Abstract. The methods of convex analysis are used to explore in greater depth the nature of the evolution equation in internal variable formulations of elastoplasticity. The evolution equation is considered in a form in which the thermodynamic force belongs to a set defined by a multi-valued map G. It is shown that the maximum plastic work inequality together with the assumption that G is maximal responsive (a term defined in Sec. 4), is necessary and sufficient to give a theory equivalent to that proposed by Moreau. Further consequences are investigated or elucidated, including the relationship between the yield function and the dissipation function; these functions are polars of each other. Examples are given to illustrate the theory.
This paper presents the results of an integrated laboratory and numerical modelling study on the effect of wellbore deviation and wellbore azimuth on fracture propagation in poorly consolidated sandstone formations. The goal of this project was to develop an understanding of how fractures would transition from single planar fractures to non-planar transverse fractures for fields in the deep-water Gulf of Mexico.The foundation of this work was over 40 fracturing laboratory tests to measure fracture propagation geometries for a range of well deviations, differential horizontal stresses and rock strength. The samples tested were from three outcrops with unconfined compressive strength (UCS) values ranging from 300 -1000 psi. For boreholes having low deviation angles and small differential stresses a vertical single planar fracture was created, aligned with the wellbore, as expected. As the well trajectory and stress contrast increased the fractures became more complex, with transverse turning fractures no-longer aligned with the wellbore.These laboratory results were used to develop and calibrate a new fully-3D finite element model that predicts non-planar fracture growth. The model matches the details of the laboratory tests, including the transition from planar vertical to nonplanar transverse fractures as the well deviation, azimuth and stress differentials increase. After initial model development and calibration was complete a model of a complex case was run before showing any experimental results to the modellers. The model successfully predicted the transverse non-planar results found in the laboratory; this gave us increased confidence in the model as a predictive tool. This work has now been applied with excellent success to four deepwater fields. We have recommended changes in maximum well deviations, performed post-job analyses on wells that had high deviations, and have increased our understanding of the impact of layered formations on fracture growth in these fields.
The solution of initial-boundary value problems involving finite elastoplastic deformations is discussed. The formulation considered differs from conventional formulations in that the evolution law is expressed in terms of the dissipation function. A generalized midpoint rule is used to obtain an incremental problem, a variational form of which is derived. The finite element method is used for spatial discretization, and an algorithm to solve the resulting discrete problem is developed. This algorithm has the predictor-corrector structure common to most solution procedures for problems in plasticity. Methods for imposing the plastic incompressibility constraint are investigated. Solutions to two axisymmetric examples obtained using the proposed algorithm are presented and compared with those obtained by other authors.
Abstract. An internal variable constitutive theory for elastic-plastic materials undergoing finite strains is presented. The theory is based on a corresponding study in the context of small strains [6], and has the following features: first, with a view to embracing the classical notions of convex yield surfaces and the normality law, the evolution law is developed within the framework of nonsmooth convex analysis, which proves to be a powerful unifying tool; secondly, the special case of elastic materials is recovered from the theory in a natural manner. After presentation of the theory a concrete example is discussed in detail.1. Introduction. The theory of plasticity in its classical small-strain form is wellestablished, especially that form which the theory takes in its application to metals. The finite-strain theory, on the other hand, while showing indications that it is on the way to becoming an established branch of mechanics, is still nevertheless the subject of considerable effort and debate, and certain of its aspects remain unsettled. The literature on the subject has in the meantime acquired voluminous proportions; without attempting a comprehensive survey we mention as important contributions the early work of Green and Naghdi [7] and of Lee [17] in which were addressed, inter alia, the question of the decomposition of deformation into elastic and plastic parts, the former proposing an additive decomposition of strain and the latter a multiplicative decomposition of deformation gradient. The multiplicative decomposition has proved more popular, and forms the basis for a number of alternative theories; as examples we mention the works of Mandel [18], Halphen and Nguyen [8], Simo and
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