基于随机体积元的各向同性细纤维网络随机本构模型
Stochastic Constitutive Model of Isotropic Thin Fiber Networks Based on Stochastic Volume Elements
摘要：
薄纤维网络在自然界中广泛存在，并且可以在人造材料如纸张和包装中找到。由于遗传的随机性和尺寸依赖性，这种材料的强度是一个复杂的问题。直接的纤维级数值模拟可以提供深入了解这些网络的组成成分的作用，它们的形态，以及由它们制成的产品的强度的安排。然而，随机生成的大而细的纤维网络的直接机械模拟的特点是压倒性的计算成本。本文提出了一种预测任意尺寸各向同性细纤维网络随机力学响应的随机本构模型。该模型是基于随机体积元（SVE）与SVE尺寸特定的确定性和随机本构关系参数。网络中的随机性由单轴应变和失效强度的空间场来描述，使用多变量核函数和近似单变量概率密度函数来制定。建议的随机连续体方法显示出良好的协议相比，直接数值模拟的机械响应。此外，应变局部化模式与直接模拟中观察到的模式相匹配，这表明对失效位置的准确预测。这项工作表明，所提出的随机本构模型可以用来预测随机各向同性纤维网络的响应的任意尺寸。
英文摘要：
Thin fiber networks are widely represented in nature and can be found in man-made materials such as paper and packaging. The strength of such materials is an intricate subject due to inherited randomness and size-dependencies. Direct fiber-level numerical simulations can provide insights into the role of the constitutive components of such networks, their morphology, and arrangements on the strength of the products made of them. However, direct mechanical simulation of randomly generated large and thin fiber networks is characterized by overwhelming computational costs. Herein, a stochastic constitutive model for predicting the random mechanical response of isotropic thin fiber networks of arbitrary size is presented. The model is based on stochastic volume elements (SVEs) with SVE size-specific deterministic and stochastic constitutive law parameters. The randomness in the network is described by the spatial fields of the uniaxial strain and strength to failure, formulated using multivariate kernel functions and approximate univariate probability density functions. The proposed stochastic continuum approach shows good agreement when compared to direct numerical simulation with respect to mechanical response. Furthermore, strain localization patterns matched the one observed in direct simulations, which suggests an accurate prediction of the failure location. This work demonstrates that the proposed stochastic constitutive model can be used to predict the response of random isotropic fiber networks of arbitrary size.
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