A three-dimensional lattice architecture with a thickness hierarchy includes a first surface and a second surface separated from each other with a distance therebetween defining a thickness of the three-dimensional lattice architecture; a plurality of angled struts extending along a plurality of directions between the first surface and the second surface; a plurality of nodes connecting the plurality of angled struts with one another forming a plurality of unit cells. At least a portion of the plurality of angled struts are internally terminated along the thickness direction of the lattice structure and providing a plurality of internal degrees of freedom towards the first or second surface of the lattice architecture.