| Frictional contact interactions between deformable bodies are ubiquitous and often create interesting and complex behavior. This dissertation focuses on the solution of this type of problem, set in the full generality of finite-deformation and evolving interface response. To this end, a constitutive framework drawn from an analogy with rigid-plasticity and satisfying the fundamental tenets of mechanics is employed. The model encompasses the classical Amontons-Coulomb law as well as more complex behavior, such as wear-driven evolution and orientation-dependent anisotropy. In agreement with the characteristic phenomenology of friction, a yield function is defined by the range of tangential traction an interface may transmit. The limiting tangential traction, which corresponds to a slipping state, is also given a constitutive definition. On the other hand, the Lagrange multipliers necessary to satisfy the geometric constraints of impenetrability and ‘stick’ are associated with the normal and tangential components of surface tractions, respectively, through energetic arguments. Thus, the scheme provides a dear means of describing the non-smooth behavior the tangential traction exhibits during stick-slip episodes.; Since even some of the most basic examples of the frictional contact problem elude purely analytical methods, a numerical treatment is necessary for solution. The yield-limited Lagrange multiplier formulation is carried over to a finite element-based method which allows imposition of the contact constraints with an acuity absent in penalty-based methods. The contact traction fields are approximated in a continuous fashion, in keeping with the underlying mechanics and in contrast with node-on-surface treatments. Moreover, unlike traditional methods, the constraint fields are constructed so as to prevent globally over-constraining the contacting surfaces. To accommodate the non-smooth behavior specifically associated with friction and to produce a robust and efficient algorithm, an iterative predictor-corrector solution method is developed. This solution process is stabilized by the relaxation of an artificially inflated yield surface, which initially generates a global state of stick. Physically plausible transition conditions are employed during the iteration process. Finally, by way of demonstration and validation of the methodology, a number of numerical simulations of quasi-static, planar problems ranging from simple patch tests to common manufacturing processes are presented. |
