“…Even though a large amount of experiments have been conducted, there is no suggestion of the material design in practical use to control the crack width, which is important in civil engineering. The cracking phenomena of materials [Hamdia, Silani, Zhuang et al (2017); Nanthakumar, Lahmer, ; Vu-Bac, Lahmer, ; Zhuang, Huang, Rabczuk et al (2014)] have been investigated widely including efficient remeshing techniques [Areias, Reinoso, Camanho et al (2018); Areias and Rabczuk (2017); Areias, Rabczuk and Msekh (2016); Areias, Msekh and Rabczuk (2016); Areias, Rabczuk and Camanho (2014); Areias, Rabczuk and Dias-da-Costa (2013); Areias and Rabczuk (2013); Anitescu, Hossain and Rabczuk (2018)], phase field methods [Badnava, Msekh, Etemadi et al (2018); Msekh, Cuong, Zi et al (2017)], multiscale methods for fracture [Budarapu, Gracie, Bordas et al (2014); Budarapu, Gracie, Yang et al (2014); Talebi, Silani and Rabczuk (2015); Talebi, Silani, Bordas et al (2014)], peridynamics [Ren, Zhuang and Rabczuk (2017); Ren, Zhuang, Cai et al (2016)], DEM [Zhou, Zhu, Ju et al (2017)], meshfree methods [Amiri, Milan, Shen et al (2014); Amiri, Anitescu, Arroyo et al (2014); Rabczuk, Gracie, Song et al (2010); Rabczuk, Areias and Belytschko (2007); Zhuang, Cai and Augarde (2014); Zhuang, Zhu and Augarde (2014)], the phantom node method [Chau-Dinh, Zi, Lee et al (2012)], the smooth extended finite element method [Chen, Rabczuk, Bordas et al (2012)] as well as other partition of unity based methods like the extended isogeometric analysis [Ghorashi, Valizadeh, Mohammadi et al (2015);Nguyen-Thanh, Valizadeh, Nguyen et al (2015); Nguyen-Xuan, Liu, Bordas et al (2013)]. However, the healing effects of such materials are not well simulated.…”