Uzawa-like methods for numerical modeling of unsteady viscoplastic Bingham medium flows

The Uzawa-like algorithm is implemented for two-dimensional flows of viscoplastic fluids. The rheological model employed is the ideal Bingham model. As a test the lid-driven square-cavity benchmark problem is considered. The results for the steady-state problem are faithfully reproduced as compared to those in the literature for the shape and location of the yield surface. The proposed method is very successful at capturing both yielded and unyielded regions.     

A comparison of adaptive time stepping methods for coupled flow and deformation modeling

Many subsurface reservoirs compact or subside due to production-induced pressure changes. Numerical simulation of this compaction process is important for predicting and preventing well-failure in deforming hydrocarbon reservoirs. However, development of sophisticated numerical simulators for coupled fluid flow and mechanical deformation modeling requires a considerable manpower investment. This development time can be shortened by loosely coupling pre-existing flow and deformation codes via an interface. These codes have an additional advantage over fully-coupled simulators in that fewer flow and mechanics time steps need to be taken to achieve a desired solution accuracy. Specifically, the length of time before a mechanics step is taken can be adapted to the rate of change in output parameters (pressure or displacement) for the particular application problem being studied. Comparing two adaptive methods (the local error method—a variant of Runge–Kutta–Fehlberg for solving ode’s—and the pore pressure method) to a constant step size scheme illustrates the considerable cost savings of adaptive time stepping for loose coupling. The methods are tested on a simple loosely-coupled simulator modeling single-phase flow and linear elastic deformation. For the Terzaghi consolidation problem, the local error method achieves similar accuracy to the constant step size solution with only one third as many mechanics solves. The pore pressure method is an inexpensive adaptive method whose behavior closely follows the physics of the problem. The local error method, while a more general technique and therefore more expensive per time step, is able to achieve excellent solution accuracy overall.     

Formulation of the material force approach for elastic and inelastic materials

Fracture mechanical investigations are important for the durability of fracture sensitive products. Fracture mechanical simulations help to shorten the product development cycle and to decrease product costs. The so-called material force approach as an efficient tool is used to determine fracture mechanical parameters for elastic and inelastic materials. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An implicit three-dimensional model for describing the inelastic response of solids undergoing finite deformation

The aim of this paper is to develop a new unified class of 3D nonlinear anisotropic finite deformation inelasticity model that (1) exhibits rate-independent or dependent hysteretic response (i.e., response wherein reversal of the external stimuli does not cause reversal of the path in state space) with or without yield surfaces. The hysteresis persists with quasistatic loading. (2) Encompasses a wide range of different types of inelasticity models (such as Mullins effect in rubber, rock and soil mechanics, traditional metal plasticity, hysteretic behavior of shape memory materials) into a simple unified framework that is relatively easy to implement in computational schemes and (3) does not require any a priori particular notion of plastic strain or yield function. The core idea behind the approach is the development of an system of implicit rate equations that allow for the continuity of the response but with different rates along different directions. The theory, which is in purely mechanical setting, subsumes and generalizes many commonly used approaches for hypoelasticity and rate-independent plasticity. We illustrate its capability by modeling the Mullins effect which is the inelastic behavior of certain rubbery materials. We are able to simulate the entire cyclic response without the use of additional internal variables, i.e., the entire response is modeled by using an implicit function of stress and strain measures and their rates.     

On a general iterative scheme for newton-type methods

A class of Newton-type iterative processes for solving nonlinear operator equations in Banach spaces is described by a general scheme, in which the approximate inverses of the derivatives are obtained recursively. Convergence conditions as well as error estimates are given. Some particular cases are finally discussed.     

Creep damage modeling of a polycrystalline material

A polycrystalline material is investigated under creep conditions within the framework of continuum micromechanics. Geometrical 3D model of a polycrystalline microstructure is represented as a unit cell with grains of random crystallographical orientation and shape. Thickness of the plains, separating neighboring grains in the unit cell, can have non-zero value. Obtained geometry assigns a special zone in the vicinity of grain boundaries, possessing unordered crystalline structure. A mechanical behavior of this zone should allow sliding of the adjacent grains. Within the grain interior crystalline structure is ordered, what prescribes cubic symmetry of a material. The anisotropic material model with the orthotropic symmetry is implemented in ABAQUS and used to assign elastic and creep behavior of both the grain interior and grain boundary material. Appropriate parameters set allows transition from the orthotropy to the cubic symmetry for the grain interior. Material parameters for the grain interior are identified from creep tests for single crystal copper. Model parameters for the grain boundary are set from the physical considerations and numerical model validation according to the experimental data of the grain boundary sliding in a polycrystalline copper [2]. As the result of analysis representative number of grains and grain boundary thickness in the unit cell are recommended. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Automatic structure and parameter training methods for modeling of mechanical systems by recurrent neural networks

