The mechanical behaviour of cells is essential in ensuring continued physiological function, and deficiencies therein can result in a variety of diseases. Also, altered mechanical response of cells can in certain cases be an indicator of a diseased state, and even actively promoting progression of pathology. In this thesis, methods to model cell and cytoskeletal mechanics are developed and analysed. In Paper A, a constitutive model for the response of transiently cross-linked actin networks is developed using a continuum framework. A strain energy function is proposed and modified in terms of chemically activated cross-links. In Paper B, a finite element framework was used to assess the influence of numerous geometrical and material parameters on the response of cross-linked actin networks, quantifying the influence of microstructural properties and cross-link compliance. Also, a micromechanically motivated constitutive model for cross-linked networks in a continuum framework was proposed. In Paper C, the discrete model is extended to include the stochastic nature of cross-links. The strain rate dependence observed in experiments is suggested to depend partly on this. In Paper D, the continuum model for cross-linked networks is extended to encompass more composite networks. Favourable comparisons to experiments indicate the interplay between phenomenological evolution laws to predict effects in biopolymer networks. In Paper E, experimental and computational techniques are used to assess influence of the actin cytoskeleton on the mechanical response of fibroblast cells. The influence of cell shape is assessed, and experimental and computational aspects of cell mechanics are discussed. In Paper F, the filament-based cytoskeletal model is extended with an active response to predict active force generation.  Importantly, experimentally observed stiffening of cells with applied stress is predicted. / <p>QC 20151209</p>

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Chapter 2 contains the continuum mechanical notions for the description of the plastic behavior of sheet metal under large deformations at room temperature. As such, it includes the kinematics of a continuum body, strain and stress definitions, and a general elasto-plastic constitutive model description. This last point is complemented by the definition of anisotropy, as well as the description of some yield criteria and hardening laws. Next, Chapter 3 defines the stress strain states required to be experimentally reproduced in order to describe the initial yield locus and its displacement in the stress axis representation during plastic deformation. A review of the available experimental equipment capable of reproducing the required stress strain states is presented in order to choose the best for further construction. After consideration, those deemed the highest performing are the Miyauchi device, able to perform simple shear tests and the bi-axial testing machine, able to perform plane strain and simple shear tests separately or simultaneously. This chapter presents the mechanical features of the Miyauchi device and the bi-axial test machine that were built at the M&S Laboratory, followed by a description of the optical strain gauge chosen that allows the computation of the strain field throughout the specimens deformation area. Chapter 4 focuses on the validation of the experimental equipment. First, the homogeneity of the stress and strain fields is verified. Then, the availability of performing the plane strain, simple shear, Bauschinger and orthogonal tests is checked. The repeatability (precision) of the tests is corroborated and the accuracy is validated by comparison with finite elements simulations. In Chapter 5, the identification methods are proposed and DC06 (0,8mm thick), DP1000 (1,6mm thick) and S320GD (0,69mm thick) steels are identified according to those methods. The initial yield surface for DC06 is identified by two methods (one using the strain measurements, the other using stress measurements) for two yield criteria, which are then compared with a texture-based yield criterion and the experimental points. The initial yield surface for the other two materials is described by the Hill 1948 yield criterion identified using strain measurements. The yield surface evolution (hardening) for DC06 and S320GD is described by the Teodosiu and Hu hardening law due to the observed mechanical behavior, i.e., the Bauschinger effect and strong influence of the pre-strain when strain-path changes take place. DP1000 exhibits a high Bauschinger effect and its flow stress is not influenced by the amount of pre-strain when reversing the load; hence, its behavior is described by a kinematic hardening law. Finally, in Chapter 6, conclusions about the present work are established and equipment improvement and further topics for research are proposed, namely, the study of texture evolution, the material axis rotation and the experimental validation of new yield criteria.

