SSR =Solid State Relay, which is what you asked for. However, as you have found, most SSR are used in AC applications where they inherently turn off when the control voltage is removed.
In a DC application, an AC circuit using a triac or SCR will not work unless you have a method of disrupting the current to turn them off. When turned on they will stay in the on condition until the current being passed drops below sustaining level which may be only a few mA.
If you want true relay operation where you use one voltage to switch another larger one, consider MOSFET or IGBT designs. All electronic relays will drop some voltage so be careful with heat dissipation at 100A.
Brian.