Aylin Ahadi

Characteristic state plasticity for granular materials Part II: Model calibration and results

A non-associated plasticity theory for granular materials has been developed in Part 1 based on the concept of a characteristic stress state of vanishing incremental dilation. The model is fully three-dimensional and is defined by six material parameters: two for elastic stiffness, one for plastic stiffness, two for the shapes of yield and plastic potential surfaces and one for the dilation at failure. In this paper a calibration procedure is developed using test data only from a standard triaxial test. It is found that the shape parameter for the yield surface can be estimated from the plastic how parameters, thus reducing the number of free parameters to five. Calibration examples are shown, as well as predictions made, for different confining stress levels and constant volume tests on sand. The model is found to represent stress-strain behaviour and development of volumetric strain in standard triaxial tests well. The model provides good predictions of constant volume behaviour of dense as well as loose sand on the basis of calibration by standard triaxial test data. A simple explicit formula is derived for the failure asymptote in constant volume testing, enabling explicit adjustment of the parameters, if incompressible-test data is available. (Less)

Implicit integration of plasticity models for granular materials

A stress integration algorithm for granular materials based on fully implicit integration with explicit updating is presented. In the implicit method the solution makes use of the gradient to the potential surface at the final stress state which is unknown. The final stress and hardening parameters are determined solving the non-linear equations iteratively so that the stress increment fulfills the consistency condition. The integration algorithm is applicable for models depending on all the three stress invariants and it is applied to a characteristic state model for granular material. Since tensile stresses are not supported the functions and their derivatives are not representative outside the compressive octant of the principal stress space. The elastic predictor is therefore preconditioned in order to ensure that the first predictor is within the valid region. Capability and robustness of the integration algorithm are illustrated by simulating both drained and undrained triaxial tests on sand. The algorithm is developed in a standard format which can be implemented in several general purpose finite element codes. It has been implemented as an ABAQUS subroutine, and a traditional geotechnical problem of a flexible strip footing resting on a surface of sand is investigated in order to demonstrate the global accuracy and stability of the numerical solution.

Three-dimensional simulation of nanoindentation response of viral capsids. shape and size effects

The nanoindentation response of empty viral capsids is modeled using three-dimensional finite element analysis. Simulation with two different geometries, spherical and icosahedral, is performed using the finite element code Abaqus. The capsids are modeled as nonlinear Hookean elastic, and both small and large deformation analysis is performed. The Youngs modulus is determined by calibrating the force-indentation curve to data from atomic force microscopy (AFM) experiments. Force-indentation curves for three different viral capsids are directly compared to experimental data. Predictions are made for two additional viral capsids. The results from the simulation showed a good agreement with AFM data. The paper demonstrates that over the entire range of virus sizes (or Foppl-von Karman numbers) spherical and icosahedral models yield different force responses. In particular, it is shown that capsids with dominantly spherical shape (for low Foppl-von Karman numbers) exhibit nearly linear relationship between force and indentation, which has been experimentally observed on the viral shell studies so far. However, we predict that capsids with significant faceting (for large Foppl-von Karman numbers) and thus more pronounced icosahedral shape will exhibit rather nonlinear deformation behavior.

Modeling and simulation of the mechanical response from nanoindentation test of DNA-filled viral capsids.

Viruses can be described as biological objects composed mainly of two parts: a stiff protein shell called a capsid, and a core inside the capsid containing the nucleic acid and liquid. In many double-stranded DNA bacterial viruses (aka phage), the volume ratio between the liquid and the encapsidated DNA is approximately 1:1. Due to the dominant DNA hydration force, water strongly mediates the interaction between the packaged DNA strands. Therefore, water that hydrates the DNA plays an important role in nanoindentation experiments of DNA-filled viral capsids. Nanoindentation measurements allow us to gain further insight into the nature of the hydration and electrostatic interactions between the DNA strands. With this motivation, a continuum-based numerical model for simulating the nanoindentation response of DNA-filled viral capsids is proposed here. The viral capsid is modeled as large- strain isotropic hyper-elastic material, whereas porous elasticity is adopted to capture the mechanical response of the filled viral capsid. The voids inside the viral capsid are assumed to be filled with liquid, which is modeled as a homogenous incompressible fluid. The motion of a fluid flowing through the porous medium upon capsid indentation is modeled using Darcy’s law, describing the flow of fluid through a porous medium. The nanoindentation response is simulated using three-dimensional finite element analysis and the simulations are performed using the finite element code Abaqus. Force-indentation curves for empty, partially and completely DNA-filled capsids are directly compared to the experimental data for bacteriophage λ. Material parameters such as Young’s modulus, shear modulus, and bulk modulus are determined by comparing computed force-indentation curves to the data from the atomic force microscopy (AFM) experiments. Predictions are made for pressure distribution inside the capsid, as well as the fluid volume ratio variation during the indentation test.