Constitutive model parameters are identified during model calibration through trial-and-error process driven to fit test data. In this research, the calibration of constitutive models is formally handled as an inverse problem. The first phase of this research explores error propagation. Data errors, experimental biases (e.g. improper boundary conditions), and model errors affect the inversion of model parameters and ensuing numerical predictions. Drained and undrained tests are simulated to study the effect of these three classes of errors. Emphasis is placed on the analysis of error surfaces computed by successive forward simulations. The second phase of this research centers on test procedures. Conventional soil tests were developed to create uniform stress and strain fields; consequently, they provide limited amount of information, the inversion is ill-posed, and results enhance uncertainty and error propagation. This research examines soil testing using new, non-conventional loading and boundary conditions to create rich, diverse, non-uniform strain and stress fields. In particular, the flexural excitation of cylindrical soil specimens is shown to provide rich data leading to a more informative test than conventional geotechnical tests. The new test is numerically optimized. Then a set of unique experimental studies is conducted.

A thermodynamics-based constitutive model is derived which predicts the nonlinear strain and magnetization response that magnetic shape memory alloys (MSMAs) exhibit when subjected to mechanical and magnetic loads. The model development is conducted on the basis of an extended thermo-magneto-mechanical framework. A novel free energy function for MSMAs is proposed, from which the constitutive equations are derived in a thermodynamically-consistent manner. The nonlinear and hysteretic nature of the macroscopic material behavior is captured through the evolution of internal state variables which are motivated by the crystallographic and magnetic microstructures of MSMAs. Model predictions are presented for different relevant loading cases and analyzed in detail. Finally, magnetostatic boundary value problems for MSMAs are considered and numerically solved using the finite element method. For these computations the developed constitutive model provides the nonlinear magnetic properties of the MSMA. The knowledge of the magnetic field distribution in the computational domain as a function of the applied field, which results from this magnetostatic analysis, is useful for the proper interpretation of experimental results as well as the design of experiments and applications.

The deformation and failure properties of granular soils largely affect the stability of upper structures built on or in such soils. Owing to its discrete nature as well as the randomness of particle shape and inter-particle connectivity, the internal structure of a granular material usually exhibits a certain level of anisotropy. In addition, the microstructure of a granular material evolves following certain patterns, which are influenced by the initial fabric, void ratio, stress level, as well as the stress or deformation history. It has been a major challenge to properly describe the deformation of anisotropic granular materials in constitutive models especially when the materials are subjected to cyclic loading. The existing constitutive models usually have limited capabilities in describing the behaviour of granular materials subjected to repeated loading with principal stress rotation. How to quantify the microstructure change and how to consider the changing microstructure in constitutive models have been two missing links for building a comprehensive model framework. This research aimed at developing a constitutive model that can properly describe the deformation of granular soils under repeated multi-directional loading. To achieve this goal, a systematic study was performed, including a comprehensive experimental study and a theoretical development of a stress-strain model with proper consideration of the influence of fabric. The developed model was verified with experimental results and then implemented into a finite element code to solve boundary-valued problems. In the first part of this study, a comprehensive experimental study was carried out to investigate the behaviours of granular materials under both monotonic and cyclic loading to investigate the influence of the intermediate principal stress and the major principal stress direction on soil responses. The results of monotonic loading tests showed that both the strength and dilatancy of sand decreased notably with an increase of either the intermediate principal stress or the inclination angle of the major principal stress direction relative to the major principal fabric direction. The stress states at failure from the tests suggested that the benchmarked Matsuoka-Nakai and Lade-Duncan failure criteria are only valid under certain conditions. From the cyclic loading tests, it was observed that, in addition to the increased intermediate principal stress, varied cyclic loading direction caused a significant increase in accumulative volumetric compaction. To consider the microstructural dependencies of granular materials, a more general mathematical formulation of stress-dilatancy was developed based on the assumption of the existence of a critical state fabric surface that is expressed as a function of the invariants of the fabric tensor. This assumption was also used to establish the fabric evolution law. The implementation of the resulting stress-dilatancy formulation and the fabric evolution law in elasto-plasticity theory produced interesting modelling results consistent with experimental observations with respect to the microstructural aspects of granular materials. The developed constitutive model was further extended to cyclic loading within the framework of hypo-plasticity with kinematic hardening. The model was capable of describing the behaviour of sand subjected cyclic loading under various conditions including the variation of loading directions. Finally, the constitutive model was implemented into a commercial software package ABAQUS via the subroutine UMAT. The capacity of the proposed stress-strain model in solving boundary value problems was examined. Six series of elements tests were designed to examine the proposed model under different initial void ratios, degrees of anisotropy, loading directions, and stress paths. Furthermore, a series of simulations were performed for the settlement of footing on sands with different bedding plane orientations. Results from the simulations were found to be consistent with experimental observations. / Thesis / Doctor of Philosophy (PhD)

