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首页> 外文期刊>Journal of the Mechanics and Physics of Solids >Iterated linear comparison bounds for viscoplastic porous materials with 'ellipsoidal' microstructures
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Iterated linear comparison bounds for viscoplastic porous materials with 'ellipsoidal' microstructures

机译：具有“椭圆形”微结构的粘塑性多孔材料的迭代线性比较边界

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摘要

Analytical estimates are obtained for the effective constitutive response of porous viscoplastic materials consisting of aligned ellipsoidal voids that are distributed randomly with "ellipsoidal" symmetry in the matrix material. These estimates are obtained by means of a novel iterative homogenization strategy recently proposed by Ponte Castaneda (2012), and can be shown to be bounds for certain classes of multi-scale microstructures. By design, the resulting constitutive model agrees exactly with the earlier "variationa! linear comparison" model at the first iteration (N=1), and provides estimates that get progressively more accurate as the number of iterations increases (N→∞), especially for high-triaxiality loading conditions, and low porosity and strain-rate sensitivity. However, in practice, a small number of iterations (N≈10) is sufficient to get very accurate results. It is important to emphasize that, unlike other models that have been proposed in the literature, the new model requires no fitting parameters, solely depending on the properties of the matrix phase and microstructural information, such as the porosity, the average void shape and orientation, as well as the generally different shape and orientation of their distribution. Results are given for the yield and gauge surfaces of ideally plastic and power-law viscoplastic porous materials for the special cases of aligned spheroidal and ellipsoidal voids, and the results are compared with available numerical results and with the results of other models. Compared to available numerical results, the new estimates are found to be quite accurate, while they also provide more flexibility than competing models in terms of the characterization of the microstructure. In particular, it was found that the effect of different shapes for the average pore shape and distribution on the yield surfaces of the porous materials can be significant at high triaxialities, even for very small porosities. In addition, consistent estimates are obtained for the average strain rate in the voids, and explicit results have been computed for initially spherical voids, which exhibit a strong effect of the triaxiality, especially at low porosities and strain-rate sensitivities.
机译：对于多孔粘塑性材料的有效本构响应获得了分析估计，该材料由对准的椭圆形空隙组成，该椭圆形空隙以“椭圆形”对称性随机分布在基质材料中。这些估计是通过Ponte Castaneda（2012）最近提出的一种新颖的迭代均化策略获得的，并且可以证明对于某些类的多尺度微结构是有界的。通过设计，生成的本构模型与第一次迭代（N = 1）时的早期“变量线性比较”模型完全吻合，并提供随着迭代次数增加（N→∞）而变得越来越准确的估计值，尤其是适用于高三轴载荷条件，低孔隙率和应变率敏感性。但是，实际上，少量的迭代（N≈10）足以获得非常准确的结果。需要强调的是，与文献中提出的其他模型不同，新模型不需要拟合参数，仅取决于基质相的性质和微观结构信息（例如孔隙率，平均空隙形状和取向） ，以及它们的分布通常具有不同的形状和方向。给出了球状和椭球形对准空隙的特殊情况下理想塑性和幂律粘塑性多孔材料的屈服面和规范面的结果，并将结果与​​可用的数值结果和其他模型的结果进行了比较。与可用的数值结果相比，新的估计值被认为是非常准确的，同时在微观结构的表征方面，它们也比竞争模型更具灵活性。特别地，发现在高三轴度下，即使对于非常小的孔隙率，不同形状对于多孔材料的屈服表面上的平均孔形状和分布的影响也可能是显着的。另外，对空隙中的平均应变率获得了一致的估计，并且对最初的球形空隙计算出了明确的结果，这些结果显示出三轴性的强烈影响，尤其是在低孔隙率和应变率敏感性的情况下。

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