Soft Contact Mechanics with Gradient-Stiffness Surfaces

Abstract

The stiffness in the top surface of many biological entities like cornea or articular cartilage, as well as chemically cross-linked synthetic hydrogels, can be significantly lower or more compliant than the bulk. When such a heterogeneous surface comes into contact, the contacting load is distributed differently from typical contact models. The mechanical response under indentation loading of a surface with a gradient of stiffness is a complex, integrated response that necessarily includes the heterogeneity. In this work, we identify empirical contact models between a rigid indenter and gradient elastic surfaces by numerically simulating quasi-static indentation. Three key case studies revealed the specific ways in which (I) continuous gradients, (II) laminate-layer gradients, and (III) alternating gradients generate new contact mechanics at the shallow-depth limit. Validation of the simulation-generated models was done by micro- and nanoindentation experiments on polyacrylamide samples synthesized to have a softer gradient surface layer. The field of stress and stretch in the subsurface as visualized from the simulations also reveals that the gradient layers become confined, which pushes the stretch fields closer to the surface and radially outward. Thus, contact areas are larger than expected, and average contact pressures are lower than predicted by the Hertz model. The overall findings of this work are new contact models and the mechanisms by which they change. These models allow a more accurate interpretation of the plethora of indentation data on surface gradient soft matter (biological and synthetic) as well as a better prediction of the force response to gradient soft surfaces. This work provides examples of how gradient hydrogel surfaces control the subsurface stress distribution and loading response.

Recent advances in responsive hydrogels for diabetic wound healing

“…Recently, smart hydrogels with stimulus-responsive functions have attracted considerable attention. Briefly, stimulus-responsive hydrogels can respond to internal physiological signals (i.e., temperature [ 28 , 29 ], pH [ 30 , 31 ], redox [ 32 , 33 ], glucose [ 34 , 35 ], or enzymes [ 36 , 37 ]), external stimuli (i.e., temperature [ 38 , 39 ], magnetic field [ 40 , 41 ], pressure [ 42 , 43 ], reactive oxygen species (ROS) [ 44 , 45 ], light [ 46 , 47 ] and electric field [ 48 , 49 ]) or a combination of the above, which can reversibly or irreversibly change the physical properties or chemical structure ( Fig. 2 ).…”

Brushing Up on Cartilage Lubrication: Polyelectrolyte-Enhanced Tribological Rehydration

“…Moreover, the curves did not adhere to Hertzian contact theory at forces approximately lower than 0.5 nN. The accurate determination of surface contact for soft materials poses a significant challenge, requiring the mathematical delineation of the indentation range that accurately fits the Hertz model (Figure c). , …”

“…Indentation force measurements were performed in a 16 × 16 grid (256 total) over a 50 × 50 μm area, and two force maps were each performed on two SPMK- g -PEEK samples. Each force–displacement curve was performed with a ramp size of 5.0 μm at a 2 μms –1 indentation velocity, as used in similar soft contact research. , Data was analyzed using a custom Python script to identify the contact displacement at which the probe engaged with the surface indicated by a reduction in noise and subsequently identify the data region that complies with Hertzian contact theory to calculate elastic modulus. , The elastic modulus was calculated for only the first 1 μm of indentation to isolate substrate effects.…”

Biomimetic-Engineered Silicone Hydrogel Contact Lens Materials

“…This shape was also confirmed by AFM observations (Figure b). With the application of AFM technologies, the surface stiffness on the hydrated polymer layer can be evaluated as shown in Figure c. , The elastic modulus of the surface of this contact lens was ∼350 kPa for the untreated silicone hydrogel contact lens and reduced to ∼30 kPa by the surface treatment. , It was found that this is equivalent to the elastic modulus of human and rabbit corneas. In addition, it was confirmed that there was no change in the elastic modulus of the surface of the contact lens after wearing it for 30 days.…”