Finite element simulation of metal cutting processes offers a cost-effective method to optimize the cutting conditions and to select the right tool material and geometry. A key input to such simulations is a constitutive model that describes material behavior during severe plastic deformation. However, the vast majority of material models used in prior work are phenomenological in nature and are usually obtained by fitting a non-physically based mathematical equation to the macro-scale stress-strain response of the material. Moreover, the deformation range covered by the stress-strain response used in the model calibration process usually falls short of the ranges typically observed in metal cutting. This thesis seeks to develop a unified material model that explicitly incorporates microstructure evolution into the constitutive law to describe the macro-scale plastic deformation response of the material valid over the range of strains, strain rates and temperatures experienced in machining. The proposed unified model is based on the underlying physics of interactions of mobile dislocations with different short and long range barriers and accounts for various physical mechanisms such as dynamic recovery and dynamic recrystallization. In addition, the inclusion of microstructure evolution into the constitutive model enables the prediction of microstructure in the chip and the machined surface. In this study, the unified material model is calibrated and validated in the severe plastic deformation regime characteristic of metal machining and is then implemented in finite element simulations to evaluate its ability to predict continuous and segmented chip formation in machining of pure metals such as OHFC copper and commercially-pure titanium (CP-Ti). Due to the physical basis of the proposed unified material model, the continuous chip formation observed in orthogonal cutting of OFHC copper is shown to be successfully predicted by the finite element model utilizing a version of the unified material model that explicitly accounts for microstructure evolution as well as dislocation drag as a plausible deformation mechanism applicable at the high strain rates common in metal cutting operations. The segmented or shear localized chip formation in orthogonal cutting of CP-Ti is also shown to be successfully simulated by the unified model after incorporating the inverse Hall-Petch effect arising from the ultrafine grain structure within the shear band. For both metals, the model is experimentally validated using flow stress data as well as machining data including cutting and thrust forces and relevant chip morphology parameters. Machining simulations carried out using the unified material model also yield useful insights into the microstructure evolution during the machining process, which is shown to be consistent with the available experimental data and the known physical understanding of severe plastic deformation behavior of the metals.

Breast cancer is one of the most frequently diagnosed cancers affecting women in the United States. An ongoing objective of many research groups is to develop a biomechanical breast model for different applications, ranging from surgical outcome predictions for patients undergoing breast reconstruction surgery, to image registration for planning plastic surgery. Achieving the goal of developing a physics based biomechanical model of the human breast requires the determination of material properties of the various tissues constituting the breast. The objective of this thesis is to develop an appropriate hybrid experimental-numerical technique to enable the calibration of material parameters of skin for different constitutive models (commonly used for skin). The quantification of the material parameters thus obtained validates the bulge test method to be used in testing soft tissue specimens like skin. A bulge test device was custom-built for this work; it consists of a pressure chamber, two digital cameras, and a syringe pump as its main components. The syringe pump provides a constant flow rate of water into the pressure chamber and results in the bulging of specimens with a diameter between 45 mm and 80 mm. Three-dimensional Digital Image Correlation technique is used to obtain full field displacement measurements of the three dimensional shape of the bulge. Tests were performed on commercial rubber sheets of different thickness and on porcine skin specimens; in these tests, the bulge shape was measured at monotonically increasing and decreasing pressure levels, as well as during cyclic loading allowing determination of the deformation and strain fields over the specimen surface. In order to extract the material properties, a hybrid experimental-numerical method was used: the experiment was modeled numerically using the finite element analysis software Abaqus, imposing the commonly used Mooney-Rivlin model for isotropic materials and the Gasser-Ogden-Holzapfel model for anisotropic materials. A comparison between the experimentally measured and numerically simulated bulge shapes was used to determine the optimized material parameters under biaxial loading conditions over a large range of stretch levels. / text

