“…In this context, The combined effect of pre-existing cracks and pores on the considerable damaged region were addressed for brittle materials (Bai et al., 2022; Li et al., 2017; McDowell et al., 1993; Ouaar et al., 2007; Sisodiya and Zhang, 2022; Wasantha et al., 2020) and quasi-brittle materials (Feng and Yu, 2010) in which damage of micro-cracks evolutionary were introduced in basis of crack growth trajectory. Moreover, the effects of ductile and anisotropic material (McDowell et al., 1993; Park et al., 2021; Pensée et al., 2015; Riku et al., 2009; Satouri et al., 2022; Shen and Shao, 2014; Siddiq, 2018) porosity have been evaluated based on overall modulus of multiaxial inelastic and large strain deformation.…”