A fully coupled thermomechanical two-dimensional simulation model for orthogonal cutting: formulation and simulation

In this paper a fully coupled thermomechanical two-dimensional simulation model for orthogonal cutting is presented. The model is based on the arbitrary Lagrangian–Eulerian formulation with the remeshing technique. The material model used for the workpiece material includes Johnson–Cook plasticity, and as the chip separation criterion the Johnson–Cook damage law is employed. The different friction zones are modelled by the Coulomb friction law with a maximum limit for the friction. The capability of the model to represent the cutting process realistically is validated by performing simulations for different feed depths. The model is validated by comparison of the simulated values and measured experimental data for several different important process parameters, such as the feed force, the cutting force, the chip thickness ratio, the relative deformation widths, and the temperature distribution. The results from the simulations showed very good agreement with the experimental data.

A Numerical and Experimental Investigation of the Deformation Zones and the Corresponding Cutting Forces in Orthogonal Cutting

This study are focused on the deformation zones occurring in the work piece in a machining process and the corresponding cutting forces. The fully coupled thermo-mechanical FE-model for orthogonal cutting, developed in [1] is utilized. The work piece material is modeled with Johnson-Cook plasticity including damage formulation. Simulations for different feed depths were performed. The cutting forces, the chip thickness ratio and the deformation widths were determined experimentally by the quick-stop images and a force measurements. The results from the simulations have been compared to experimental data for the cutting forces and the chip thickness ratio as a function of the theoretical chip thickness.

Modeling subsurface deformation induced by machining of Inconel 718

ABSTRACT Traditionally, the development and optimization of the machining process with regards to the subsurface deformation are done through experimental method which is often expensive and time consuming. This article presents the development of a finite element model based on an updated Lagrangian formulation. The numerical model is able to predict the depth of subsurface deformation induced in the high- speed machining of Inconel 718 by use of a whisker-reinforced ceramic tool. The effect that the different cutting parameters and tool microgeometries has on subsurface deformation will be investigated both numerically and experimentally. This research article also addresses the temperature distribution in the workpiece and the connection it could have on the wear of the cutting tool. The correlation of the numerical and experimental investigations for the subsurface deformation has been measured by the use of the coefficient of determination, R2. This confirms that the finite element model developed here is able to simulate this type of machining process with sufficient accuracy.

Characterization of probe contact effects on diffuse reflectance spectroscopy measurements

Diffuse reflectance spectroscopy (DRS) is a rapid, non-invasive optical method widely adopted to gain diagnostic information of tissue. The most flexible approach to this method is a fiber-optic contact-probe used with a spectroscopy system. A challenge of this method is that the external pressure brought by the probe can significantly affect the tissue optical properties as well as the light coupling into the probe, and thus influence the collected DRS-spectrum. In this study we investigate and characterize the effect of probe pressure on DRS-spectra obtained with a calibrated loaded-spring system used with a fiber optic probe in the range (400 − 1600) nm. A multilayer FE-model of the indentation is developed to get a better insight of the distribution of pressure and stresses inside the skin under indentation.

Analysis of volume-average relations in continuum mechanics

In this paper, volume-average relations related to the multilevel modelling process in continuum mechanics are analysed and the concept of average consistency is investigated both analytically and numerically. These volume averages are used in the computational homogenization technique, where a transition of the mechanical properties from the local, microscopic, to the global, macroscopic, length scale is obtained. The representative volume element (RVE) is used as a reference placement and the solution, in terms of volume-averaged stress, will depend on which boundary conditions are chosen for the RVE. Three types of boundary conditions – periodic, affine and anti-periodic – are analysed with respect to the average consistence for the kinematical and stress relations used in continuum mechanics. The inconsistence is quantified by introducing the inconsistence ratio. It is shown analytically that some average stress relations are fulfilled, assuming the periodic boundary condition and anti-periodic traction vector, whereas the average relations connected to the deformation are in general not average consistent. The inconsistence is investigated in a plane model using the finite element technique. The numerical investigation has shown that the inconsistence ratios related to the deformation are also average consistent in the examples considered.

Determination of hyperelastic properties of viral capsids using finite element calculation and nanoindentation

In this paper a calibration procedure for determining the elastic parameters of empty and filled viral capsids is presented. The procedure combines finite element calculations and results from nanoindentation experiments. The experimental data is from indentation on individual viral particles performed with atomic force microscope. Experimental force–indentation curves for the viral capsid are extracted and compared to force–indentation curves obtained from finite element simulations. The nanoindentation response is simulated using three-dimensional finite element analysis, and the simulations are performed using the finite element code Abaqus. Material parameters such as the Young’s modulus, the shear modulus and the bulk modulus are determined by fitting the force–indentation curves to experimental data by the means of the least squares method. Two different viral capsid are considered: the cowpea chlorotic mottle virus and bacteriophage λ. Predictions are made for the pressure distribution inside the capsid.