Theoretical models of fracture deformation based on aperture distribution Haichun Ma, Peichao Feng, Jiazhong Qian, Xiaohui Tan, Jingping Wang, Lei Ma and Qiankun Luo Eur. Phys. J. Plus, 137 8 (2022) 898 Published online: 06 August 2022 DOI: 10.1140/epjp/s13360-022-03129-0