Author
Peter Wriggers
Other affiliations: Darmstadt University of Applied Sciences, Ohio State University, Northwestern University ...read more
Bio: Peter Wriggers is an academic researcher from Leibniz University of Hanover. The author has contributed to research in topics: Finite element method & Mixed finite element method. The author has an hindex of 67, co-authored 582 publications receiving 19212 citations. Previous affiliations of Peter Wriggers include Darmstadt University of Applied Sciences & Ohio State University.
Papers published on a yearly basis
Papers
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15 Nov 2004
TL;DR: The mathematical structure of the contact formulation for finite element methods is derived on the basis of a continuum description of contact, and several algorithms related to spatial contact search and fulfillment of the inequality constraints at the contact interface are discussed.
Abstract: 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
1,761 citations
Book•
30 Aug 2002
TL;DR: In this article, Gauss integration rules are used to solve the contact boundary value problem and small deformation contact problem, and a solution algorithm is proposed for the large deformation problem.
Abstract: Preface. Introduction. Introduction to Contact Mechanics. Continuum Solid Mechanics and Weak Forms. Contact Kinematics. Constitutive Equations for Contact Interfaces. Contact Boundary Value Problem and Weak Form. Discretization of the Continuum. Discretization, Small Deformation Contact. Discretization, Large Deformation Contact. Solution Algorithms. Thermo--mechanical Contact. Beam Contact. Adaptive Finite Element Methods for Contact Problems. Computation of Critical Points with Contact Constraints. Appendix A: Gauss Integration Rules. Appendix B: Convective Coordinates. Appendix C: Parameter Identification for Friction Materials. References. Index.
1,153 citations
Book•
15 Feb 2009
TL;DR: In this article, the Finite Element Method for Continuum Mechanics has been used for solving nonlinear problems in the field of metamodel physics, including contact problems and time dependent problems.
Abstract: Nonlinear Phenomena.- Basic Equations of Continuum Mechanics.- Spatial Discretization Techniques.- Solution Methods for Time Independent Problems.- Solution Methods for Time Dependent Problems.- Stability Problems.- Adaptive Methods.- Special Structural Elements.- Special Finite Elements for Continua.- Contact Problems.- Automation of the Finite Element Method by J. Korelc.
1,003 citations
TL;DR: In this paper, three-dimensional geometrical models for concrete are generated taking the random structure of aggregates at the mesoscopic level into consideration, where the aggregate particles are generated from a certain aggregate size distribution and then placed into the concrete specimen in such a way that there is no intersection between the particles.
594 citations
Book•
01 Jan 2005
TL;DR: Some basics of the Mechanics of Solid Continua can be found in this article, including fundamental weak formulations, fundamental micro-macro concepts, and fundamental Micro-Macro concepts.
Abstract: Some Basics of the Mechanics of Solid Continua.- Fundamental Weak Formulations.- Fundamental Micro-Macro Concepts.- A Basic Finite Element Implementation.- Computational/Statistical Testing Methods.- Various Extensions and Further Interpretations of Partitioning.- Domain Decomposition Analogies and Extensions.- Nonconvex-Nonderivative Genetic Material Design.- Modeling Coupled Multifield Processes.- Closing Comments.
531 citations
Cited by
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TL;DR: In this article, the concept of isogeometric analysis is proposed and the basis functions generated from NURBS (Non-Uniform Rational B-Splines) are employed to construct an exact geometric model.
5,137 citations
TL;DR: A large selection of solution methods for linear systems in saddle point form are presented, with an emphasis on iterative methods for large and sparse problems.
Abstract: 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.
2,253 citations
2,140 citations
Dissertation•
01 Oct 1948
TL;DR: In this article, it was shown that a 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.
Abstract: 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.
2,042 citations
15 Nov 2004
TL;DR: The mathematical structure of the contact formulation for finite element methods is derived on the basis of a continuum description of contact, and several algorithms related to spatial contact search and fulfillment of the inequality constraints at the contact interface are discussed.
Abstract: 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
1,761 citations