Autoclave processing of large scale, one-piece structural parts made of carbon fiber-reinforced polymer composite materials is the key to decreasing manufacturing costs while at the same time increasing quality. Nonetheless, even in manufacturing simple flat parts, residual strains and stresses are unavoidable. For structural design purposes and to aid in the assembly procedures, it is desirable to have proven numerical tools that can be used to predict these residual geometrical and material properties in advance, thus avoid the costly experimental trial and error methods. A 2-D finite element-based code, COMPRO, has previously been developed in-house for predicting autoclave process-induced deformations and residual stresses in composite parts undergoing an entire cure cycle. To simulate the tool-part interaction, an important source of residual deformations/stresses, COMPRO used a non-zero thickness elastic shear layer as its only interface option. Moreover, the code did not account for the large deformations and strains and the resulting nonlinear effects that can arise during the early stages of the cure cycle when the material is rather compliant. In the present work, a contact surface employing a penalty method formulation is introduced at the tool-part interface. Its material-dependent parameters are a function of temperature, degree of cure, pressure and so forth. This makes the stick-slip condition plus separation between the part and the tool possible. The large displacements/rotations and large shear strains that develop at the early stages of the cure cycle when the resin has a very low elastic modulus provided the impetus to include a large strain/deformation option in COMPRO. A new “co-rotational stress formulation” was developed and found to provide a robust method for numerical treatment of very large deformation/strain problems involving anisotropic materials of interest here. Several verification and validation examples are used to calibrate the contact interface parameters and to demonstrate the correctness of implementation and the accuracy of the proposed method. A number of comparisons are made with exact solutions, other methods, other experiments and the same models in other commercial codes. Finally, several interesting cases are examined to explore the results of COMPRO predictions with the added options.

Autoclave processing of large scale, one-piece structural parts made of carbon fiber-reinforced polymer composite materials is the key to decreasing manufacturing costs while at the same time increasing quality. Nonetheless, even in manufacturing simple flat parts, residual strains and stresses are unavoidable. For structural design purposes and to aid in the assembly procedures, it is desirable to have proven numerical tools that can be used to predict these residual geometrical and material properties in advance, thus avoid the costly experimental trial and error methods. A 2-D finite element-based code, COMPRO, has previously been developed in-house for predicting autoclave process-induced deformations and residual stresses in composite parts undergoing an entire cure cycle. To simulate the tool-part interaction, an important source of residual deformations/stresses, COMPRO used a non-zero thickness elastic shear layer as its only interface option. Moreover, the code did not account for the large deformations and strains and the resulting nonlinear effects that can arise during the early stages of the cure cycle when the material is rather compliant. In the present work, a contact surface employing a penalty method formulation is introduced at the tool-part interface. Its material-dependent parameters are a function of temperature, degree of cure, pressure and so forth. This makes the stick-slip condition plus separation between the part and the tool possible. The large displacements/rotations and large shear strains that develop at the early stages of the cure cycle when the resin has a very low elastic modulus provided the impetus to include a large strain/deformation option in COMPRO. A new “co-rotational stress formulation” was developed and found to provide a robust method for numerical treatment of very large deformation/strain problems involving anisotropic materials of interest here. Several verification and validation examples are used to calibrate the contact interface parameters and to demonstrate the correctness of implementation and the accuracy of the proposed method. A number of comparisons are made with exact solutions, other methods, other experiments and the same models in other commercial codes. Finally, several interesting cases are examined to explore the results of COMPRO predictions with the added options.

Autoclave processing of large scale, one-piece structural parts made of carbon fiber-reinforced polymer composite materials is the key to decreasing manufacturing costs while at the same time increasing quality. Nonetheless, even in manufacturing simple flat parts, residual strains and stresses are unavoidable. For structural design purposes and to aid in the assembly procedures, it is desirable to have proven numerical tools that can be used to predict these residual geometrical and material properties in advance, thus avoid the costly experimental trial and error methods. A 2-D finite element-based code, COMPRO, has previously been developed in-house for predicting autoclave process-induced deformations and residual stresses in composite parts undergoing an entire cure cycle. To simulate the tool-part interaction, an important source of residual deformations/stresses, COMPRO used a non-zero thickness elastic shear layer as its only interface option. Moreover, the code did not account for the large deformations and strains and the resulting nonlinear effects that can arise during the early stages of the cure cycle when the material is rather compliant. In the present work, a contact surface employing a penalty method formulation is introduced at the tool-part interface. Its material-dependent parameters are a function of temperature, degree of cure, pressure and so forth. This makes the stick-slip condition plus separation between the part and the tool possible. The large displacements/rotations and large shear strains that develop at the early stages of the cure cycle when the resin has a very low elastic modulus provided the impetus to include a large strain/deformation option in COMPRO. A new “co-rotational stress formulation” was developed and found to provide a robust method for numerical treatment of very large deformation/strain problems involving anisotropic materials of interest here. Several verification and validation examples are used to calibrate the contact interface parameters and to demonstrate the correctness of implementation and the accuracy of the proposed method. A number of comparisons are made with exact solutions, other methods, other experiments and the same models in other commercial codes. Finally, several interesting cases are examined to explore the results of COMPRO predictions with the added options. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

