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) is a combined thermal and mechanical loading process to compact and sinter a powder material within one process step In this short essay a constitutive model of thermo-viscoplasticity is proposed representing most of the phenomena observed in the experiments The constitutive model is calibrated to the experimental data and some predicted experiments are compared with constitutive model showing appropriate results (© 2014 Wiley-VCH Verlag GmbH & Co KGaA, Weinheim)

Powder compaction. Experiments, modeling and simulation

The identification of material parameters with a nonlinear least‐squares approach and finite elements is an established task in solid mechanics. There, full‐field experimental data can be employed in the material parameter identification procedure. The focus of this contribution is on the application of full‐field temperature data, measured with infrared thermography, to identify the coefficients of the thermal conductivity tensor of unidirectional fiber‐reinforced composites. Because of the unidirectional fiber reinforcement, transversely isotropic thermal behavior is assumed and the corresponding two thermal conductivities are identified from full‐field data. Beforehand performing the experiments, numerical re‐identifications are used to optimize the experimental procedure in a sensitivity analysis. Further, the uncertainties of the identified material parameters as well as the uncertainties of subsequent simulations are computed with the Gaussian error propagation concept.

https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/pamm.202200026

Parameter identification and uncertainty quantification of the thermal conductivity tensor for transversely isotropic composite materials

This short essay treats a bending theory for long beams made from laminates, i.e. a beam theory is derived for linear, elastic, isotropic material at small strains. It is a generalization to anarbitrary number of layers. As an example layered steel-polymer-steel (SPS) laminates are looked at, which are treated in metal-polymer-metal(MPM) bending forming processes, where the stress state influences the failure behavior.

Classical beam theory with arbitrary number of layers

Commonly, thermo-mechanically coupled problems, where the material properties change due to thermal agencies due to thermal agencies, and where the heat evolution is additionally caused by internal dissipation through mechanical loadings, are solved using staggered solution schemes, see, for example, [1, 2]. This may lead to unstable situations. Accordingly, fully coupled sche mes are of major interests in some situations, which, however, may lead to more computational costs. In order to solve the coupled system, which is influenced by the temperature dependence of the evolutions equations of the constitutive equations like models of thermo-viscoelasticity and thermo-viscoplasticity, one h as to ask in a first step for the entire structure of the coupled field problem solved using finite elemen ts. The classical approach using the method of vertical lines leads after the spatial discretization to a syste m of differential-algebraic equations. The algebraic part results from the discretized principle of vir tual displacements and the differential part consists of the discretized equation of heat conduction and the evolution equations of all internal variables in the spatially discretized structure

Thermo-mechanically coupled finite element analysis using high- order time integrators

The present paper is focused on the solution of differential–algebraic equation systems (DAE), which arise in large viscoelastic deformations within the quasi–static finite element context. For this purpose linearly implicit methods of Rosenbrock–type are used, which avoid completely the solution of non–linear equations. This article investigates a possible treatment of the new global approach with respect to expense and achievable accuracy. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Stefan Hartmann

Papers

Powder compaction. Experiments, modeling and simulation

Parameter identification and uncertainty quantification of the thermal conductivity tensor for transversely isotropic composite materials

Classical beam theory with arbitrary number of layers

Thermo-mechanically coupled finite element analysis using high- order time integrators

Application of Rosenbrock-type methods to a finite element formulation based on large strain viscoelasticity