Stochastic modeling of the Ogden class of stored energy functions for hyperelastic materials: the compressible case
Stochastic modeling of the Ogden class of stored energy functions for hyperelastic materials: the compressible case
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超弹性材料 Ogden 类储能函数的随机建模：可压缩情况
DOI：
10.1002/zamm.201500255
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
J. Guilleminot
中科院分区：
文献类型：
--
作者：
B. Staber;J. Guilleminot
本文研究了可压缩超弹性材料的响应函数在一定尺度上表现出不确定性的问题。奥格登类的储能函数的参数概率表示的建设是专门考虑和制定的信息论的框架内。整个方法依赖于最大熵的原则，这是调用下产生的存在定理和线性弹性的一致性的约束。至于不可压缩的情况下，在其他地方讨论，推导基本上涉及的随机体积和剪切模量，这是统计依赖的随机变量在本例中的一些变量的条件。明确的建设的概率措施首先解决在最一般的设置。随后，提供了经典Neo-Hookean和Mooney-Rivlin材料的特定结果。概率表示的显著特征最终通过前向蒙特卡罗模拟突出显示。特别是，可以看出，该模型允许再现典型的实验趋势，如在大范围内的方差增加。还提出了随机多尺度分析，其中通过所提出的方法考虑了基质相本构律的不确定性。
This paper is devoted to the modeling of compressible hyperelastic materials whose response functions exhibit uncertainties at some scale of interest. The construction of parametric probabilistic representations for the Ogden class of stored energy functions is specifically considered and formulated within the framework of Information Theory. The overall methodology relies on the principle of maximum entropy, which is invoked under constraints arising from existence theorems and consistency with linearized elasticity. As for the incompressible case discussed elsewhere, the derivation essentially involves the conditioning of some variables on the stochastic bulk and shear moduli, which are shown to be statistically dependent random variables in the present case. The explicit construction of the probability measures is first addressed in the most general setting. Subsequently, particular results for classical Neo‐Hookean and Mooney‐Rivlin materials are provided. Salient features of the probabilistic representations are finally highlighted through forward Monte‐Carlo simulations. In particular, it is seen that the models allow for the reproduction of typical experimental trends, such as a variance increase at large stretches. A stochastic multiscale analysis, where uncertainties on the constitutive law of the matrix phase are taken into account through the proposed approach, is also presented.