No / A finite element based method for solution of large-deformation hyperelastic constitutive models is developed, which solves the Cauchy-stress balance equation using a single rotation of stress from principal directions to a fixed co-ordinate system. Features of the method include stress computation by central differencing of the hyperelastic energy function, mixed integration-order incompressibility enforcement, and an iterative solution method that employs notional `small strain¿ stiffness. The method is applied to an interesting and difficult elastic model that replicates polymer `necking¿; the method is shown to give good agreement with published results from a well-established finite element package, and with published experimental results. It is shown that details of the manner in which incompressibility is enforced affects whether key experimental phenomena are clearly resolved.

This thesis examines and identifies the problems of shape collapse in large deformation image registration. Shape collapse occurs in image registration when a region in the moving image is transformed into a set of near zero volume in the target image space. Shape collapse may occur when the moving image has a structure that is either missing or does not sufficiently overlap the corresponding structure in the target image. We state that shape collapse is a problem in image registration because it may lead to the following consequences: (1) Incorrect pointwise correspondence between different coordinate systems; (2) Incorrect automatic image segmentation; (3) Loss of functional signal. The above three disadvantages of registration with shape collapse are illustrated in detail using several examples with both real and phantom data. Shape collapse problem is common in image registration algorithms with large degrees of freedom such as many diffeomorphic image registration algorithms. This thesis proposes a shape collapse measurement algorithm to detect the regions of shape collapse after image registration in pairwise and group-wise registrations. We further compute the shape collapse for a whole population of pairwise transformations such as occurs when registering many images to a common atlas coordinate system. Experiments are presented using the SyN diffeomorphic image registration algorithm and diffeomorphic demons algorithm. We show that shape collapse exists in both of the two large deformation registration methods. We demonstrate how changing the input parameters to the SyN registration algorithm can mitigate the collapse image registration artifacts.

<p dir="ltr">This thesis investigates the large deflection behavior of cantilever beams under various configurations and loading conditions. The primary objective is to uset an analytical model using elliptic integrals to solve the second-order non-linear differential equations that govern the deflection of these beams. The analytical model is implemented in Python and compared against Finite Element Analysis (FEA) results obtained from ANSYS, ensuring the accuracy and reliability of the model. The study examines multiple beam configurations, including straight and inclined beams, with both free and fixed tip slopes. Sensitivity analysis is conducted to assess the impact of key parameters, such as Young’s modulus, beam height, width, and length, on the deflection behavior. This analysis reveals critical insights into how variations in material properties and geometric dimensions affect beam performance. A detailed error analysis using Root Mean Square Error (RMSE) is performed to compare the analytical model's predictions with the FEA results. The error analysis highlights any discrepancies, demonstrating the robustness of the analytical approach. The results show that the analytical model, based on elliptic integrals, closely matches the FEA results across a range of configurations and loading scenarios. The insights gained from this study can be applied to optimize the design of cantilever beams in various engineering applications, including prosthetics, robotics, and structural components. Overall, this research provides a comprehensive understanding of the large deflection behavior of cantilever beams and offers a reliable analytical tool for engineers to predict beam performance under different conditions. The integration of Python-based numerical methods with classical elliptic integral solutions presents a useful approach that enhances the precision and applicability of beam deflection analysis.</p>

