RESEARCH PAPER Micromechanical analysis of non-coaxiality between stress and strain increment in granular materials Jingshan Shi 1 • Peijun Guo 2 • Dieter Stolle 2 Received: 24 December 2018 / Accepted: 28 January 2020 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract It is known that non-coaxiality between the directions of the principal stresses and the principal plastic strain increments in granular material is physically resulted from the material and mechanical anisotropy as well as their evolutions. A novel study was conducted to verify the contributions of the material and mechanical anisotropies to the magnitude of non- coaxiality during the rotation of the principal stress orientation. Micromechanical analysis indicates that the non-coaxial behavior can occur in a granular assembly with mostly non-sliding contacts acting. Moreover, the magnitude of non- coaxiality is a function of the stress level, the ratio of contact stiffness, the material and mechanical anisotropy as well as their evolutions. This has been confirmed by numerical simulation. The numerical results indicate that the non-sliding interparticle connectivity is one of the dominant sources of non-coaxiality. The interparticle sliding has been found to reduce the magnitude of the non-coaxiality. Keywords Fabric anisotropy  Granular material  Mechanical anisotropy  Micromechanical analysis  Non-coaxiality  Simple shear 1 Introduction Non-coaxiality in cohesionless material refers to the divergence between the principal orientation of the stress tensor and that of plastic strain increment tensor, which has been observed at a small strain level in both experimental studies and numerical simulations, even for initially iso- tropic specimens [1, 9, 12, 14, 16, 21, 24, 32, 33, 44, 49]. Attempts have been made to quantify non-coaxiality and its application to constitutive models [9, 11, 14, 27, 48]. However, most quantifications of non-coaxiality are based on empirical observation; see, for example, Symes et al. [42], Miura et al. [17] and Cai et al. [5]. Owing to the discrete nature of granular materials, the macroscopic behavior of a granular assembly can be regarded as an integration or homogenization of all interparticle activities over the spatial arrangement of particles and their con- nectivity which is also known as the microstructure [40]. Therefore, the stress tensor (strain increment tensor) can be obtained from contact force (relative displacement) toge- ther with the branch vectors that characterize the inter- particle connectivity [2, 3, 7, 10, 29]. Hence, the non- coaxiality between the stress and strain increment is inevitably connected with the microstructure as well as the particle-level activities such as interparticle sliding. Coaxial plastic theory assumes that the material is iso- tropic, inferring that the initial fabric anisotropy within a granular material could produce non-coaxiality between the stress and strain increments. Following this line, Miura et al. [17] pointed out that the initial fabric anisotropy has a significant effect on the shear deformation during the rotation of major principal stress that is not coaxial with the strain increment. In a series of DEM simulations, for example simple shear tests, Thornton and Zhang [43] found that the evolution of the angle of non-coaxiality depends on the initial stress state as well as stress path. According to Shi and Guo [38, 39], the initial stress ratio can be related to the initial fabric anisotropy via the stress–fabric rela- tions. Therefore, the magnitude of non-coaxiality could be & Jingshan Shi shiquanxj@outlook.com 1 School of Civil Engineering, Southeast University, Nanjing 210 000, China 2 Department of Civil Engineering, McMaster University, Hamilton, ON L8S 4L7, Canada 123 Acta Geotechnica https://doi.org/10.1007/s11440-020-00923-x