Model reduction techniques for quantitative nano-mechanical AFM mode

Abstract

A recently developed atomic force microscope (AFM) process, the Peak-Force Quantitative Nanomechanical Mapping (PF-QNM) mode, allows to probe over a large spatial region surface topography together with a variety of mechanical properties (e.g. apparent modulus, adhesion, viscosity). The resulting large set of data often exhibits strong coupling between material response and surface topography. This letter proposes the use of a proper orthogonal decomposition (POD) technique to analyze and segment the force-indentation data obtained by the PF-QNM mode in a highly efficient and robust manner. Two samples illustrate the proposed methodology. In the first one, low density polyethylene nanopods are deposited on a polystyrene film.The second is made of carbonyl iron particles embedded in a polydimethylsiloxane matrix. The proposed POD method permits to seamlessly identify the underlying phase constituents in both samples and decouple them from the surface topography by compressing voluminous force-indentation data into a subset with a much lower dimensionality.

Insights into the viscohyperelastic response of soft magnetorheological elastomers: Competition of macrostructural versus microstructural players

“…For lower particle volume fractions, an underestimation of the stress-strain curve is observed in most of the cases. This fact may be attributed to particle clustering in the actual experimental specimens (see [61]), which are not taken into account in the creation of the numerical microstructures of the present study. Moreover, it can be observed from Figure 5 that the SC arrangements show a stiffer behavior, which is attributed to the special alignment of the particles in the loading direction and reach a compression buckling-type instability.…”

“…In the present case, the goal is to study the qualitative features of soft MREs and the relative effect of the matrix viscoelasticity upon the coupled magneto-mechanical response. For that reason, we will use in the next section relatively simplified random and periodic particle distributions, as compared to the actual experiments that may exhibit particle clustering (see for instance recent work exhibiting particle clusters in MREs via an AFM surface analysis [61]).…”

PeakForce AFM Analysis Enhanced with Model Reduction Techniques

“…A brief presentation of PeakForce AFM is first presented. Interested readers can refer to [ 10 , 22 ] for more details.…”

“…In the previous work [ 22 ], proper orthogonal decomposition (POD [ 23 ], also known as SVD [ 24 ] or PCA [ 25 ]) was shown to be an efficient way to ‘visually’ uncover these “state variables” by offering a low-dimensional representation of the entire force-mechanical data. By selecting the most relevant POD modes as the subset to represent the initial AFM data, in the subspace generated by POD (usually 2D or 3D representations), the user can have an intuitive visual inspection of the corresponding data manifold, which is of great practical interest.…”

“…The present work presents the use of the above-mentioned “classical” algorithms, as available in different toolboxes, (Matlab was used in this study), to the novel context of voluminous data achieved from PF-QNM AFM measurements. After appropriate editing and formatting, the raw initial data is firstly compressed into a subset with a much lower dimensionality through proper orthogonal decomposition [ 22 ]. The subset is then visually inspected inside the POD subspace.…”