共查询到18条相似文献,搜索用时 156 毫秒
1.
梯度弹性理论在描述材料微结构起主导作用的力学行为时具有显著优势,将其与损伤理论相结合,可在材料破坏研究中考虑微结构的影响.基于修正梯度弹性理论,将应变张量、应变梯度张量和损伤变量作为Helmholtz自由能函数的状态变量,并在自然状态附近对自由能函数作Taylor展开,进而由热力学基本定律,推导出修正梯度弹性损伤理论本构方程的一般形式.编制有限元程序,模拟土样损伤局部化带的发展演化过程.结果表明,修正梯度弹性损伤理论消除了网格依赖性;损伤局部化带不是与损伤同时发生,而是在损伤发展到一定程度后再逐渐显现出来. 相似文献
2.
3.
4.
5.
6.
7.
基于弹塑性力学和损伤力学理论,将岩土材料视为孔隙-裂隙双重介质,假设孔隙介质不发生损伤,而裂隙介质随应变的增加发生损伤,建立了单轴作用下岩土类材料的双重介质本构模型隐式表达式,并利用Newton迭代法得出了材料的全程应力-应变曲线.分析结果表明,岩土材料中裂隙空间展布的多态性(均匀展布、集中展布和随机展布)是岩土材料本构关系千变万化的根本原因.由于双重介质本构模型将岩土材料的弹性主体(孔隙介质部分)和损伤主体(裂隙介质部分)分化开来,对于研究岩土或含损伤材料的破坏具有实用价值和理论意义. 相似文献
8.
自由边问题一直是三维弹性力学中的难题,通常很难满足自由边上一个正应力和两个剪应力都等于0.基于三维弹性力学基本方程和状态空间方法,引入自由边界位移函数并考虑全部弹性常数,建立了正交异性具有自由边单层和叠层板的状态方程.对状态方程中的变量以级数形式展开,通过边界条件的满足精确求解任意厚度具有自由边叠层板的位移和应力,此解满足层间应力和位移的连续条件.算例计算表明,采用引入的位移函数形式,简化了计算过程并且采用较少的级数项可以获得收敛解.与有限元方法计算结果进行了对比,可以得到较高精度的数值结果.其解可以作为其它数值方法和半解析方法的参考解. 相似文献
9.
形状记忆合金(SMA)一直被作为智能材料开发,并被用于阻尼器、促动器和智能传感器元件.形状记忆合金(SMA)的一项重要特性,是它具有恢复在机械加卸载周期下产生的大变形而不表现出永久变形的能力.该文旨在介绍一种由应力产生的相变且可以描述马氏体和奥氏体之间的超弹性滞回环现象本构方程.形状记忆合金的马氏体系数假设为应力偏张量的函数,因此形状记忆合金在相变过程中锁定体积.本构模型是在大变形有限元的基础上执行的,采用了现时构型Lagrange大变形算法.为了方便地使用Cauchy应力和线性应变本构关系,使用了与旋转无关的Jaumann应力增率计算应力.数值分析结果表明,相变引起的超弹性滞回环可以有效地通过该文提出的本构方程和大变形有限元模拟. 相似文献
10.
11.
本文提出一种脆性材料损伤应变软化的数学模型,本构方程是基于热力学原理建立的。虽然是各向同性损伤模型,用标量表示损伤状态,但通过等效损伤应变的定义,能区分拉伸、压缩和剪切载荷对材料损伤的不同响应。由于本构模型中的多数参数均可由材料材料手册简单确定,便于工程应用。 相似文献
12.
The expressions of the constitutive equations of dilute polymer solutions, as predicted by the main microscopic rheological models, are shown to be in agreement with these derived from extended irreversible thermodynamics. Accord between the thermodynamic and Boltzmann microscopic expressions of entropy is also completed for steady state flows. 相似文献
13.
