An algorithm is presented for the solution of mechanical contact problems using the displacement based Finite Element Method. The corrections are applied as forces at the global level, together with any corrections for other nonlinearities, without having to nominate either body as target or contactor. The technique requires statically reducing the global stiffness matrices to each degree of freedom involved in contact. Nodal concentrated force are redistributed as continuous tractions. These tractions are re-integrated over the element domains of the opposing body. This creates a set of virtual elements which are assembled to provide a convenient mesh of the properties of the opposing body no matter what its actual discretizaton into elements. Virtual nodal quantities are used to calculate corrective forces that are optimal to first order. The work also presents a derivation of refereritial strain tensors. This sheds new light on the updated Lagrangian formulation, gives a complete and correct incremental form for the Lagrangian strain tensor and illustrates the role of the reference configuration and what occurs when it is changed. / Thesis / Doctor of Philosophy (PhD)

The present thesis is composed of two parts. The first part presents the chemo-mechanical effect on the volumetric and shearing behaviour of saturated soil as a continuum. The second part presents the chemo-mechanical effect on the shearing behaviour of a discontinuity. Following Gajo and Loret, 2003, saturated soil is considered as a two-phase deformable porous medium, namely solid and fluid phase consisting of different species. There are clay particles, adsorbed water and ion in the solid phase. The fluid phase includes pore water and salt which may diffuse through the porous medium. In addition, water may be exchanged between solid and fluid phases while the mass of clay particles and ions in the solid phase remains constant. Thus, the balance equations are momentum balance, the mass balance of pore water and salt in the fluid phase, the mass balance of absorbed water. A two-dimensional element is proposed to approximate the solution of the balance equations which has been implemented in a user-defined subroutine (UEL) of the commercial code ABAQUS. This element has taken into account the 2D displacement of the soil skeleton, multidimensional flow of water, osmotic effect, advection and diffusion of salt. A new hyperelastic law is presented by extending the chemo-mechanical model proposed by Loret et al., 2002. The innovative aspects of the proposed model are the following: 1) both the tangent shear stiffness and bulk stiffness depend on the applied stress state and pore water solution, 2) the anisotropy of fabric tensor is introduced in the elasticity law. Moreover, the yield function has been modified to obtain smaller peak strength for highly overconsolidated samples to have better agreement with experimental results. The proposed 2D model is validated with experimental results on natural bentonite (a very active clay) and the soil extracted from low activity clay of Costa della Gaveta slope in Southern Italy. The swelling and swelling pressure of these two types of soil have been computed and compared with the experimental data to show the accuracy and reliability of the proposed model. Furthermore, the effects of elastic anisotropy are investigated on the soil behaviour such as swelling, swelling pressure, stress paths and horizontal stress. Furthermore, a simplified analysis has been performed to show the effect of swelling pressure on slope stability. In the second part, a contact element is proposed to account for the flow of water and diffusion of salt in addition to displacement in the simulation of interface behaviour. This element has been implemented in a user-defined subroutine (UEL) of ABAQUS. Moreover, a nonlinear elasticity law is proposed in which traction in the contact region has been taken into account. The Mohr-Columb yield criterion is used for the plastic regime in which it is assumed that the friction angle is a function of salt concentration and displacement rate based on the experimental data. Some preliminary results are shown for the flux of salt and water through the element. In addition, the effects of salt concentration and displacement rate are presented on the shearing behaviour of the contact element.

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The objective of this research is to simulate a pushorming operation for the manufacturing of copper tube elbows using the finite element method. This model may be useful in the design of tooling. The influences of lubricant type, the tube blank material, and a minute surface defect are considered in the model. Tensile tests of annealed copper specimens are conducted to derive stress-strain data, defining the material behavior of the copper tube blank. In addition, friction tests are performed to obtain static and dynamic friction coefficients for a wet and dry lubricant types, which are used in the forming process. The finite element study of the forming operation has proven to require a considerable amount of time for modeling and processing. The verification examples and the pushorming models demonstrate the ability of the finite element program to include: contact with friction, the actuating of hydraulically controlled components, buckling, and nonlinearity.

Compressive residual stresses induced by tensile overloads, compressive under loads, or by a cold-expansion process in specimens containing a circular hole and their influence on subsequent fatigue crack growth in aluminum alloys are studied. The finite element method is used to calculate residual stresses. The superposition method, which uses crack-tip stress intensity factors for cases involving remote loading and residual stresses, is used to calculate crack growth life for three kinds of tests from the literature: (1) fatigue of a circular hole specimen after an overload or under load, (2) single crack growing from a circular hole after a severe tensile overload, and (3) single crack growing from a circular hole after cold-working, reaming and notching. All specimens were subjected to subsequent constant amplitude loading. The superposition method worked fairly well for most cases, but tended to over predict fatigue life for small cracks and for cracks growing under residual stresses, which produce compressive (maximum and minimum) stress intensity factors.

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