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With the successful application of deep learning to magnetic resonance (MR) imaging, parallel imaging techniques based on neural networks have attracted wide attention. However, in the absence of high-quality, fully sampled datasets for training, the performance of these methods is limited. And the interpretability of models is not strong enough. To tackle this issue, this paper proposes a Physics-bAsed unsupeRvised Contrastive rEpresentation Learning (PARCEL) method to speed up parallel MR imaging. Specifically, PARCEL has a parallel framework to contrastively learn two branches of model-based unrolling networks from augmented undersampled multi-coil k-space data. A sophisticated co-training loss with three essential components has been designed to guide the two networks in capturing the inherent features and representations for MR images. And the final MR image is reconstructed with the trained contrastive networks. PARCEL was evaluated on two vivo datasets and compared to five state-of-the-art methods. The results show that PARCEL is able to learn essential representations for accurate MR reconstruction without relying on fully sampled datasets.