A flexoelectric peridynamic (PD) theory is proposed. In the PD framework, the formulation introduces a nanoscale flexoelectric coupling that entails non-uniform strain in centrosymmetric dielectrics. This potentially enables PD modeling of a large class of phenomena in solid dielectrics involving cracks, discontinuities etc. wherein large strain gradients are present and the classical electromechanical theory based on partial differential equations do not directly apply. PD electromechanical equations, derived from Hamilton's principle, satisfy the global balance laws. Linear PD constitutive equations reflect the electromechanical coupling effect, with the mechanical force state affected by the polarization state and the electrical force state in turn by the displacement state. An analytical solution to the PD electromechanical equations is presented for the static case when a point mechanical force and a point electric force act in an infinite 3D solid dielectric. A parametric study on how different length scales influence the response is undertaken. In addition, the model is extended to incorporate damage using phase field – an order parameter, supplemented with a PD bond breaking criterion to study flexoelectric effects in damage and fracture problems. To demonstrate the performance of our proposal, we first simulate, considering small flexoelectricity effect and no damage, an externally pressured 2D flexoelectric disk subjected to a potential difference between the inner and outer surfaces and compare the results with existing solutions in the literature. Next, we simulate a plate with a central pre-crack under tension considering damage and flexoelectricity effects, and study the effect of various constitutive parameters on the damage evolution. We also furnish a classical derivation of phase field based flexoelectricity in Appendix I. 相似文献
14.
P. M. A. Areias J. M. A. Csar de S C. A. Conceio Antnio 《Finite Elements in Analysis and Design》2003,39(13):1191-1235
This paper describes the formulation of an implicit gradient damage model for finite strain elastoplasticity problems including strain softening. The strain softening behavior is modeled through a variant of Lemaitre's damage evolution law. The resulting constitutive equations are intimately coupled with the finite element formulation, in contrast with standard local material models. A 3D finite element including enhanced strains is used with this material model and coupling peculiarities are fully described. The proposed formulation results in an element which possesses spatial position variables, nonlocal damage variables and also enhanced strain variables. Emphasis is put on the exact consistent linearization of the arising discretized equations.
A numerical set of examples comparing the results of local and the gradient formulations relative to the mesh size influence is presented and some examples comparing results from other authors are also presented, illustrating the capabilities of the present proposal. 相似文献
15.
To construct constitutive equations for hyperelastic materials, one increasingly often proposes new strain measures, which result in significant simplifications and error reduction in experimental data processing. One such strain measure is based on the upper triangular (QR) decomposition of the deformation gradient. We describe a finite element method for solving nonlinear elasticity problems in the framework of finite strains for the case in which the constitutive equations are written with the use of the QR-decomposition of the deformation gradient. The method permits developing an efficient, easy-to-implement tool for modeling the stress–strain state of any hyperelastic material. 相似文献
16.
17.
Granular frictional materials show a complex stress‐strain behaviour depending on the stress state and the load history. Furthermore, biaxial experiments exhibit the occurrence of shear band phenomena as the result of the localization of plastic strains. It is well known that the onset of shear bands is associated with microrotations of the granular microstructure, which has a significant influence on the macroscopic behaviour. Consequently, the macroscopic material must result in a micropolar model, which incorporates rotational degrees of freedom. After the formulation of the constitutive equations and the numerical implementation, it is necessary to determine all required material parameters. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
18.
In this paper, Mindlin’s second strain gradient theory is formulated and presented in an arbitrary orthogonal curvilinear coordinate system. Equilibrium equations, generalized stress-strain constitutive relations, components of the strain tensor and their first and second gradients, and the expressions for three different types of traction boundary conditions are derived in any orthogonal curvilinear coordinate system. Subsequently, for demonstration, Mindlin’s second strain gradient theory is represented in the spherical coordinate system as a highly-practical coordinate system in nanomechanics. Second strain gradient elasticity have been developed mainly for its ability to capture the surface effects in the presence of micro-/nano- structures. As a numeric illustration of the theory, the surface relaxation of spherical domains in Mindlin’s second strain gradient theory is considered and compared with that in the framework of Gurtin–Murdoch surface elasticity. It is observed that Mindlin’s second strain gradient theory predicts much larger value for the radial displacement just near the surface in comparison to Gurtin–Murdoch surface elasticity. 相似文献