## 1 Introduction
Tensile testing revealed that the physical fragmentation of the amorphous phase in HAP consumed substantial energy, which reinforced and toughened the gel matrix. [PERSON] et al. [19]. successfully fabricated a ceramic/biopolymer hybrid hydrogel biomimetic osteosynthesis membrane using electrospinningning technology. This membrane induced in situ mineralization and controlled the localized, long-term release of ions, thereby promoting osteogenic differentiation and angiogenesis. [PERSON] et al. [20] prepared bioactive nanoparticles/gelatin composite hydrogel osteogenic materials through 3D printing. In summary, ceramic/polymer composites offer a wide range of applications and development potential due to their diverse and excellent properties, meeting the various needs of modern industry and science and technology. Ceramic materials such as calcium carbonate (CaCO\({}_{3}\)) have received widespread attention because of their biocompatibility in the human body, which makes them very suitable for the field of biomedicine [21]. These applications mainly include using artificial bones and cartilage substitutes, promoting tissue regeneration and repair, and promoting drug delivery [22]. Chitosan is a natural biopolymer extracted from chitin. It has aroused great interest due to its biocompatibility, biodegradability, and the ability to form hydrogels. This three-dimensional hydrogel network provides excellent matrix conditions for the nucleation and growth of inorganic nanocrystals [23; 24; 25; 26; 27]. In this study, we draw inspiration from the mineralized organic matrices found in organisms to develop an innovative method for the in situ growth of CaCO\({}_{3}\) nanocrystals in chitosan hydrogels. This approach, grounded in biomimetic biomineralization, effectively strengthens the hydrogel. The chitosan hydrogel network synthesized in the experiment mimics the organic matrix in organisms by creating an environment that restricts ionic diffusion and controls crystal formation. Compared to direct ceramic/polymer blending, this in situ growth technique produced more uniformly distributed nanoparticles, reduced agglomeration, and achieved a structure that more closely resembles natural biological tissues. This research is significant for understanding the mechanism of crystal growth in organic three-dimensional networks and exploring the potential medical applications of hydrogel materials. By combining 3D printing technology with ion diffusion mechanism, we successfully prepared a chitosan/CaCO\({}_{3}\) hydrogel, which facilitated the formation of CaCO\({}_{3}\) nanocrystals in the hydrogel matrix. This method allows for controlled mineral deposition within polymers, thereby forming a composite structure that mimics natural mineralized tissue. We investigated the size, morphology, and distribution of CaCO\({}_{3}\) nanocrystals across various mineralization reactions, as well as their impact on the mechanical properties of composite hydrogels. Our findings demonstrate that the incorporation of CaCO\({}_{3}\) nanocrystals into the chitosan hydrogel matrix significantly enhances the mechanical strength and stiffness of the hydrogel, making it more suitable for load-bearing applications in tissue engineering.