Zaoyang Guo

Hyperelastic Anisotropic Microplane Constitutive Model for Annulus Fibrosus

In a recent paper, Peng et al. (2006, An Anisotropic Hyperelastic Constitutive Model With Fiber-Matrix Interaction for the Human Annulus Fibrosis, ASME J. Appl. Mech., 73(5), pp. 815-824) developed an anisotropic hyperelastic constitutive model for the human annulus fibrosus in which fiber-matrix interaction plays a crucial role in simulating experimental observations reported in the literature. Later, Guo et al. (2006, A Composites-Based Hyperelastic Constitutive Model for Soft Tissue With Application to the Human Fibrosis, J. Mech. Phys. Solids, 54(9), pp. 1952-1971) used fiber reinforced continuum mechanics theory to formulate a model in which the fiber-matrix interaction was simulated using only composite effect. It was shown in these studies that the classical anisotropic hyperelastic constitutive models for soft tissue, which do not account for this shear interaction, cannot accurately simulate the test data on human annulus fibrosus. In this study, we show that the microplane model for soft tissue developed by Caner and Carol (2006, Microplane Constitutive Model and Computational Framework for Blood Vessel Tissue, ASME J. Biomech. Eng., 128(3), pp. 419-427) can be adjusted for human annulus fibrosus and the resulting model can accurately simulate the experimental observations without explicit fiber-matrix interaction because, in microplane model, the shear interaction between the individual fibers distributed in the tissue provides the required additional rigidity to explain these experimental facts. The intensity of the shear interaction between the fibers can be adjusted by adjusting the spread in the distribution while keeping the total amount of the fiber constant. A comparison of results obtained from (i) a fiber-matrix parallel coupling model, which does not account for the fiber-matrix interaction, (ii) the same model but enriched with fiber-matrix interaction, and (iii) microplane model for soft tissue adapted to annulus fibrosus with two families of fiber distributions is presented. The conclusions are (i) that varying degrees of fiber-fiber and fiber-matrix shear interaction must be taking place in the human annulus fibrosus, (ii) that this shear interaction is essential to be able to explain the mechanical behavior of human annulus fibrosus, and (iii) that microplane model can be fortified with fiber-matrix interaction in a straightforward manner provided that there are new experimental data on distribution of fibers, which indicate a spread so small that it requires an explicit fiber-matrix interaction to be able to simulate the experimental data.

In situ mechanical testing of templated carbon nanotubes

A new microelectromechanical system (MEMS)-based tensile testing stage (with integrated actuator, direct load sensing beam, and electrodes for controlled assembly of an individual nanostructure) was developed and used for in situ tensile loading of a templated carbon nanotube (T-CNT) inside a scanning electron microscope (SEM). Specifically, an increasing tensile load was applied to the T-CNT by actuating the device and high-resolution scanning electron microscopy images were acquired at different loads. The load (from the bending of the direct force-sensing beam), the elongation of the specimen during loading, and the specimen geometry were all obtained from analysis of SEM images. The stress versus strain curve and Young’s modulus were thus obtained. A model is presented for the tensile loading experiment, and the fit value of Young’s modulus from this model is compared to values obtained by an independent method. The results of this experiment on a T-CNT suggest the use of this device for loading other...

Size effect and asymptotic matching approximations in strain-gradient theories of micro-scale plasticity

Abstract To explain the size effect found in the testing of plastic behavior of metals on the micrometer scale, four theories of strain-gradient plasticity, representing generalizations of the deformation theory of plasticity, have been developed since 1993––the pioneering original theory of Fleck and Hutchinson in two subsequent versions, the mechanism-based strain-gradient (MSG) plasticity of Gao and co-workers (the first theory anchored in the concept of geometrically necessary dislocations), and Gao and Huang’s recent update of this theory under the name Taylor-based nonlocal theory. Extending a recent study of Bažant in 2000 focused solely on the MSG theory, the present paper establishes the small-size asymptotic scaling laws and load–deflection diagrams of all the four theories. The scaling of the plastic hardening modulus for the theory of Acharya and Bassani, based on the incremental theory of plasticity, is also determined. Certain problematic asymptotic features of the existing theories are pointed out and some remedies proposed. The advantages of asymptotic matching approximations are emphasized and an approximate formula of the asymptotic matching type is proposed. The formula is shown to provide a good description of the experimental and numerical results for the size range of the existing experiments (0.5–100 μm).

