Trata-se uma análise elastoplástica de tensões planas nos métodos de conformação em forjamentos com matriz aberta ou fechada e trefilação. Emprega-se o método das linhas de fluência, desenvolvido por Hencky e Prager. O estudo visa a determinação das tensões na região plástica e do campo de velocidades na região deformada, utilizando o método de Prager aplicado a um processo analítico. / An elastoplastic analysis of plane strain in axisymmetric flat and closed punch die and wiredrawing was made using the slip lines method, developed by Hencky and Prager. Studies were made to determine the strains in the plastic zone and the velocities in deformed zone using the Prager\'s method applyed in an analytical process.

Trata-se uma análise elastoplástica de tensões planas nos métodos de conformação em forjamentos com matriz aberta ou fechada e trefilação. Emprega-se o método das linhas de fluência, desenvolvido por Hencky e Prager. O estudo visa a determinação das tensões na região plástica e do campo de velocidades na região deformada, utilizando o método de Prager aplicado a um processo analítico. / An elastoplastic analysis of plane strain in axisymmetric flat and closed punch die and wiredrawing was made using the slip lines method, developed by Hencky and Prager. Studies were made to determine the strains in the plastic zone and the velocities in deformed zone using the Prager\'s method applyed in an analytical process.

The aim of this thesis is to develop a numerical method to find approximations to solutions of the double-slip and double-spin model for the deformation and flow of granular materials. The model incorporates the physical and kinematic concepts of yield, shearing motion on slip lines, dilatation and average grain rotation. The equations governing the model comprise a set of five first order partial differential equations for the five dependent variables comprising two stress variables, two velocity components and the density. For steady state flows, the model is hyperbolic and the characteristic directions and relations along the characteristics are presented. The numerical approximation for the rate of working of the stresses are also presented. The model is then applied to a number of granular flow problems using the numerical method.