Thesis (M.S.)--Worcester Polytechnic Institute. / Keyword: elastoviscoplasticity. Includes bibliographical references (p. 43-44).

published_or_final_version / Civil and Structural Engineering / Doctoral / Doctor of Philosophy

Two topics, i.e., the scale effects and the geodesics of random heterogeneous materials will be discussed in this work. / When the separation of scales in random media does not hold, the representative volume element (RVE) of deterministic continuum mechanics does not exist in the conventional sense, and new concepts and approaches are needed. This subject is discussed here in the context of microstructures of two types - planar random chessboards, and planar random inclusion-matrix composites -- with microscale behavior being elastic-plastic-hardening (power-law). The microstructure is assumed to be spatially homogeneous and ergodic. Principal issues under consideration are those of yield and incipient plastic flow of statistical volume elements (SVE) on mesoscales, and the scaling trend of SVE to the RVE response on macroscale. Indeed, the SVE responses under uniform displacement (or traction) boundary conditions bound from above (respectively, below) the RVE response, and we show via extensive simulations in plane stress that the larger is the mesoscale, the tighter are both bounds. However, the mesoscale flows under both kinds of loading do not, in general, display normality. Also, with the limitation imposed by currently available computational resources, we do not recover normality (or even a trend towards it) when studying the largest possible SVE domains. / The second topic is the geodesic (i.e., shortest path) character of strain fields occurring in elasto-plastic response of planar inclusion-matrix composites. The composites' spatially random morphology is created by generating the disk centers through a sequential inhibition process based on a poisson point field in plane. Both phases (inclusions and matrix) are elastic-plastic-hardening with the matrix being more compliant and weaker than the inclusions, and perfect bonding everywhere. A quantitative comparison of a response pattern obtained by computational micromechanics with that found only by mathematical morphology indicates that (i) the regions of plastic flow are very close to geodesics, and (ii) a purely geometric, and orders of magnitude more rapid than by computational mechanics assessment of these regions is possible.

Thesis (M.S.)--Rochester Institute of Technology, 1988. / Includes bibliographical references (leaves 67-69).

Thesis (Ph. D.)--University of Hong Kong, 1992.

Bibliography: pages 316-322. / In this thesis we study the mathematical structure and numerical approximation of two boundary-value problems in small strain elastoplasticity. The first problem, which we call the incremental holonomic problem, is based on a consistent incremental holonomic constitutive law, which in turn derives from the notion of extremal paths in stress and strain space as originally proposed by PONTER & MARTIN (1972); the second problem which we study is the classical rate problem. We show that both problems can be formulated as variational inequalities, with internal variables being included explicitly in the formulation. Corresponding minimisation problems follow naturally from standard results in convex analysis.

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The partial differential equation governing the problem of elastoplasticity is linear in the elastic region and nonlinear in the plastic region. In the elastic region, we encounter the problem of elasticity which is governed by the Navier Lame equations. We present a solution to the above problem through numerical schemes such as the finite element method. problem. This is hard to achieve from a numerical point of view however. is explained and a new method to solve the problem is proposed. The path us improve Newton's method by a better choice of the initial guess. this method for the penalty parameter as close to zero as we want and thereby we obtain an exact solution to our original PDE. Plots with results are presented.

published_or_final_version / Civil and Structural Engineering / Master / Master of Philosophy

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