关于非线性非局部应变梯度模型的探讨

考虑线性软化模型不能反映材料软化变形复杂性的不足,选取高斯正态分布函数作为非局部理论的权函数,同时采用指数型应力衰减模式考虑软化的非线性特征,进一步地将这种非线性非局部理论与采用Laplace算子考虑塑性应变梯度效应的塑性梯度理论相结合,建议了一种非线性非局部应变梯度模型,并据此针对各向同性单向拉伸杆的力学响应进行了分析,将计算结果与线性软化模型进行了对比.结果表明:在非线性软化模型中,尽管塑性应变分布形式与线性软化模型的相同,但塑性应变同时依赖于应力降与破坏极限应变,两者最大应变是不同的.

Exploration of non-linear and non-local strain gradient model

Considering deficiency of linear softening model which can not reproduce distortion complexity of geo-material, a non-linear and non-local model of plastic-strain gradient is presented by incorporating the non-linear and non-local theory with the theory of plastic strain gradient. The model uses an exponential pattern of strain softening and weighted by Gaussian distribution function while the effect of plastic strain gradient is taken into account. The mechanical characteristics of isotropic bar under uniaxial tension are examined by the proposed model and analysis results of the proposed model are compared with those of the linear-softening model. It is indicated that the plastic strain is dependent on both the rate of stress drop and the failure strain. Although the variation patterns of plastic strain in both linear and non-linear softening models are almost identical, the maximum plastic strains of both models are different. Furthermore, in the non-linear softening model, the plastic strain decays with the relative distance of the point under consideration with the center of the plastic zone.