Homogenization-based multiscale crack modelling: From micro-diffusive damage to macro-cracks |
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| Authors: | Vinh Phu Nguyen Oriol Lloberas-Valls Martijn Stroeven Lambertus Johannes Sluys |
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| Affiliation: | 1. State Key Laboratory of Disaster Reduction in Civil Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China;2. School of Engineering & Computing Sciences, Durham University, United Kingdom;1. Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee 247667, Uttarakhand, India;2. Department of Civil and Environmental Engineering, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo, Japan |
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| Abstract: | The existence of a representative volume element (RVE) for a class of quasi-brittle materials having a random heterogeneous microstructure in tensile, shear and mixed mode loading is demonstrated by deriving traction–separation relations, which are objective with respect to RVE size. A computational homogenization based multiscale crack modelling framework, implemented in an FE2 setting, for quasi-brittle solids with complex random microstructure is presented. The objectivity of the macroscopic response to the micro-sample size is shown by numerical simulations. Therefore, a homogenization scheme, which is objective with respect to macroscopic discretization and microscopic sample size, is devised. Numerical examples including a comparison with direct numerical simulation are given to demonstrate the performance of the proposed method. |
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