usually their applicability is restricted to aspect ratios of about 10. In this paper a renewed algorithm of the discrete sources method is described, which allows computer simulation of light scattering by highly elongated cylinders with aspect ratios up to 100 and length up to 40 μm. 相似文献
10.
Joseph Goldmann Jörg Brummund Volker Ulbricht 《International journal for numerical methods in engineering》2018,113(1):1-21
This paper presents an adaption of periodic boundary conditions (BC), which is termed tessellation BC. While periodic BC restrict strain localization zones to obey the periodicity of the microstructure, the proposed tessellation BC adjust the periodicity frame to meet the localization zone. Thereby, arbitrary developing localization zones are permitted. Still the formulation is intrinsically unsusceptible against spurious localization. Additionally, a modification of the Hough transformation is derived, which constitutes an unbiased criterion for the detection of the localization zone. The behavior of the derived formulation is demonstrated by various examples and compared with other BC. It is thereby shown that tessellation BC lead to a reasonable dependence of the effective stress on the localization direction. Furthermore, good convergence of stiffness values with increasing size of the representative volume element is shown as well as beneficial characteristics in use with strain softening material. 相似文献
11.
Kristoffer Carlsson Fredrik Larsson Kenneth Runesson 《International journal for numerical methods in engineering》2019,119(4):281-304
This paper presents the application of variationally consistent selective homogenization applied to a polycrystal with a subscale model of gradient-enhanced crystal inelasticity. Although the full gradient problem is solved on Statistical Volume Elements (SVEs), the resulting macroscale problem has the formal character of a standard local continuum. A semi-dual format of gradient inelasticity is exploited, whereby the unknown global variables are the displacements and the energetic micro-stresses on each slip-system. The corresponding time-discrete variational formulation of the SVE-problem defines a saddle point of an associated incremental potential. Focus is placed on the computation of statistical bounds on the effective energy, based on virtual testing on SVEs and an argument of ergodicity. As it turns out, suitable combinations of Dirichlet and Neumann conditions pertinent to the standard equilibrium and the micro-force balance, respectively, will have to be imposed. Whereas arguments leading to the upper bound are quite straightforward, those leading to the lower bound are significantly more involved; hence, a viable approximation of the lower bound is computed in this paper. Numerical evaluations of the effective strain energy confirm the theoretical predictions. Furthermore, heuristic arguments for the resulting macroscale stress-strain relations are numerically confirmed. 相似文献
12.
13.
F. Asllanaj A. Milandri G. Jeandel J. R. Roche 《International journal for numerical methods in engineering》2002,54(11):1649-1668
A finite difference solution for a system of non‐linear integro–differential equations modelling the steady‐state combined radiative–conductive heat transfer is proposed. A new backward–forward finite difference scheme is formulated for the Radiative Transfer Equation. The non‐linear heat conduction equation is solved using the Kirchhoff transformation associated with a centred finite difference scheme. The coupled system of equations is solved using a fixed‐point method, which relates to the temperature field. An application on a real insulator composed of silica fibres is illustrated. The results show that the method is very efficient. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
14.
Isaac Harari Paul E. Barbone Joshua M. Montgomery 《International journal for numerical methods in engineering》1997,40(15):2791-2805
We develop formulations for finite element computation of exterior acoustics problems. A prominent feature of the formulations is the lack of integration over the unbounded domain, simplifying the task of discretization and potentially leading to numerous additional benefits. These formulations provide a suitable basis for hybrid asymptotic-numerical methods in scattering, non-reflecting boundary conditions and infinite elements. © 1997 John Wiley & Sons, Ltd. 相似文献
15.
V.G. Boborykin 《Engineering Analysis with Boundary Elements》2012,36(4):613-625
A method is proposed for the construction of Green's functions for the Sophie Germain equation in regions of irregular shape with mixed boundary conditions imposed. The method is based on the boundary integral equation approach where a kernel vector function B satisfies the biharmonic equation inside the region. This leads to a regular boundary integral equation where the compensating loads and moments are applied to the boundary. Green's function is consequently expressed in terms of the kernel vector function B, the fundamental solution function of the biharmonic equation, and kernel functions of the inverse regular integral operators. To compute moments and forces, the kernel functions are differentiated under the integral sign. The proposed method appears highly effective in computing both displacements and stress components. 相似文献
16.
