TY - JOUR

T1 - Multiscale modeling of diffuse damage and localized cracking in quasi-brittle materials under compression with a quadratic friction law

AU - Zhao, Lun Yang

AU - Ren, Lu

AU - Liu, Ling Hui

AU - Lai, Yuan Ming

AU - Niu, Fu Jun

AU - You, Tao

N1 - Publisher Copyright: © 2024 The Author(s)

PY - 2024/11/1

Y1 - 2024/11/1

N2 - 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.

AB - 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.

KW - Homogenization-based multiscale modeling

KW - Integration algorithm

KW - Phase-field model

KW - Quadratic friction law

KW - Quasi-brittle materials

UR - http://www.scopus.com/inward/record.url?scp=85202295966&partnerID=8YFLogxK

U2 - 10.1016/j.ijsolstr.2024.113038

DO - 10.1016/j.ijsolstr.2024.113038

M3 - Article

AN - SCOPUS:85202295966

VL - 304.2024

JO - International journal of solids and structures

JF - International journal of solids and structures

SN - 0020-7683

IS - 1 November

M1 - 113038

ER -