Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

During the last decade, a big progress has been achieved in the analysis and numerical treatment of Initial Value Problems (IVPs) in Differential Algebraic Equations (DAEs) and Ordinary Differential Equations (ODEs). In spite of the rich variety of results available in the literature, there are still many specific problems that require special attention. Two of such, which are considered in this work, are the optimization of order of accuracy and reduction of cost of functional evaluations of Explicit Runge - Kutta (ERK) methods.

Traditionally, the maximum attainable order p of an s-stage ERK method for advancing the solution of an IVP is such that
p(s)
 4
 
In 1999, Goeken presented an s-stage ERK Method of order p(s)=s +1,s>2.
However, this work focuses on the design of a new approximation algorithm that reduces the cost of functional evaluations and yet increases the attainable order higher 
U n and Jonhson [94]; and the classical ERK methods. The order p of 
the new scheme called Multiderivative Explicit Runge-Kutta (MERK) Methods is such that p(s) 2. The stability, convergence and implementation for the optimization of IVPs in DAEs and ODEs systems are also considered.

Numerical solution of initial value problems in differential - algebraic equations

A flux splitting scheme is proposed for the general nonequilibrium flow equations with an aim at removing numerical dissipation of Van-Leer-type flux-vector splittings on a contact discontinuity. The scheme obtained is also recognized as an improved Advection Upwind Splitting Method (AUSM) where a slight numerical overshoot immediately behind the shock is eliminated. The proposed scheme has favorable properties: high-resolution for contact discontinuities; conservation of enthalpy for steady flows; numerical efficiency; applicability to chemically reacting flows. In fact, for a single contact discontinuity, even if it is moving, this scheme gives the numerical flux of the exact solution of the Riemann problem. Various numerical experiments including that of a thermo-chemical nonequilibrium flow were performed, which indicate no oscillation and robustness of the scheme for shock/expansion waves. A cure for carbuncle phenomenon is discussed as well.

A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities(Proceedings of the 12th NAL Symposium on Aircraft Computational Aerodynamics)

The Physics of Rubber Elasticity (J. Meixner)

https://hal.archives-ouvertes.fr/hal-00457010/document

B¯ and F¯ projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements

Field-assisted sintering technology (FAST) implies a multifield problem between electrical, thermal and mechanical fields. Based on a constitutive model proposed in [1], the numerical treatment of the three-field problem in a monolithic finite element framework is discussed. Apart from algorithmic considerations, numerical simulations are performed treating the complex contact problem, large deformations and the multifield issues themselves. This is combined with a PID-controller, which is required when the temperature process is given at specific positions in the graphite tool system and the electrical current is uncertain. The numerical simulations are validated by real experiments.

Field Assisted Sintering Technology, Part II: Simulation

Digital Image Correlation techniques (DIC) constitute a growing field of experimental measurement tools to determine the displacement and strain distribution on the surface of a specimen under external mechanical loads. In this article, the aspect of strain computation in surfaces is recapped in a first step. Here, two different approaches are compared. One method is related to the basic ideas emerging in finite elements, while the other approach is frequently applied in commercial DIC-systems. Unfortunately, there are no adequate measures to investigate the accuracy of the strain calculations. This article provides analytical examples concerning strain determination, stretches in arbitrary surface directions, and shear angles. The provided verification examples can be used either to study existing DIC-codes or can be applied by code developers working on new systems. In this regard, the focus will first be on determining strains and strain-rates within a surface. Second, particular surface descriptions are used to investigate examples of homogeneous and inhomogeneous deformations such as simple shear, combined tension-torsion of a cylindrical bar, bending of a thin sheet and a deep-drawing process. It will be shown that some situations show accurate results, while other problems demand special care concerning the interpretation of the final strain field distribution. Thus, the article does not focus on assessing image patterns, but addresses strain determination on point clouds.

Verification Examples for Strain and Strain-Rate Determination of Digital Image Correlation Systems

In this article the multiplicative decomposition of the deformation gradient into one part constrained in the direction of the axis of anisotropy and one part describing the directional deformation is proposed. This leads to a clear division of the deformation and stress states in the direction of anisotropy and a remaining part. The decomposition is explained in detail and a constitutive model of hyper-elasticity is proposed for the case of transversal isotropy, where the behavior of the model is investigated with the aid of simple analytical examples. The model is also investigated for inhomogeneous deformation states using high-order finite elements based on hierarchical shape functions showing the sensitivity of the accuracy of the results in the case of anisotropic media.

ERRATUM: Transversal isotropy based on a multiplicative decomposition of the deformation gradient within p-version finite elements

The insertion of holes into laminates can be done by producing a fiber reinforced composite plate and, subsequently, drilling the borehole Alternatively, we can bypass the fibers around the final hole before injecting the matrix material In the first case, the spatial distribution of the axis of anisotropy, and the structural tensor concerned, are spatially constant In the second case, ie the fiber circumplacement around the hole, a space-dependent anisotropy has to be considered Instead of the common approach of defining region-wise constant fiber orientations, we propose a continuous formulation of fiber orientations using streamlines To estimate the final stress and strain state for a unidirectional composite plate, three-dimensional finite element simulations are performed, where spatially constant transverse isotropy is compared to inhomogeneously distributed fiber orientation around the hole It will turn out that the resulting stress states lead to both reduced stress amplitudes in loading direction as well as compressive strains in lateral direction A detailed mathematical derivation of the basic equations accompanies the investigations

/pdf/modeling-of-fiber-circumplacement-around-a-hole-using-a-33s6ublpp4.pdf

Stefan Hartmann

Papers

Field Assisted Sintering Technology, Part II: Simulation

Verification Examples for Strain and Strain-Rate Determination of Digital Image Correlation Systems

ERRATUM: Transversal isotropy based on a multiplicative decomposition of the deformation gradient within p-version finite elements

Modeling of fiber circumplacement around a hole using a streamline approach

Field assisted sintering technology. Part I: Experiments, constitutive modeling and parameter identification