Torsion of Functionally Graded Material Structures: An Overview

Abstract

Examining torsion in functionally graded materials (FGMs) is crucial because their properties vary spatially. FGMs with continuously graded architectures provide a robust basis for investigating mechanical behavior. Current understanding of torsional response draws on analytical, numerical, and experimental approaches. This review synthesizes how material gradation influences stress distribution, stiffness, and failure modes, and compares advances in FGM torsion across diverse models and geometries. The theoretical background is framed by classical torsion theories, including Saint-Venant, Prandtl’s membrane analogy, and Vlasov formulations. We further discuss modeling with isoparametric finite elements and summarize established homogenization schemes for FGMs. A tabulated overview of torsion-related results is also provided. The novelty of this review lies in its exclusive focus on torsion in FGMs, the systematic tabulation of prior contributions, and a coherent exposition of homogenization models and torsion theories tailored to FGM structures. To our knowledge, this is among the first reviews to focus specifically on torsion of FGM structures, distinguishing it from prior overviews that address torsion only briefly. Methodologically, we conduct a structured scoping review that screens peer-reviewed sources, classifies studies by geometry, torsion theory, homogenization scheme, and numerical strategy, and synthesizes observed trends. Finally, we present concise conclusions and future research directions. This review covers analytical, numerical, and experimental studies of torsion in FGMs, identified via a structured Google Scholar search and prioritized by citation impact and relevance.