Van Den Abeele K, Schubert F, Aleshin V, Windels F, Carmeliet J
Interdisciplinary Research Center, Catholic University Leuven Campus Kortrijk, Etienne Sabbelaan 53, B-8500 Kortrijk, Belgium.
Ultrasonics. 2004 Apr;42(1-9):1017-24. doi: 10.1016/j.ultras.2003.12.021.
As a rule, problems of wave propagation in finite media with non-uniform spatial distribution of material properties can only be tackled by numerical models. In addition, the modeling of damage features in a material requires the introduction of locally non-linear and--more important--non-unique equations of state. Using a multiscale approach, we have implemented a non-linear hysteretic stress-strain relation based on the Preisach-Mayergoyz (PM) model, into a numerical elastodynamic finite integration technique program, which has originally been developed for linearly elastic wave propagation in inhomogeneous media. The simulation results show qualitatively good agreement with data of non-linear resonant bar experiments in homogeneously non-linear and hysteretic media. When the PM density distribution of hysteretic units at the mesoscopic level is not uniform and/or confined to a finite area in stress-stress space, the response at high amplitude excitation tend to deviate from the quasi-analytical results obtained in the case of a uniform PM-space density. Localized microdamage features in an intact medium can be modeled by conceiving finite zones with pronounced hysteretic stress-strain relations within a "linear" surrounding. Forward calculations reveal a significant influence of the amplitude dependent resonance behavior on the location (edge versus center of a bar), the extend (width of the zone) and the degree (density of hysteretic units) of damage.
通常，对于材料特性具有非均匀空间分布的有限介质中的波传播问题，只能通过数值模型来解决。此外，对材料中的损伤特征进行建模需要引入局部非线性且更重要的是非唯一的状态方程。我们采用多尺度方法，将基于Preisach-Mayergoyz（PM）模型的非线性滞后应力-应变关系，应用到一个数值弹性动力学有限积分技术程序中，该程序最初是为非均匀介质中的线性弹性波传播而开发的。模拟结果与均匀非线性和滞后介质中的非线性共振棒实验数据在定性上吻合良好。当细观层面滞后单元的PM密度分布不均匀和/或局限于应力-应力空间中的有限区域时，高振幅激励下的响应往往会偏离均匀PM空间密度情况下获得的准解析结果。完整介质中的局部微损伤特征可以通过在“线性”环境中设想具有明显滞后应力-应变关系的有限区域来建模。正向计算表明，与振幅相关的共振行为对损伤的位置（棒的边缘与中心）、范围（区域宽度）和程度（滞后单元密度）有显著影响。
