Multiscale modeling of diffuse damage and localized cracking in quasi-brittle materials under compression with a quadratic friction law - Zhao, Lun-Yang; Ren, Lu; Liu, Ling-Hui; Lai, Yuan-Ming; Niu, Fu-Jun; You, Tao (International journal of solids and structures, 2024)
The diffuse damage and localized cracking of quasi-brittle materials (i.e., rocks and concretes) under compression can be delineated by a matrix-microcrack system, wherein a solid matrix phase is weakened by a large number of randomly oriented and distributed microcracks, and the macroscopic cracking is formed by a progressive evolution of microcracks. Several homogenization-based multiscale models have been proposed to describe this matrix-microcrack system, but most of them are based on a linear friction law on the microcrack surface, rendering a linear strength criterion. In this paper, we propose a new quadratic friction law within the local multiscale friction-damage (LMFD) model to capture the plastic distortion due to frictional sliding along the rough microcrack surface. Following that, a macroscopic Ottosen-type nonlinear strength criterion is rationally derived with up-scaling friction-damage coupling analysis. An enhanced semi-implicit return mapping (ESRM) algorithm with a substepping scheme is then developed to integrate the complex nonlinear constitutive model. The performance of LMFD model is evaluated compared to a wide range of experimental data on plain concretes, and the robustness of ESRM algorithm is assessed through a series of numerical tests. Subsequently, to effectively describe the localized cracking process, a regularization scheme is proposed by combining the phase-field model with the established LMFD model, and the discretization independent crack localization is numerically verified. •A novel local multiscale friction-damage model for quasi-brittle material is proposed.•An Ottosen-type nonlinear strength criterion is derived with up-scaling analysis.•An original enhanced semi-implicit return mapping algorithm is developed.•A regularized model is extended to describe the process of localized cracking.