<p>Discrete element method and theoretical analyses were performed to investigate the evolution characteristics of dynamic normal stress on a silo wall with hyperbolic hopper. Results show that the hyperbolic hopper promotes the development of stagnant zone, which avoids the concentration of large dynamic normal stress on a silo wall effectively. Compared with the conical hopper, the hyperbolic hopper reduces the peak normal stress by 14.42%, and increases the range of large normal stress from 0.2 to 0.5&#xa0;m. The large stagnant zone causes a flow zone with large velocity gradient to develop, which drives the granular materials to flow out from the hyperbolic hopper in an orderly manner, thereby weakening the oscillation strength of the granular materials against silo wall. The hyperbolic hopper weakens the inertial force generated by the instantaneous arch during its formation and breaking, resulting in reducing the dynamic normal stress on silo wall with a hyperbolic hopper.</p> Graphical Abstract <p></p>