Ce travail porte sur la modélisation micromécanique des élastomères chargés. On cherche principalement à d'une part identifier l'influence des propriétés des différentes phases (morphologie et comportement) sur la réponse macroscopique, et d'autre part explorer les mécanismes d'interactions qui peuvent avoir lieu au sein de la micro-structure. Pour ce faire, on a mené une étude à deux échelles d'observations et ce à l'aide de simulations numériques basées sur l'homogénéisation. Le premier niveau correspond à une échelle mésoscopique pour laquelle on considère un Volume Élémentaire Représentatif (VER) bi-phasique, constitué d'un agglomérat de charge dissipatif, noyé dans une matrice hyperélastique. Le second niveau consiste, à une plus petite échelle, à explorer le comportement d'un agglomérat idéalisé, constitué de particules de charges infiniment rigides liées entre elles par une mince couche de gomme. Cette micro-structure est générée de manière aléatoire par un tirage de polygones de Voronoï. Des calculs éléments finis sont réalisés en élasticité linéaire et non-linéaire dans un contexte d'homogénéisation numérique en utilisant diverses techniques de localisation. Les différentes analyses menées montrent notamment que l'hypothèse d'affinité n'est pas adaptée à ce type de micro-structures et que le caractère incompressible de la gomme ainsi que son confinement jouent un rôle prépondérant sur le comportement mécanique de l'agglomérat. / This work focuses on the micro mechanical modeling of filled elastomers. The major question to be identified: firstly the influence of the properties of different phases (morphology and behavior) on the macroscopic response, and also to explore the mechanisms of interactions that take place within the micro-structure. To do this, we conducted a study at two scales of observations and using the numerical simulations based on homogenization. The first level corresponds to a mesoscopic scale for which we consider a representative elementary volume (REV), biphasic, consisting of a homogeneous dissipative inclusion (agglomerate) embedded in a hyperelastic matrix. The second level is at a smaller scale, to explore the behavior of an idealized agglomerate, consisting of infinitely rigid filler particles bounded together by a thin layer of rubber. This micro-structure is randomly generated by a random Voronoï polygons. Finite element calculations are performed in linear elasticity and nonlinear in the context of numerical homogenization using various localization techniques. The results show in particular that the assumption of affinity is not suitable for this type of micro-structures and the incompressibility of the rubber and its containment play an important role on the mechanical behavior of the agglomerate.

In the simulation of deformations of plates it is well known that we have to use a special treatment of the thickness dependence. Therewith we achieve a reduction of dimension from 3D to 2D. For linear elasticity and small deformations several techniques are well established to handle the reduction of dimension and achieve acceptable numerical results. In the case of large deformations of plates with non-linear material behaviour there exist different problems. For example the analytical integration over the thickness of the plate is not possible due to the non-linearities arising from the material law and the large deformations themselves. There are several possibilities to introduce a hypothesis for the treatment of the plate thickness from the strong Kirchhoff assumption on one hand up to some hierarchical approaches on the other hand.

<p>In the finite element simulation of problems with contact there arises</p><p>the need to change the mesh and continue the simulation on a new mesh.</p><p>This is encountered when the mesh has to be changed because the original mesh experiences severe distortion or the mesh is adapted to minimize errors in the solution. In such instances a crucial component is the transfer of data from the old mesh to the new one. </p><p>This work proposes a strategy by which such remeshing can be accomplished in the presence of mortar-discretized contact, </p><p>focusing in particular on the remapping of contact variables which must occur to make the method robust and efficient. </p><p>By splitting the contact stress into normal and tangential components and transferring the normal component as a scalar and the tangential component by parallel transporting on the contact surface an accurate and consistent transfer scheme is obtained. Penalty and augmented Lagrangian formulations are considered. The approach is demonstrated by a number of two and three dimensional numerical examples.</p> / Dissertation

abstract: Finite element simulations modeling the hydrodynamic impact loads subjected to an elastomeric coating were performed to develop an understanding of the performance and failure mechanisms of protective coatings for cavitating environments. In this work, two major accomplishments were achieved: 1) scaling laws were developed from hydrodynamic principles and numerical simulations to allow conversion of measured distributions of pressure peaks in a cavitating flow to distributions of microscopic impact loadings modeling individual bubble collapse events, and 2) a finite strain, thermo-mechanical material model for polyurea-based elastomers was developed using a logarithmic rate formulation and implemented into an explicit finite element code. Combining the distribution of microscopic impact loads and finite element modeling, a semi-quantitative predictive framework is created to calculate the energy dissipation within the coating which can further the understanding of temperature induced coating failures. The influence of coating thickness and elastomer rheology on the dissipation of impact energies experienced in cavitating flows has also been explored. The logarithmic formulation has many desired features for the polyurea constitutive model, such as objectivity, integrability, and additive decomposition compatibility. A review and discussion on the kinematics in large deformation, including a comparison between Lagrangian and Eulerian descriptions, are presented to explain the issues in building rate-dependent constitutive models in finite strains. When comparing the logarithmic rate with other conventional rates in test examples, the logarithmic rate shows a better conservation of objectivity and integrability. The modeling framework was validated by comparing predictions against temperatures measured within coatings subjected to a cavitating jet. Both the experiments and models show that the temperatures generated, even under mild flow conditions, raise the coating temperature by a significant amount, suggesting that the failure of these coatings under more aggressive flows is thermally induced. The models show that thin polyurea coatings synthesized with shorter molecular weight soft segments dissipate significantly less energy per impact and conduct heat more efficiently. This work represents an important step toward understanding thermally induced failure in elastomers subjected to cavitating flows, which provides a foundation for design and optimization of coatings with enhanced erosion resistance. / Dissertation/Thesis / Doctoral Dissertation Mechanical Engineering 2016