Please help editing the following sentencesAn extended multi-material topology optimization method is developed for the design of spatially graded lattice structuresThe secondary solid material phase

An extended multi-material topology optimization method has been developed to design spatially graded lattice structures.

The secondary "solid" material phase is made up of a predefined lattice type with mechanical behaviors that vary, controlled by a gradient variable.

The method enables the creation of designs using hybrid material types, including solid, void, and spatially varying lattices of one or multiple types.

The gradient variables' lower and upper bounds can be flexibly controlled, providing greater design freedom