Magnetic gels with embedded micro/nano-sized magnetic particles in crosslinked polymer networks can be actuated by external magnetic fields, with changes in their internal microscopic structures and macroscopic mechanical properties. We investigate the responses of such magnetic gels to an external magnetic field, by means of coarse-grained molecular dynamics simulations. We find that the dynamics of magnetic particles are determined by the interplay of between magnetic dipole-dipole interactions, polymer elasticity and thermal fluctuations. The corresponding microscopic structures formed by the magnetic particles such as elongated chains can be controlled by the external magnetic field. Furthermore, the magnetic gels can exhibit reinforced macroscopic mechanical properties, where the elastic modulus increases algebraically with the magnetic moments of the particles in the form of $\propto(m-m_{\mathrm{c}})^{2}$ when magnetic chains are formed. This simulation work can not only serve as a tool for studying the microscopic and the macroscopic responses of the magnetic gels, but also facilitate future fabrications and practical controls of magnetic composites with desired physical properties.
