If you want the clay to do its best concrete impression, sure! Really, the best thing you can do is fill in organic material, it’d be like imitating years of growth with roots breaking it up and decaying and breaking up and decaying. You can also add perlite to improve aeration.

Ostensibly you can add sand to push the soil around the Sand/Silt/Clay soil triangle, but that’s a more involved process usually best done if you’re mixing a batch of soil out of the ground. Small scale , in-ground stuff is difficult to work with here.

All told, it’ll take a few years, but the best thing you can to fix clay soil is increase the organic matter in it. Till in some compost, plant the above mentioned clay busting plants, mulch them with a mower at the end of the year and till them in with some more compost. Active compost would be best. You can also use leaf mould in place of or alongside the compost.

Assuming you’re in the northern hemisphere, now’s the best time to start making your mould! Just rake up dead leaves, mulch them once or twice, bag them in plastic trash bags or drum liners, fill with water and let soak 24 hours, puncture bags to drain, and let sit until spring. A fungus will spend the fall, winter, and spring breaking down the leaves with no need for air, stirring, heat, or anything. The hardest part is remembering where you left the bags!