Full-field indentation microscopy: Reimagining indentation-based characterization of soft matter with the virtual fields method

Indentation is a powerful technique for characterizing soft materials, prized for its simplicity, non-destructive nature, and compatibility with small, layered, and heterogeneous systems. However, due to a fundamental reliance on single-point force-displacement data, conventional indentation methods (e.g., atomic force microscopy) offer limited sensitivity to the constitutive behaviors most critical for understanding structure-function relationships in soft matter: anisotropy and nonlinearity. This work presents the development and validation of full-field indentation microscopy (FIM), a new, image-based material characterization framework that overcomes many of the limitations of traditional indentation methods. FIM employs volumetric imaging to capture a spatially resolved, 3D deformation field beneath and around a spherical indenter, generating a dataset that is fundamentally richer than those produced by traditional indentation methods. This dataset is then analyzed using the virtual fields method (VFM), a full-field inverse technique. The objectives of this initial work are to (1) develop an inverse analysis framework for FIM for anisotropic linear elastic materials, (2) test the feasibility of identifying hyperelastic material properties, (3) investigate the effect of an incomplete field-of-view on FIM performance, and (4) examine the robustness of FIM to experimental noise. Results indicate that FIM can enable accurate and unique identification of anisotropic and hyperelastic constitutive parameters with experimentally measurable data, redefining what can be learned from a single indentation test.