Discrete particle simulation of particulate systems: Theoretical developments

Discrete particle simulation of particulate systems: A review of major applications and findings

Thank you for downloading regularization of inverse problems. Maybe you have knowledge that, people have search hundreds times for their favorite novels like this regularization of inverse problems, but end up in malicious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they juggled with some infectious bugs inside their computer. regularization of inverse problems is available in our book collection an online access to it is set as public so you can download it instantly. Our book servers spans in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the regularization of inverse problems is universally compatible with any devices to read.

Regularization Of Inverse Problems

Thank you for downloading linear and nonlinear programming. As you may know, people have search numerous times for their favorite novels like this linear and nonlinear programming, but end up in malicious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they juggled with some infectious bugs inside their desktop computer. linear and nonlinear programming is available in our book collection an online access to it is set as public so you can download it instantly. Our digital library spans in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the linear and nonlinear programming is universally compatible with any devices to read.

Linear And Nonlinear Programming

In this paper, we suggest a variational model for optic flow computation based on non-linearised and higher order constancy assumptions. Besides the common grey value constancy assumption, also gradient constancy, as well as the constancy of the Hessian and the Laplacian are proposed. Since the model strictly refrains from a linearisation of these assumptions, it is also capable to deal with large displacements. For the minimisation of the rather complex energy functional, we present an efficient numerical scheme employing two nested fixed point iterations. Following a coarse-to-fine strategy it turns out that there is a theoretical foundation of so-called warping techniques hitherto justified only on an experimental basis. Since our algorithm consists of the integration of various concepts, ranging from different constancy assumptions to numerical implementation issues, a detailed account of the effect of each of these concepts is included in the experimental section. The superior performance of the proposed method shows up by significantly smaller estimation errors when compared to previous techniques. Further experiments also confirm excellent robustness under noise and insensitivity to parameter variations.

Highly accurate optic flow computation with theoretically justified warping

Based on the theory of porous media (mixture theories extended by the concept of volume fractions), a model describing the dynamical behaviour of a saturated binary porous medium is presented including both geometrical and material non-linearities. Transformed toward a weak formulation, the model equations are solved by use of the finite element method. Applications of the model range from one-dimensional linear problems to two-dimensional problems including the full dynamics and non-linearities.

Dynamic Analysis of a Fully Saturated Porous Medium Accounting for Geometrical and Material Non-Linearities

From particle ensembles to Cosserat continua: homogenization of contact forces towards stresses and couple stresses

Wave propagation in porous media is an important topic for example in geomechanics or oil-industry. Especially due to the interplay of the solid skeleton with the fluid the so-called second compressional wave appears. The existence of this wave is reported in the literature not only for Biot's theory (BT) but also for theoretical approaches based on the Theory of Porous Media (TPM – mixture theory extended by the concept of volume fractions). Assuming a geometrically linear description (small displacements and small deformation gradients) and linear constitutive equations (Hooke's law) the governing equations are derived for both theories, BT and the TPM, respectively. In both cases, the solid displacements and the pore pressure are the primary unknowns. Note that this is only possible in the Laplace domain leading to the same structure of the coupled differential equations for both approaches. But the differential equations arising in BT and TPM possess different coefficients with different physical interpretations. Correlating these coefficients to each other leads to the well-known problem of Biot's “apparent mass density”. Furthermore, some inconsistencies are observed if Biot's stress coefficient is correlated to the structure arising in TPM. In addition to the comparison of the governing equations and the identification of the model parameters, the displacement and pressure solutions of both theories are presented for a one-dimensional column. The results show good agreement between both approaches in case of incompressible constituents whereas in case of compressible constituents large differences appear.

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A Comparative Study of Biot’s Theory and the Linear Theory of Porous Media for Wave Propagation Problems

Experimental data for foams lead to different values of the elastic moduli depending on the performed test, i.e. compression and tension tests give a different set of parameters than shear and bending tests. This may be explained by the size effect, which depends on the microstructure of the foams. Thus, in this paper, the behaviour of foams is investigated on the basis of both microscopic and macroscopic mechanical models. The microscopic approach is based on a lattice beam model. The solution of this model shows that the boundary–layer effect is strongly local but allows for the explanation of the size effect. Furthermore, the size effect can be included in the macroscopic continuum model by application of a Cosserat formulation. The extended continuum model allows for the independent fit of material parameters to different load cases, i.e. to compression and shear. The solution of the macroscopic Cosserat model permits a relation of the internal length–scale to the average cell size of the microstructure.

The size effect in foams and its theoretical and numerical investigation

The paper presents a higher order homogenization scheme based on non-linear micropolar kinematics representing the macroscopic variation within a representative volume element (RVE) of the material. On the microstructural level the micro–macro kinematical coupling is introduced as a second-order Taylor series expansion of the macro displacement field, and the microstructural displacement variation is gathered in a fluctuation term. This approach relates strongly to second gradient continuum formulations, presented by, e.g. Kouznetsova et al. (Int. J. Numer. Meth. Engng 2002; 54:1235–1260), thus establishing a link between second gradient and micropolar theories. The major difference of the present approach as compared to second gradient formulations is that an additional constraint is placed on the higher order deformation gradient in terms of the micropolar stretch. The driving vehicle for the derivation of the homogenized macroscopic stress measures is the Hill–Mandel condition, postulating the equivalence of microscopic and macroscopic (homogenized) virtual work. Thereby, the resulting homogenization procedure yields not only a stress tensor, conjugated to the micropolar stretch tensor, but also the couple stress tensor, conjugated to the micropolar curvature tensor. The paper is concluded by a couple of numerical examples demonstrating the size effects imposed by the homogenization of stresses based on the micropolar kinematics. Copyright © 2006 John Wiley & Sons, Ltd.

Stefan Diebels

Papers

Dynamic Analysis of a Fully Saturated Porous Medium Accounting for Geometrical and Material Non-Linearities

From particle ensembles to Cosserat continua: homogenization of contact forces towards stresses and couple stresses

A Comparative Study of Biot’s Theory and the Linear Theory of Porous Media for Wave Propagation Problems

The size effect in foams and its theoretical and numerical investigation

A second-order homogenization procedure for multi-scale analysis based on micropolar kinematics