Cauchy弹性复合材料高阶连续体的识别
Identification of higher-order continua equivalent to a Cauchy elastic composite
摘要：
非均匀柯西弹性材料可以显示微观力学效应，其可以通过引入高阶弹性连续体在均匀等效材料中建模。渐近均匀化技术提供了一个优雅的和严格的路线，等价的高阶材料的评估，但往往是困难和尴尬的实际执行。另一方面，识别技术，虽然依赖于简化的假设，是直接使用。提出了一种新的等效二阶梯度Mindlin固体的识别策略，试图将渐近技术的准确性与识别方法的简单性结合起来。遵循渐进均匀化方案，整体行为通过扰动函数来定义，这些扰动函数（与渐进方案不同）在有限域上进行评估，该域是作为单元的周期性重复获得的，并受到二次位移边界条件的约束。因此，扰动函数的周期性仅在近似意义上得到满足，然而所提出的识别算法的结果被证明是相当准确的。
英文摘要：
A heterogeneous Cauchy elastic material may display micromechanical effects that can be modeled in a homogeneous equivalent material through the introduction of higher-order elastic continua. Asymptotic homogenization techniques provide an elegant and rigorous route to the evaluation of equivalent higher-order materials, but are often of difficult and awkward practical implementation. On the other hand, identification techniques, though relying on simplifying assumptions, are of straightforward use. A novel strategy for the identification of equivalent second-gradient Mindlin solids is proposed in an attempt to combine the accuracy of asymptotic techniques with the simplicity of identification approaches. Following the asymptotic homogenization scheme, the overall behaviour is defined via perturbation functions, which (differently from the asymptotic scheme) are evaluated on a finite domain obtained as the periodic repetition of cells and subject to quadratic displacement boundary conditions. As a consequence, the periodicity of the perturbation function is satisfied only in an approximate sense, nevertheless results from the proposed identification algorithm are shown to be reasonably accurate.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