Automatic nonlinear-system identification is very useful for various disciplines including, e.g., automatic control, mechanical diagnostics and financial market prediction. This paper describes a fully automatic structural and weight learning method for recurrent neural networks (RNN). The basic idea is training with residuals, i.e., a single hidden neuron RNN is trained to track the residuals of an existing network before it is augmented to the existing network to form a larger and, hopefully, better network. The network continues to grow until either a desired level of accuracy or a preset maximal number of neurons is reached. The method requires no guessing of initial weight values or the number of neurons in the hidden layer from users. This new structural and weight learning algorithm is used to find RNN models for a two-degree-of-freedom planar robot, a Van der Pol oscillator and a Mackey–Glass equation using their simulated responses to excitations. The algorithm is able to find good RNN models in all three cases.     

Motion planning for a piezo-actuated structure modeling a wingsail

This contribution presents the modeling and the motion planning of a flexible interconnected beam structure representing a wingsail. The structure is equipped with spatially distributed embedded actuators. The solution of the motion planning provides a feedforward control law to realize a desired spatial-temporal out-of-plane deflection trajectory. For this, a systematic flatness-based methodology is proposed, that allows for an efficient numerical solution exploiting, e.g., finite element approximations. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of contact deformation for a pinch gripper in automated material handling

Grasping analysis is concerned with relating the characteristics of the grasped object to the requirements of the gripper structure. When a gripper presses a flexible specimen with a size larger than that of the gripping surface, complex deformations are produced (compression, shearing, bending and tension). The boundary conditions are complex too because of the changing compressed region and, for many grippers, a changeable contact area. In this paper a mathematical predictive model is presented for simulating these complex deformations, relating a flat gripper’s performance to the properties of flexible gripped materials using elasticity theory. In particular, the distributions of stress and strain within the materials are derived when the gripper presses them. The main variables in the picking-up action have been identified. Moreover, a contact solution has been derived for calculating the contact length between a sample and a rigid support table. The change in the compressed region within a sample as a function of external load has been calculated. In order to match experimental behaviour the non-linear elastic response of the flexible material and the large deformations have to be incorporated in the model. The model predictions have been tested against experimental data and the results of finite element analysis and reasonably good agreement has been obtained.     

一般基下矩阵多项式的张量Bezoutian

给出矩阵多项式在一般基下的张量Bezoutian的定义,推广了标准幂基下的古典张量Bezoutian.讨论了该矩阵的Barnett型分解,缠绕关系和关于可控制/可观测矩阵的表示等重要性质.     

Strength and deformation properties of fiberglass-plastic in the flat stressed state as a function of reinforcement structure

Conclusion Limiting strength values have been ascertained in the flat stressed state as a function of reinforcement structure. The change in each strength surface tensor component as a function of reinforcement intensity has been approximated by the piecewise-linear approximation method. A strength condition has been derived which can be used in optimization problems. The problem of the optimum reinforcement structure of a composite at various ratios of the stresses ₁₁, ₂₂, and ₁₂ has been examined. By using the strength condition, one can predict strength values for structures which appear in the class of materials in question with various reinforcement intensities. The procedure developed can be used in designing composite materials.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 848–859, September–October, 1978.     

Convergence of coercive approximations for strictly monotone quasistatic models in inelastic deformation theory

This article studies coercive approximation procedures in the infinitesimal inelastic deformation theory. For quasistatic, strictly monotone, viscoplastic models using the energy method and the Young measures approach a convergence theorem in generalized Orlicz spaces is proved. The main step in the proof is a characterization of the weak limit of non‐linear terms by the convergence in measure. Copyright © 2007 John Wiley & Sons, Ltd.     

Space-time ray method for waves of small deformation in a nonlinear elastic medium

Space-time ray solutions for longitudinal waves of small deformation in a non-linear elastic medium are constructed.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 140, pp. 61–72, 1984.