A computational framework is established to implement time-dependent data-driven surrogate constitutive models for the homogenised mechanical response of porous elastomers at large strains. The aim is to enhance the computational efficiency of multiscale analyses through the use of these surrogate models. To achieve this, explicit finite element (FE) simulations are conducted to predict the homogenised response of a cubic unit cell of a porous elastomer, using two different viscoelastic descriptions of the parent material, subject to pseudo-random, multiaxial, non-proportional histories of macroscopic strains. The histories of homogenised variables extracted from each set of FE predictions form a training dataset, which is used to train two different surrogate models, both relying on artificial neural networks (NNs). The first model predicts the increment in macroscopic stress over a simulation step, as a function of the macroscopic stress and strain at the beginning of the step, of the prescribed macroscopic strain increment, and of the corresponding time increment. The second model uses the same inputs and outputs but tests a knowledge-based modelling approach: it relies on the aid of an additional nonlinear elastic constitutive model, which is time- and path-independent and known a priori. This model represents an existing base of knowledge which is augmented and corrected by a NN after training on viscoelastic data. The data-driven surrogate model, therefore, learns the viscoelastic behaviour of the unit cell starting from knowledge of its elastic response. The two surrogate models are found to have comparable and very high accuracies, capturing the response of the homogenised unit cell to complex loading histories. Hyperparameter optimisation shows that the second, knowledge-based model requires a simpler NN and therefore incurs a smaller computational cost.

中文翻译：

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粘弹性多孔弹性体的数据驱动均质化：前馈与基于知识的神经网络


建立了一个计算框架，用于实现多孔弹性体在大应变下的均质机械响应的瞬态数据驱动的代理本构模型。目的是通过使用这些代理模型来提高多尺度分析的计算效率。为了实现这一目标，进行了显式有限元 （FE） 模拟，以预测多孔弹性体的立方晶胞的均质响应，使用母体材料的两种不同的粘弹性描述，受制于宏观应变的伪随机、多轴、非比例历史。从每组 FE 预测中提取的同质变量的历史记录形成一个训练数据集，用于训练两个不同的代理模型，这两个模型都依赖于人工神经网络 （NN）。第一个模型预测了仿真步骤中宏观应力的增加，作为步骤开始时的宏观应力和应变、规定的宏观应变增量和相应时间增量的函数。第二个模型使用相同的输入和输出，但测试基于知识的建模方法：它依赖于一个附加的非线性弹性本构模型，该模型与时间和路径无关，并且是先验已知的。该模型代表了一个现有的知识基础，在对粘弹性数据进行训练后，它由 NN 进行增强和校正。因此，数据驱动的代理模型从了解基本单元的弹性响应开始学习其粘弹性行为。发现这两个替代模型具有可比且非常高的精度，捕获了均质晶胞对复杂加载历史的响应。 超参数优化表明，第二个基于知识的模型需要更简单的 NN，因此产生的计算成本较小。