Thermoplastic elastomers such as polyether-b-polyamides (or -polyesters), polyurethanes (or with -urea) and olefin block copolymers are commonly processed through a stretching process for achieving high elasticity and high toughness in their products, while the size diversity of semicrystalline microdomains of hard blocks appears as the key factor. By means of dynamic Monte Carlo simulations of strain-induced crystallization of locally concentrated and diluted crystallizable blocks alternatingly connected with noncrystallizable blocks in diblock and tetrablock copolymers, we have studied the size diversity of semicrystalline microdomains presumably raised by local concentration fluctuations of crystallizable blocks and found the dilution effects to persist from diblock to tetrablock copolymers. In the present work, we continued to study the effects of asymmetric block rigidity between crystallizable and noncrystallizable blocks on strain-induced crystallization of concentrated and diluted crystallizable blocks in diblock copolymers. The results showed that when crystallizable blocks hold higher thermodynamic rigidity than noncrystallizable blocks, the large semicrystalline domains become larger and the small semicrystalline domains become more, enhancing their size diversity. However, asymmetric kinetic rigidity has little effect. Our observations imply that industrial stretching processing could enhance the toughness of semicrystalline thermoplastic elastomers when their crystallizable blocks hold a higher thermodynamic rigidity relative to noncrystallizable blocks. Our integrated approach paved the way for a better understanding of the structure-property relationship in thermoplastic elastomers.