基于满足周期性假设和尺度分离假设的渐进展开均匀化原理,应用商业有限元软件ABAQUS实现了快速识别颗粒增强复合材料的等效弹性参数,及获取其宏-细观尺度下的非线性应力应变场信息。在细观尺度上,为了更好地逼近实际的复合材料结构,其增强颗粒采用不同直径和随机分布的球形进行近似。通过对不同颗粒含量的等效弹性参数的误差分析,证明了细观模型构造的合理性。此外,通过宏-细观尺度间的耦合机制,利用ABAQUS多个用户自定义子程序,实现了颗粒增强复合材料的非线性多尺度耦合分析,并提出了一套加速算法。最后据此研究了颗粒增强材料细观模型塑性演化过程对宏观力学性能的影响。由于编写的程序及分析的思路具有良好的通用性,这一工作为研究颗粒增强及其它复合材料的宏观力学性能提供了有益的参考。 相似文献
17.
Canh V. Le Phuong H. Nguyen H. Askes D. C. Pham 《International journal for numerical methods in engineering》2017,112(10):1381-1401
The macroscopic strength domain and failure mode of heterogeneous or composite materials can be quantitatively determined by solving an auxiliary limit analysis problem formulated on a periodic representative volume element. In this paper, a novel numerical procedure based on kinematic theorem and homogenization theory for limit analysis of periodic composites is developed. The total velocity fields, instead of fluctuating (periodic) velocity, at microscopic level are approximated by finite elements, ensuring that the resulting optimization problem is similar to the limit analysis problem formulated for structures, except for additional constraints, which are periodic boundary conditions and averaging relations. The optimization problem is then formulated in the form of a standard second‐order cone programming problem to be solved by highly efficient solvers. Effects of loading condition, representative volume element architecture, and fiber/air void volume fraction on the macroscopic strength of perforated and fiber reinforced composites are studied in numerical examples. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
18.
二维机织复合材料弹性常数的有限元法预测 总被引：1，自引：0，他引：1
为了预测二维机织复合材料的弹性性能,建立了有限元力学分析模型。基于二维机织复合材料的几何特征,建立了参数化的单胞模型;考虑了织物纤维束呈现出的各向异性材料特征,将有限元中材料主方向转化到纤维屈曲方向,建立其力学分析有限元模型;分析了单胞边界面保持平面假设的不足,提出了对于二维机织复合材料通用的周期边界条件,获得了更为准确的二维机织复合材料的工程弹性常数。结果表明:织物衬垫单胞边界面,在单向拉伸载荷和纯剪切载荷下,呈凹凸翘曲变形,即为周期边界;应用给出的织物参数化几何建模方法与有限元求解方法,可以精确地获得工程弹性常数,数值计算结果与实验值吻合较好。 相似文献
19.
M. Tur J. Albelda E. Nadal J. J. Ródenas 《International journal for numerical methods in engineering》2014,98(6):399-417
The use of Cartesian meshes independent of the geometry has some advantages over the traditional meshes used in the finite element method. The main advantage is that their use together with an appropriate hierarchical data structure reduces the computational cost of the finite element analysis. This improvement is based on the substitution of the traditional mesh generation process by an optimized procedure for intersecting the Cartesian mesh with the boundary of the domain and the use efficient solvers based on the hierarchical data structure. One major difficulty associated to the use of Cartesian grids is the fact that the mesh nodes do not, in general, lie over the boundary of the domain, increasing the difficulty to impose Dirichlet boundary conditions. In this paper, Dirichlet boundary conditions are imposed by means of the Lagrange multipliers technique. A new functional has been added to the initial formulation of the problem that has the effect of stabilizing the problem. The technique here presented allows for a simple definition of the Lagrange multipliers field that even allow us to directly condense the degrees of freedom of the Lagrange multipliers at element level. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
20.
Zhenfeng Zhao Wanji Chen 《International journal for numerical methods in engineering》1995,38(7):1201-1214
A new kind of approach to formulate an isotropic thin plate bending element is presented. The strain energy of the element is decomposed into two parts: an integral concerning the first strain invariant and a line integral around the elemental boundary. The former can be discretized by quasi-conforming technique1 and the latter can be directly calculated using the interpolation of the deflection and its normal slope along the element boundary. By this method, an assumed first strain invariant quadrilateral element (AFSIQ) is derived. The procedure of formulating the element and the numerical examples show that the new kind of element not only simplifies the formulation considerably but also has excellent accuracy. 相似文献