https://hal.archives-ouvertes.fr/hal-01513346/document

Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement

Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems, and numerous solution techniques have been proposed for this type of system. The aim of this paper is to present and discuss a large selection of solution methods for linear systems in saddle point form, with an emphasis on iterative methods for large and sparse problems.

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Numerical solution of saddle point problems

Introduction to linear and nonlinear programming

IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

This paper describes modern techniques used to solve contact problems within Computational Mechanics. On the basis of a continuum description of contact, the mathematical structure of the contact formulation for finite element methods is derived. Emphasis is also placed on the constitutive behavior at the contact interface for normal and tangential (frictional) contact. Furthermore, different discretization schemes currently applied to solve engineering problems are formulated for small and finite strain problems. These include isoparametric interpolations, node-to-segment discretizations and also mortar and Nitsche techniques. Furthermore, several algorithms related to spatial contact search and fulfillment of the inequality constraints at the contact interface are discussed. Here, especially the penalty and Lagrange multiplier schemes are considered and also SQP- and linear-programming methods are reviewed.


Keywords:

contact mechanics;
friction;
penalty method;
Lagrange multiplier method;
contact algorithms;
finite element method;
finite deformations;
discretization methods

Computational Contact Mechanics

The surface-to-surface master–master contact treatment is a technique that addresses pointwise contact between bodies with no prior election of slave points, as in master–slave case. For a given configuration of contact-candidate surfaces, one needs to find the material points associated with a pointwise contact interaction. This is the local contact problem (LCP). The methodology can be applied together with numerical models such as geometrically nonlinear finite elements, discrete elements and multibody dynamics. A previous publication has addressed the possibility of degenerating the local contact problem, which yields the derivation of point-surface, curve-surface and other simplifications on the geometric treatment in the same mathematical formulation, sharing a single numerical implementation. This has useful applications for singularities or non-uniqueness scenarios on the LCP. The present work provides a framework for the degenerated master–master contact formulation including friction. An enhanced friction model is proposed, accounting for a combination of elastic and dissipative effects at the interface. Details of derivations and numerical implementation are given as well as examples related to beam-shell interaction.

Master-master frictional contact and applications for beam-shell interaction

A computational framework for extracting effective diffusivities from microtomographic images is presented. As an example of the capabilities of this framework, the effective diffusivity of a cement paste whose microstructure has been digitized to a resolution of 1 μm is derived. Besides presenting a consistent homogenization procedure, the importance of statistical testing is also highlighted. Indeed, for the problem at hand, it appears that statistical testing and subsequent interpretation of the results in terms of statistical quantities is a necessity for obtaining quantitative information on the property of interest.

Computation of Effective Cement Paste Diffusivities from Microtomographic Images

In this paper, a 3D computational model has been developed to investigate biofilms in a multi-physics framework using smoothed particle hydrodynamics (SPH) based on a continuum approach. Biofilm formation is a complex process in the sense that several physical phenomena are coupled and consequently different time-scales are involved. On one hand, biofilm growth is driven by biological reaction and nutrient diffusion and on the other hand, it is influenced by fluid flow causing biofilm deformation and interface erosion in the context of fluid and deformable solid interaction. The geometrical and numerical complexity arising from these phenomena poses serious complications and challenges in grid-based techniques such as finite element. Here the solution is based on SPH as one of the powerful meshless methods. SPH based computational modeling is quite new in the biological community and the method is uniquely robust in capturing the interface-related processes of biofilm formation such as erosion. The obtained results show a good agreement with experimental and published data which demonstrates that the model is capable of simulating and predicting overall spatial and temporal evolution of biofilm.

Numerical simulation and experimental validation of biofilm in a multi-physics framework using an SPH based method

Decision making in river floodplain management is a complex process that involves many stakeholders and experts. Since stakeholders and experts often pursue mutually exclusive objectives and are often geographically distributed, decision making process takes a long time and not as optimal as it should be. Use of intelligent decision support system (IDSS) allows to decrease the duration of decision making process and to improve the quality and efficiency of decisions. In this paper we present the knowledge-based system for intelligent support of decision making in river floodplain management. This system integrates the case based reasoning (CBR), qualitative reasoning (QR) and ontological knowledge base. Proposed knowledge representation model is formally represented by the OWL DL ontology. For this model we give the descriptions of case retrieval, adaptation and revising algorithms. Designed and implemented CBR-based IDSS for river floodplain management uses object-oriented analysis and Java2 technology.

Peter Wriggers

Papers

Master-master frictional contact and applications for beam-shell interaction

Computation of Effective Cement Paste Diffusivities from Microtomographic Images

Numerical simulation and experimental validation of biofilm in a multi-physics framework using an SPH based method

Intelligent Decision Support System for River Floodplain Management

Multiscale Modeling of Heterogeneous Structures