非局部核与应变局部化问题解的相关性

Correlation Between Nonlocal Kernel Function and Strain-Localization Solution

在非局部理论框架下,研究了应变局部化现象模拟结果与所用非局部核函数的相关性。首先,在非局部损伤理论框架中,提出一个以应变与损伤参量为独立变量的新的自由能泛函形式,并由热力学定律,推导非局部弹性损伤本构方程。然后,通过二次线性化的方法,给出一维情况下的支配方程。最后,给出对应不同形式非局部核的损伤局部化现象模拟结果。通过与模拟结果的比较,分析非局部核与解的相关性,得到了一些有价值的结论。

Based on the nonloeal theory the correlation is studied between the nonlocal kernel function and the simulating result for the strain-localization behavior of brittle materials. Firstly, a new free energy function by using strain and damage as its independent variables is proposed in the framework of the nonlocal damage theory, and the nonlocal elastic damage constitutive equation is deduced according to the thermodynamics principles. By using the quadratie-linearization method, the governing equations of one-dimensional nonlocal brittle damage model are established. Finally, different nonlocal kernel functions are simulated. Compared with the simulation results, the correlation between the nonlocal kernel and the localization solution is discussed. Some valuable conclusions can be obtained.