The present invention provides a continuous process for solid-state expansion of a biopolymer, e.g., polylactic acid, which can be used to manufacture reduced-density thermoplastic materials with improved physical and thermal properties. By incorporating multiple stages of heating into the process as a means to regulate heat flux, unprecedented control of microstructure and crystallinity can be achieved. Thermoplastic sheets with the distinct cellular characteristics imparted by the process disclosed herein were found to be thicker and stronger than materials prepared by conventional processes. Thermoforming sheets with such characteristics enabled the production of light-weight, thermally-stable, compostable products that resist warping, and are thus suitable for a range of industrial applications.