考虑损伤的修正梯度弹性理论

A Modified Gradient Elastic Theory Considering Damage

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.

To describe the material mechanics behaviors depending on microstructure,the gradient theory with significant advantages was investigated. The gradient elastic theory was combined with the damage theory to consider the influence of microstructure on material failure. Then a modified gradient elasticity damage theory was proposed,based on which the basic law of thermodynamics,the strain tensor,the damage variable and the scalar strain gradient tensor were taken as the state variables of the Helmholtz free energy. The Taylor expansion of the Helmholtz free energy function was conducted near the natural state,and the general expressions of the modified gradient elasticity damage constitutive functions were derived. The finite element code was programmed to simulate the development process of damage localization in soil specimens. The results show that,the traditional mesh dependence in numerical simulation can be removed under the modified gradient elasticity damage theory. The band of the damage localization does not concur with the damage,but occurs after the damage development to some extent.