In this thesis, we propose a new microstructural model to describe the rheology of entangled linear polymers. In order to reduce the number of non-linear adjustable parameters, we develop a model capable of predicting both the linear and the non-linear response, using a single set of material parameters. In a first step, a linear differential formulation of the thermal constraint release mechanism is introduced and validated against experimental results for linear polystyrene melts. In a second step, we extend the linear model to the non-linear regime by generalizing the state variables to conformation tensors and accounting for the relevant non-linear relaxation phenomena. The numerical predictions of the resulting model are then compared to experimental data for entangled polymer melts and solutions in different flow regimes. Finally, we show, on a simple reptation model, how the single generator bracket formalism of non-equilibrium thermodynamics can be used for the phenomenological improvement of microstructural constitutive models.

Unsaturated swelling clays are used in engineered barriers for waste disposal facilities due to their self-sealing ability and low hydraulic conductivity. The characterization of unsaturated clay behaviour is required for design of these barriers. In recent years, several small-scale laboratory and full-scale field tests have been conducted to characterize the mechanical and hydraulic behaviour of the unsaturated swelling clay. This focus of the present study is towards the development of constitutive models to simulate hydraulic and mechanical behaviour of precompacted unsaturated swelling clay, called the bentonite-sand buffer (BSB) material. Development, calibration, implementation, and application of the proposed constitutive models form the scope of the study. The results of laboratory triaxial tests with controlled suction and suction measurements are used to calibrate the constitutive models presented. An algorithm, called the PEM (Parameter Evaluation Method), which is useful to estimate constitutive model parameters and evaluate the performance of constitutive models is proposed. This algorithm has been used to estimate the parameters of two elasto-plastic constitutive models (i.e., the BBM (Alonso et al. 1990) and the BGM (Blatz and Graham 2003)) based on the laboratory tests results on the BSB material. New 3-dimensional porosity-dependent permeability model (kwn) and water retention surface (WRS) are developed in this study. The mathematical formulations of these models using parameters calibrated with laboratory tests conducted on the BSB material are provided. Implementation algorithms of the BBM, the BGM, the kwn, and the WRS in 2-phase flow hydraulic-mechanical (H-M) analysis using a 2D-finite difference method are also provided . Three combinations of hydraulic and mechanical constitutive models (linear elastic model, BGM, vanGenuchten (1980) and kwn models) are used to simulate small-scale infiltration processes in the BSB material. Two types of tests, constant volume (CV) and constant mean stress (CMS) tests are simulated using 2D-finite difference H-M analysis. The full-scale isothermal test (ITT) of AECL is modelled using 3 combinations of H-M constitutive models. The ITT experiment comprises of buffer, rock, and concrete materials. The selected combinations of H-M constitutive models are used in three types of analyses: buffer-only (BO); buffer-rock with 20x30m domain (BR); and time-dependent boundary conditions (BCt). The results of the study show that the applications of the elasto-plastic mechanical constitutive models and porosity-dependent permeability (kwn) model are improvements over existing constitutive models to model this class of problem. The rock properties and applied boundary conditions are significant in modelling the ITT experiment. The application of the time-dependent boundary condition can reduce the uncertainty of the rock properties and boundary conditions within the rock, so that it improves the model ability to simulate the hydraulic-mechanical behaviour of unsaturated swelling clay. / October 2007