Page
%P
-
Chapter
Neue Formprinzipien
Erwin Steins Beitrag ist die früheste publizierte Auseinandersetzung mit Arnold Schönbergs um 1920 entwickelter Methode der Komposition mit zwölf nur aufeinander bezogenen Tönen. Dabei behandelt der Text wenig...
-
Chapter
History of Computational Classical Elasto-Plasticity
This contribution was presented by the author at COMPLAS XII in 2013 as a plenary lecture but not published so far. The historical presentation of physical und mathematical modeling together with the computati...
-
Book
-
Chapter
History of the Finite Element Method – Mathematics Meets Mechanics – Part I: Engineering Developments
The birth of variational calculus and the principle of virtual work goes back to the 17th and 18th century, and the first draft of a discrete variational method with “elementwise” triangular shape functions was g...
-
Chapter
The Origins of Mechanical Conservation Principles and Variational Calculus in the 17th Century
The 17th century is considered as the cradle of modern natural sciences and technology as well as the begin of the age of enlightenment with the invention of analytical geometry by Descartes (1637), infinitesimal...
-
Chapter
History of the Finite Element Method – Mathematics Meets Mechanics – Part II: Mathematical Foundation of Primal FEM for Elastic Deformations, Error Analysis and Adaptivity
This chapter treats the history of mathematical foundation of primal FEM, especially a posteriori error estimates and adaptivity, based on functional analysis in Sobolev spaces. This is of equal importance as ...
-
Article
Goal-oriented explicit residual-type error estimates in XFEM
A goal-oriented a posteriori error estimator is derived to control the error obtained while approximately evaluating a quantity of engineering interest, represented in terms of a given linear or nonlinear func...
-
Chapter
Goal-Oriented Residual Error Estimates for XFEM Approximations in LEFM
The objective is to derive and apply residual-type goal-oriented a posteriori error estimators for the discretization error obtained while approximately evaluating the nonlinear J-integral as a fracture criterion...
-
Chapter
Martensitic Phase Transformations of Mono and Polycrystalline Shape Memory Alloys – A Theoretically and Numerically Unified Concept
The unified setting presented here is based on phase transformation (PTs) of monocrystalline shape memory alloys (SMAs) and includes polycrystalline SMAs whose microstructure is modeled using lattice variants ...
-
Chapter and Conference Paper
A Unified Variational Setting and Algorithmic Framework for Mono- and Polycrystalline Martensitic Phase Transformations
The unified setting presented here is based on phase transformations (PTs) of monocrystalline shape memory alloys (SMAs) and includes polycrystalline SMAs whose microstructure is modeled using lattice variants...
-
Article
Theory and finite element computations of a unified cyclic phase transformation model for monocrystalline materials at small strains
After a survey the refined numerical treatment and verification is presented for a rate-independent macroscopic unified PT material model (including mass conservation with respect to phase fractions and covexi...
-
Article
Error controlled hp-adaptive FE and FE-BE methods for variational equalities and inequalities including model adapitivity
-
Article
On the duality of finite element discretization error control in computational Newtonian and Eshelbian mechanics
In this paper, goal-oriented a posteriori error estimators of the averaging type are presented for the error obtained while approximately evaluating theJ-integral in nonlinear elastic fracture mechanics. Since th...
-
Book
-
Chapter and Conference Paper
Error-Controlled Adaptive Finite Element Methods in Nonlinear Elastic Fracture Mechanics
Goal-oriented a posteriori error estimators are presented in this contribution for the error obtained while approximately evaluating the J-integral, i.e. the material force acting at the crack tip, in nonlinear e...
-
Chapter
Hierarchical Model and Solution Adaptivity of Thin-walled Structures by the Finite-Elements-Method
Hierarchical discretization and model adaptivity is achieved by locally computed quantitative (absolute) global error estimators with strict upper bounds for the discretization error of the FE-solution with re...
-
Chapter and Conference Paper
Hierarchical Model- and Discretization-error Estimation of Elasto-plastic Structures
A posteriori error estimators of the discretization and model errors are presented for finite-element solutions of small-strain elasto-plasticity and large-strain elasticity problems. The described posterior equi...
-
Chapter and Conference Paper
Phase Transitions in Dissipative Materials: Theory and Interpretation of Experiments
-
Article
Symmetric coupling of boundary elements and Raviart–Thomas-type mixed finite elements in elastostatics
Both mixed finite element methods and boundary integral methods are important tools in computational mechanics according to a good stress approximation. Recently, even low order mixed methods of Raviart–Thomas...
-
Chapter and Conference Paper
Deformation Instabilities at Finite Inelastic Strains
The aim of this work is the numerical analysis and simulation of shearband localization in plastic flow processes within ductile single (fcc) crystals. Thereby, the objective is to analyse the outcome of an im...
