Geometric Nonlinearity as an Information Amplifier: Non-Destructive Stiffness Characterization of Functionally Graded Beams

Abstract Functionally Graded Beams (FGBs) offer transformative potential for lightweight, high-performance designs; however, their widespread adoption is constrained by the difficulty of verifying manufactured material properties. This paper addresses the fundamental challenge of non-destructively characterizing the spatially varying stiffness in FGBs—an ill-posed inverse problem that conventional small-deflection methods fail to resolve due to insufficient sensitivity. We introduce a novel paradigm that deliberately exploits geometric nonlinearity as an information amplifier. By driving a cantilever FGB into the large-deflection regime, we break the kinematic symmetry inherent in linear approaches, dramatically enhancing the observability of internal stiffness gradients. The methodology is established through a rigorous Digital Twin framework, integrating a derived analytical model for large-deflection kinematics with high-fidelity nonlinear finite element simulations. This validated forward solver enables a comprehensive feasibility study using synthetic data. The inverse problem is solved via a two-stage computational strategy: a deterministic optimization scheme successfully reconstructs complex stiffness profiles under ideal conditions, while a probabilistic Bayesian inference framework rigorously quantifies the identification uncertainty in the presence of realistic measurement noise. Results demonstrate the method's capability to characterize diverse grading patterns, including symmetric distributions, and confirm the property of scale invariance—effectively decoupling the relative stiffness gradient from the absolute material modulus. This study conclusively establishes that combining large deformation mechanics with statistical uncertainty quantification provides a robust, physics-informed tool for the quality control and assurance of advanced graded structures.