Analysis of a microelectromechanical system testing stage for tensile loading of nanostructures

A new analytical model is developed for interpreting tensile loading data on “templated carbon nanotubes” (T-CNTs, amorphous carbon nanotubes made by pyrolysis with the channels of nanopores in anodized alumina nanopore arrays) obtained with a microelectromechanical-system (MEMS)-based mechanical testing stage. It is found that the force output from the actuation unit of the testing stage depends on the stiffness of the force sensing beam and the nanostructure being loaded, as well as the power input. A superposition method is used to treat the mechanics of the device structure in the linear elasticity response regime. To our knowledge this is a new approach for solving the mechanical response of MEMS structures with variable force output and of the configuration described herein. An in situ mechanical testing of individual T-CNTs was undertaken in a scanning electron microscope (LEO1525) using a new device fabricated with integrated electrodes for controlled deposition of T-CNTs by electric-field guided ...

Epitaxially influenced boundary layer model for size effect in thin metallic films

It is shown that the size effect recently observed by Espinosa et al., [J. Mech. Phys. Solids51, 47 (2003)] in pure tension tests on free thin metallic films can be explained by the existence of a boundary layer of fixed thickness, located at the surface of the film that was attached onto the substrate during deposition. The boundary layer is influenced by the epitaxial effects of crystal growth on the dislocation density and texture (manifested by prevalent crystal plane orientations). This influence is assumed to cause significantly elevated yield strength. Furthermore, the observed gradual postpeak softening, along with its size independence, which is observed in short film strips subjected to pure tension, is explained by slip localization, originating at notch-like defects, and by damage, which can propagate in a stable manner when the film strip under pure tension is sufficiently thin and short. For general applications, the present epitaxially influenced boundary layer model may be combined with th...

Fibre–matrix interaction in the human annulus fibrosus

Although the mechanical behaviour of the human annulus fibrosus has been extensively studied, the interaction between the collagen fibres and the ground matrix has not been well understood and is therefore ignored by most constitutive models. The objective of this study is to identify the significance of the fibre-matrix interaction in the human annulus fibrosus by careful investigation of the experimental data, the theoretical constitutive models, and the numerical simulation results in the literature. Based on the experimental results from biaxial and uniaxial tests, it is shown that the mechanical behaviour of the matrix can be well simulated by an incompressible neo-Hookean type model, but the effective stiffness of the matrix depends on fibre stretch ratio, which can only be explained by fibre-matrix interaction. Furthermore, we find that this interaction takes place anisotropically between the matrix and the fibres distributed in different proportions in different directions. The dependence of the tangent stiffness of the matrix on the first invariant of the deformation tensor can also be explained by this fibre orientation dispersion.

Effect of cantilever nonlinearity in nanoscale tensile testing

Microcantilevers are widely used in micro-/nanoscale mechanics studies. The nonlinear response of a cantilever at large deflection is sometimes overlooked. A general study of cantilever beam nonlinearity under a variety of loading conditions was performed with analytical and finite element analyses. Analytical equations for the applied load and the cantilever deflection were obtained. The cantilever nonlinearity was found to increase with increasing cantilever deflection and/or angle of loading. Tensile tests were performed on templated carbon nanotubes (TCNTs) with a custom-made nanomanipulator inside a scanning electron microscope. Atomic force microscope (AFM) cantilevers were used to load the TCNTs and sense the force. During the tests the AFM cantilevers were loaded to relatively large deflections with nonvertical loads applied at the AFM tip. Based on the slope and the loading angle measurements, the breaking forces of the TCNTs were obtained through numerical integration of the analytical equations...

MECHANICAL BEHAVIOUR OF TRANSVERSELY ISOTROPIC POROUS NEO-HOOKEAN SOLIDS

In this paper, the mechanical responses of a recently developed hyperelastic model for the neo-Hookean solids with aligned continuous cylindrical pores under finite homogeneous deformation that can capture the anisotropic compressibility as well as the coupling between the volumetric and deviatoric behaviours are examined. To this end, the strain energy function of this hyperelastic compressible transversely isotropic model contains terms for the coupling of volumetric and deviatoric behaviours. It is shown that, the asymptotic response of this anisotropic compressible model under extreme loading situations is considerably different from that of incompressible models. The unstable behaviour of the porous solid under hydrostatic stress/strain loadings is discussed in detail. When a general simple 2D shear deformation is applied to this porous solid in i1 – i2 plane, the normal stress in the third axial direction (i3) is nonzero. The loss of monotonicity of the stress tensor under off-axis simple 2D shear loading is demonstrated as well.