Stochastic modeling and identification of a hyperelastic constitutive model for laminated composites
Stochastic modeling and identification of a hyperelastic constitutive model for laminated composites
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DOI：
10.1016/j.cma.2018.12.036
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发表时间：
2019-04
影响因子：
7.2
通讯作者：
B. Staber;J. Guilleminot;Christian Soize;J. Michopoulos;A. Iliopoulos
中科院分区：
文献类型：
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作者：
B. Staber;J. Guilleminot;Christian Soize;J. Michopoulos;A. Iliopoulos
本文研究了一种表征层合复合材料本构行为的新随机场模型的建立和识别。在这里，材料被建模为随机超弹性介质，其特征是空间依赖、随机和各向异性的应变能函数。后者由一组材料参数参数化，建模为非高斯随机场。从概率的角度来看，首先通过调用信息论和最大熵原理来实现构造。与有限弹性存在性定理相关的约束在公式中特别得到了考虑。定义随机场的参数的识别随后被处理。这个问题被攻击为一个两步问题，其中均值模型在第一步被校准，通过在线性化模型和文献中提出的标称值之间施加匹配。接下来，通过结合主成分分析和最大似然法求解一个逆问题来估计控制波动的其余参数。整个框架是说明考虑一个实验数据库，其中多轴测量进行了碳-环氧层压板。这项工作是朝着开发一个综合框架迈出的第一步，该框架将支持在不确定的情况下对复合材料和结构的设计、认证和资格进行决策。
In this paper, we investigate the construction and identification of a new random field model for representing the constitutive behavior of laminated composites. Here, the material is modeled as a random hyperelastic medium characterized by a spatially dependent, stochastic and anisotropic strain energy function. The latter is parametrized by a set of material parameters, modeled as non-Gaussian random fields. From a probabilistic standpoint, the construction is first achieved by invoking information theory and the principle of maximum entropy. Constraints related to existence theorems in finite elasticity are, in particular, accounted for in the formulation. The identification of the parameters defining the random fields is subsequently addressed. This issue is attacked as a two-step problem where the mean model is calibrated in a first step, by imposing a match between the linearized model and nominal values proposed in the literature. The remaining parameters controlling the fluctuations are next estimated by solving an inverse problem in which principal component analysis and the maximum likelihood method are combined. The whole framework is illustrated considering an experimental database where multi-axial measurements are performed on a carbon-epoxy laminate. This work constitutes a first step towards the development of an integrated framework that will support decision making under uncertainty for the design, certification and qualification of composite materials and structures.