Modeling and Design of SHPB to Characterize Brittle Materials Under Compression for High Strain Rates.

This paper presents an analytical prediction coupled with numerical simulations of a split Hopkinson pressure bar (SHPB) that could be used during further experiments to measure the dynamic compression strength of concrete. The current study combines experimental, modeling and numerical results, permitting an inverse method by which to validate measurements. An analytical prediction is conducted to determine the waves propagation present in SHPB using a one-dimensional theory and assuming a strain rate dependence of the material strength. This method can be used by designers of new SPHB experimental setups to predict compressive strength or strain rates reached during tests, or to check the consistencies of predicted results. Numerical simulation results obtained using LS-DYNA finite element software are also presented in this paper, and are used to compare the predictions with the analytical results. This work focuses on an SPHB setup that can accurately identify the strain rate sensitivities of concrete or brittle materials.

A fully nonlinear viscohyperelastic model for the brain tissue applicable to dynamic rates.

Understanding the mechanical response of the brain to external loadings is of critical importance in investigating the pathological conditions of this tissue during injurious conditions. Such injurious loadings may occur at high rates, for example among others, during road traffic or sport accidents, falls, or due to explosions. Hence, investigating the injury mechanism and design of protective devices for the brain requires constitutive modeling of this tissue at such rates. Accordingly, this paper is aimed at critically investigating the physical background for viscohyperelastic modeling of the brain tissue with scrutinizing the elastic fields pertinent to large, time dependent deformations, and developing a fully nonlinear multimode Maxwell model that can mathematically explain such deformations. The proposed model can be calibrated using the simple monotonic uniaxial deformation of the sample extracted from the tissue, and does not require additional information from relaxation or creep experiments. The performance of the proposed model is examined using the experimental results of two different studies, which reveals a desirable agreement. The usefulness, limitations, and future developments of the proposed model are discussed in this paper.

Brain modelling in the framework of anisotropic hyperelasticity with time fractional damage evolution governed by the Caputo-Almeida fractional derivative.

In this paper the human brain tissue constitutive model for monotonic loading is developed. The model in this work is based on the anisotropic hyperelasticity assumption (the transversely isotropic case) together with modelling of the evolving load-carrying capacity (scalar damage) whose change is governed by the Caputo-Almeida fractional derivative. This allows the brain constitutive law to include the memory during progressive damage, due to the characteristic time length scale which is an inherent attribute of the fractional operator. Furthermore, the rate dependence of the overall brain tissue model is included as well. The theoretical model is finally calibrated and validated with a set of experimental data.

Hyperelastic modeling of the human brain tissue: Effects of no-slip boundary condition and compressibility on the uniaxial deformation.

Being extremely soft, brain tissue is among the most challenging materials to be mechanically quantified. Despite recent advances in mechanical testing of ultra-soft matters, there still exists a need for robust procedures to analyze their behavior at large deformation. In this paper, it is shown how failing to taking into account the precise boundary conditions can result in substantial variation from the "assumed" ideal behavior, even for the case of simple loading conditions such as the uniaxial mode. For an accurate analysis, the mathematical modeling is combined with the finite element simulation to interpret the mechanical behavior of the brain tissue based on the comprehensive experiments conducted by Budday et al. (2017). It is demonstrated herein that only an Ogden hyperelastic model with both negative and positive nonlinearity constants can predict the mechanical behavior of the brain tissue in tension and compression, and the tension-compression asymmetry might arise from the difference in compressibility behavior in tension and compression. This hypothesis is utilized for modeling the mechanical behavior of the brain tissue in uniaxial loading condition and exhibits excellent agreement with the experiments. This study also provides a comprehensive explanation for nonlinear analysis of soft matters, in general, and the brain tissue, in particular, with thoroughly describing the concept of hyperelasticity and modeling incompressible or compressible behaviors utilizing the Ogden strain energy function.

A combined experimental, modeling, and computational approach to interpret the viscoelastic response of the white matter brain tissue during indentation.

Viscoelastic properties of the white matter brain tissue are systematically studied in this paper utilizing indentation experiments, mathematical modeling, and finite element simulation. It is first demonstrated that the internal stiffness of the instrument needs to be thoroughly obtained and incorporated in the analysis as its contribution to the recorded mechanical response is significant for experiments on very compliant materials. The flat-punch monotonic indentation is then performed indirectly on sagittal plane slices with pushing a large rigid coverslip into the sample surface. The recorded load and displacement data are used for calibrating different viscoelastic models and presenting numerical values for the model elements. Consequently, the accuracy of the findings based on the theoretical models is investigated by performing finite element simulations which suggest a considerable substrate effect that causes violation of the semi-infinite half-space assumption in modeling of the material behavior. Accordingly, correction factors for adjusting the viscoelastic constants are obtained and presented. Since the Maxwell model shows a superior capability in rendering the mechanical response of the brain, an extension of this model to Multimode Maxwell viscoelastic solid is proposed for modeling the tissue behavior under a more complex load-hold-unload indentation cycle that shows acceptable agreement with experimental observations.

An Indirect Indentation Method for Evaluating the Linear Viscoelastic Properties of the Brain Tissue.

Indentation experiments offer a robust, fast, and repeatable testing method for evaluating the mechanical properties of the solid-state materials in a wide stiffness range. With the advantage of requiring a minimal sample preparation and multiple tests on a small piece of specimen, this method has recently become a popular technique for measuring the elastic properties of the biological materials, especially the brain tissue whose ultrasoft nature makes its mechanical characterization very challenging. Nevertheless, some limitations are associated with the indentation of the brain tissue, such as improper surface detection, negative initial contact force due to tip-tissue moisture interaction, and partial contact between the tip and the sample. In this study, an indirect indentation scheme is proposed to overcome the aforementioned difficulties. In this way, the indentation force is transferred from a sharp tip to the surface of the tissue slices via a rigid coverslip. To demonstrate the accuracy of this method, the linear viscoelastic properties of the white and gray matters of the bovine brain samples are measured by imposing small cyclic loads at different frequencies. The rate, regional, directional, and postmortem time dependence of the viscoelastic moduli are investigated and compared with the previous results from cyclic shear and monotonic experiments on the brain tissue. While findings of this research present a comprehensive set of information for the viscoelastic properties of the brain at a wide frequency range, the central goal of this paper is to introduce a novel experimentation technique with noticeable advantages for biomechanical characterization of the soft tissue.