基于应变梯度的损伤局部化研究及应用

ON THE STRAIN-GRADIENT-ENHANCED DAMAGE MODELAND ITS APPLICATION TO THE LOCALIZATION ANALYSIS

提出一种包含应变梯度项的损伤力学模型,并将其应用于材料的局部化损伤模拟预测中．有限元实现中使用C1连续高精度单元以保证包含应变梯度的影响．简单规则矩形网格情况下将结点处有限差分应变梯度结果与有限元方法结合,可避免对传统有限元程序作较大改动,同时能在不降低精度情况下提高计算效率．计算表明该梯度损伤模型可较好避免有限元在局部化模拟时的网格依赖性,预测出的局部化损伤与实际破坏情况非常相近．

This paper presents a strain-gradient-enhanced damage model for the analysis oflocalization for rock-concrete-like brittle materials. Unlike the massive work on non-local model,which focus on the spatial average of strain of other variables and a concomitant intrinsic length tosolve the problems of zero-dissipation and mesh-dependence, the model in this paper introduces thestrain gradient and an intrinsic length scalar of the material into the constitutive law and makesuse of isotropic damage. This strain-gradient-enhanced damage model is applied to the FEMsimulation of damage localization. Comparison with conventional models illustrates the problemof mesh-dependence can be properly solved by this model. Upon the implementation of F.E.M.,C1-continuum N3U18 and N4U24 elements are adopted to reserve the continuum of the first-orderof displacement, and thus the existence of strain gradient. When rectangular elements are used,the combination of nodal strain gradient determined by fiuite deferential method (F.D.M.) mixedby traditional F.E.M. avoids large modification of the original F.E.M. codes, with the advantageof high efficiency and without any large damage to the precision. Simulation of unitaxial tensionverifies the conclusion drawn above.However, several problems remain unresolved for this model. First, by introducing of straingradient, the hardening of local stiffness is intensified, which results in a higher critical value of thebifurcation hardening modulus. Second, the mechanical mechanism of intrinsic length of materialhas no clear and universal illustrations by experiments, and the interrelation between intrinsiclength and damage evaluation is not yet verified. Finally, the isotropic model of this paper is muchtoo simplified to account for the anisotropic behaviors of rock-concrete-like material, and thus amore general anisotropic strain-gradient-enhanced damage model is under study.