A nonlinear thermomechanical formulation for anisotropic volume and surface continua

A thermomechanical, polar continuum formulation under finite strains is proposed for anisotropic materials using a multiplicative decomposition of the deformation gradient. First, the kinematics and conservation laws for three-dimensional, polar, and nonpolar continua are obtained. Next, these kinematics and conservation laws are connected to their corresponding counterparts for surface continua, based on Kirchhoff–Love assumptions. Then the shell material models are extracted from three-dimensional material models for finite-temperature problems using established connections. The weak forms are obtained for both three-dimensional nonpolar continua and Kirchhoff–Love shells. These formulations are expressed in tensorial form so that they can be used in both curvilinear and Cartesian coordinates. They can be used to model anisotropic crystals and soft biological materials.

Nanoindentation of Soft Biological Materials

Nanoindentation techniques, with high spatial resolution and force sensitivity, have recently been moved into the center of the spotlight for measuring the mechanical properties of biomaterials, especially bridging the scales from the molecular via the cellular and tissue all the way to the organ level, whereas characterizing soft biomaterials, especially down to biomolecules, is fraught with more pitfalls compared with the hard biomaterials. In this review we detail the constitutive behavior of soft biomaterials under nanoindentation (including AFM) and present the characteristics of experimental aspects in detail, such as the adaption of instrumentation and indentation response of soft biomaterials. We further show some applications, and discuss the challenges and perspectives related to nanoindentation of soft biomaterials, a technique that can pinpoint the mechanical properties of soft biomaterials for the scale-span is far-reaching for understanding biomechanics and mechanobiology.

Relevance of Indentation Test to Characterize Soft Biological Tissue: Application to Human Skin

This contribution presents a new investigation to identify the viscoelastic parameters of soft biological materials using indentation test. The purpose is to present a new independent method on experimental specificities in order to characterize these materials. The identification was done using inverse analysis based on combining finite element (FE) numerical simulations and experimental indentation tests. By considering soft tissues as an isotropic linear viscoelastic material, we firstly validate our proposed FE model via a comparison between analytic and numerical indentation responses. Secondly, the existence and uniqueness of inverse problem solution based on the comparison of numerical/numerical responses is shown. Finally, we validate the stability of the inverse approach using sensitivity analysis by setting up a design of experiment (DOE) technique which proves the relevance of this proposed method. An application is made on the forearm of human skin and shows performances of this proposed method to identify viscoelastic human skin properties in spherical loading–unloading indentation test. This method can be applied to evaluate other viscoelastic materials.

A Validation Study of the Repeatability and Accuracy of Atomic Force Microscopy Indentation Using Polyacrylamide Gels and Colloidal Probes

The elasticity of soft biological materials is a critical property to understand their biomechanical behaviors. Atomic force microscopy (AFM) indentation method has been widely employed to measure the Young's modulus (E) of such materials. Although the accuracy of the method has been recently evaluated based on comparisons with macroscale E measurements, the repeatability of the method has yet to be validated for rigorous biomechanical studies of soft elastic materials. We tested the AFM indentation method using colloidal probes and polyacrylamide (PAAM) gels of E < 20 kPa as a model soft elastic material after having identified optimal trigger force and probe speed. AFM indentations repeated with time intervals show that the method is well repeatable when performed carefully. Compared with the rheometric method and the confocal microscopy indentation method, the AFM indentation method is evaluated to have comparable accuracy and better precision, although these elasticity measurements appear to rely on the compositions of PAAM gels and the length scale of measurement. Therefore, we have confirmed that the AFM indentation method can reliably measure the elasticity of soft elastic materials.