Differential Geometry Approach to Continuous Model of Micro-Structural Defects in Finite Elasto-Plasticity

This paper concerns finite elasto-plasticity of crystalline materials with micro-structural defects. We revisit the basic concepts: plastic distortion and decomposition of the plastic connection. The body is endowed with a structure of differential manifold. The plastic distortion is an incompatible diffeomorphism. The metric induced by the plastic distortion on the intermediate configuration (considered to be a differential manifold) is a key point in the theory, in defining the defects related to point defects, or extra-matter. The so-called plastic connection is metric, with plastic metric tensor expressed in terms of the plastic distortion and its adjoint. We prove an appropriate decomposition of the plastic connection, without any supposition concerning the non-metricity of plastic connection. All types of the lattice defects, dislocations, disclinations, and point defects are described in terms of the densities related to the elements that characterize the decomposition theorem for plastic connection. As a novelty, the measure of the interplay of the possible lattice defects is introduced via the Cartan torsion tensor. To justify the given definitions, the proposed measures of defects are compared to their counterparts corresponding to a classical framework of continuum mechanics. Thus, their physical meanings can be emphasized at once.

Optimal Control of Plasticity with Inertia

The paper is concerned with an optimal control problem governed by the equations of elasto plasticity with linear kinematic hardening and the inertia term at small strain. The objective is to optimize the displacement field and plastic strain by controlling volume forces. The idea given in [10] is used to transform the state equation into an evolution variational inequality (EVI) involving a certain maximal monotone operator. Results from [27] are then used to analyze the EVI. A regularization is obtained via the Yosida approximation of the maximal monotone operator, this approximation is smoothed further to derive optimality conditions for the smoothed optimal control problem.

Optimisation of Well and Layer Selection for Re-fracturing

In initial fracturing of tight oil and gas reservoirs, due to the influence of geological and technological factors, the fracture conductivity has decreased, and the single-well productivity has been reduced. It is urgent to repeat transformation to restore or increase productivity. Well selection and layer selection is one of the key factors that affect the design of re-fracturing and the effect of stimulation. Based on a big database of well-sites, establishing machine intelligence theory determines the elasto-plasticity, permeability, porosity, completion parameters, production decline parameters and skin coefficient that affect the effect of re-fracturing stimulation by dimensionless parameter method of well and layer selection and its stimulation evaluation model. Combined with artificial neural network and BP algorithm, the index weights of strata with different reservoir physical properties are calculated to analyze the final evaluation value of fracturing effect. On the basis of remaining oil distribution research, scale extended fracture repeated fracturing is increased, injection-production well pattern is improved, scale repeated fracturing effect is increased, well pattern is improved, target layer is repeatedly fractured, and oil increase effect is obvious after fracturing.

Analysis of the Geomechanical Phenomena that Led to the Appearance of Sinkholes at the Lupeni Mine, Romania, in the Conditions of Thick Coal Seams Mining with Longwall Top Coal Caving

Thick coal seam no. 3, block V, Lupeni mine was mined by longwall top coal caving (LTCC). After the coal mining, the ground surface underwent continuous subsidence, but since 2008, three sinkholes have appeared on the surface with important dimensions, atypical for the geo-mining conditions in this coal basin. This article is a synthesis of the study meant to decipher the geo-mechanical phenomenon that led to the emergence of these sinkholes and highlighting the main factors that contributed to the development of this phenomenon. For this purpose, measurements were made on the terrain deformations using photogrammetric methods and aerial laser scanning, when modeling with 3D finite elements, in elasto-plasticity and with the help of the Knothe–Budrik influence function. The factors that contributed to the occurrence of discontinuous subsidence phenomena are shallow mining depth, the LTCC mining method, and the presence of faults in the vicinity of the mining panels. Additionally, the geo-mechanical phenomena of subsidence terrace development and sinkholes in the mining subsidence troughs at the Lupeni mine were described.

Richards' equation reconsidered

Semi-continuum modelling of unsaturated porous media flow is based on representing the porous medium as a grid of non-infinitesimal blocks that retain the character of a porous medium. Semi-continuum model is able to physically correctly describe diffusion-like flow, finger-like flow, and the transition between them. This article presents the limit of the semi-continuum model as the block size goes to zero. In the limiting process, the retention curve of each block scales with the block size and in the limit becomes a hysteresis operator of the Prandtl-type used in elasto-plasticity models. Mathematical analysis showed that the limit of the semi-continuum model is a partial differential equation with a hysteresis operator of Prandl's type. This limit differs from the standard Richards' Equation (RE), which is not able to describe finger-like flow. Since the physics behind both RE and the semi-continuum model is almost the same, we suggest a way to reformulate the RE so that it retains the ability to describe finger-like flow. We conclude that RE should be reconsidered by means of appropriate modelling of the hysteresis and correct scaling of the retention curve.

3D mixed virtual element formulation for dynamic elasto-plastic analysis

The virtual element method (VEM) for dynamic analyses of nonlinear elasto-plastic problems undergoing large deformations is outlined within this work. VEM has been applied to various problems in engineering, considering elasto-plasticity, multiphysics, damage, elastodynamics, contact- and fracture mechanics. This work focuses on the extension of VEM formulations towards dynamic elasto-plastic applications. Hereby low-order ansatz functions are employed in three dimensions with elements having arbitrary convex or concave polygonal shapes. The formulations presented in this study are based on minimization of potential function for both the static as well as the dynamic behavior. Additionally, to overcome the volumetric locking phenomena due to elastic and plastic incompressibility conditions, a mixed formulation based on a Hu-Washizu functional is adopted. For the implicit time integration scheme, Newmark method is used. To show the model performance, various numerical examples in 3D are presented.