The aim of this work is to develop a neural network for modelling incompressible hyperelastic behaviour with isotropic damage, the so-called Mullins effect. This is obtained through the use of feed-forward neural networks with special attention to the architecture of the network in order to fulfil several physical restrictions such as objectivity, polyconvexity, non-negativity, material symmetry and thermodynamic consistency. The result is a compact neural network with few parameters that is able to reconstruct the hyperelastic behaviour with Mullins-type damage. The network is trained with artificially generated plane stress data and even correctly captures the full 3D behaviour with much more complex loading conditions. The energy and stress responses are correctly captured, as well as the evolution of the damage. The resulting neural network can be seamlessly implemented in widely used simulation software. Implementation details are provided and all numerical examples are performed in Abaqus.

中文翻译：

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使用物理增强神经网络恢复 Mullins 损伤超弹性行为


这项工作的目的是开发一个神经网络，用于模拟具有各向同性损伤的不可压缩超弹性行为，即所谓的 Mullins 效应。这是通过使用前馈神经网络实现的，特别注意网络的架构，以满足几个物理限制，如客观性、多凸性、非负性、材料对称性和热力学一致性。结果是一个参数很少的紧凑神经网络，能够重建具有 Mullins 型损伤的超弹性行为。该网络使用人工生成的平面应力数据进行训练，甚至可以在更复杂的载荷条件下正确捕获完整的 3D 行为。能量和应力响应以及损伤的演变都被正确捕获。生成的神经网络可以在广泛使用的仿真软件中无缝实现。提供了实施详细信息，所有数值示例都在 Abaqus 中执行。