Micromechanics of Tension‐Compression Asymmetry of Polycrystalline Shape‐Memory‐Alloys

The asymmetry associated with martensitic transformations observed in tension/compression experiments of shape‐memory‐alloys (SMAs) is investigated on the basis of a recently suggested micromechanical model. The approach is based on crystallographic theory and utilizes a framework of energy minimization in a finite deformation context. Polycrystalline NiTi under tension demonstrates smaller phase‐transformation start‐strain, differe phase‐transformation stress‐levels and flatter phase‐transformation stress‐strain slopes than that under compression in our numerical simulation. The phase‐transformation start‐stress is followed to have a linear relationship with respect to the temperature within a certain range. These results agree well with experimental results reported in the literature.     

Werkstoffkennwerte für die Lebensdauerberechnung von Strukturen aus Stahlfeinblechen für den Automobilbau

Materials Data for Fatigue Life Calculation of Steel Sheet Structures for Automotive Engineering Within a joint project of the steel and automotive industry 17 steel sheet materials for automotive engineering in various delivery and forming conditions at temperatures of –40 °C, 22 °C and 100 °C were investigated. In the course of 37 test series strain controlled fatigue curves to crack initiation and stress‐strain‐curves under monotonic and cyclic loading were determined. All experimental data, hysteresis loops and determined cyclic properties are available in a database. A correlation between the mechanical properties from tensile tests and the properties from strain controlled cyclic experiments seems to be possible.     

Numerical modelling of void inclusions in porous media

Numerical modelling of porous flow in a low‐permeability matrix with high‐permeability inclusions is a challenging task because the large ratio of permeabilities ill‐conditions the finite element system of equations. We propose a coupled model where Darcy flow is used for the porous matrix and potential flow is used for the inclusions. We discuss appropriate interface conditions in detail and show that the head drop in the inclusions can be prescribed in a very simple way. Algorithmic aspects are treated in full detail. Numerical examples show that this coupled approach precludes ill‐conditioning and is more efficient than heterogeneous Darcy flow. Copyright © 2003 John Wiley & Sons, Ltd.     

Partition of unity enrichment for bimaterial interface cracks

Partition of unity enrichment techniques are developed for bimaterial interface cracks. A discontinuous function and the two‐dimensional near‐tip asymptotic displacement functions are added to the finite element approximation using the framework of partition of unity. This enables the domain to be modelled by finite elements without explicitly meshing the crack surfaces. The crack‐tip enrichment functions are chosen as those that span the asymptotic displacement fields for an interfacial crack. The concept of partition of unity facilitates the incorporation of the oscillatory nature of the singularity within a conforming finite element approximation. The mixed‐mode (complex) stress intensity factors for bimaterial interfacial cracks are numerically evaluated using the domain form of the interaction integral. Good agreement between the numerical results and the reference solutions for benchmark interfacial crack problems is realized. Copyright © 2004 John Wiley & Sons, Ltd.     

Combined extended and superimposed finite element method for cracks

A combination of the extended finite element method (XFEM) and the mesh superposition method (s‐version FEM) for modelling of stationary and growing cracks is presented. The near‐tip field is modelled by superimposed quarter point elements on an overlaid mesh and the rest of the discontinuity is implicitly described by a step function on partition of unity. The two displacement fields are matched through a transition region. The method can robustly deal with stationary crack and crack growth. It simplifies the numerical integration of the weak form in the Galerkin method as compared to the s‐version FEM. Numerical experiments are provided to demonstrate the effectiveness and robustness of the proposed method. Copyright © 2004 John Wiley & Sons, Ltd.     

On the Galerkin formulation of the smoothed particle hydrodynamics method

In this paper, we propose a Galerkin‐based smoothed particle hydrodynamics (SPH) formulation with moving least‐squares meshless approximation, applied to free surface flows. The Galerkin scheme provides a clear framework to analyse several procedures widely used in the classical SPH literature, suggesting that some of them should be reformulated in order to develop consistent algorithms. The performance of the methodology proposed is tested through various dynamic simulations, demonstrating the attractive ability of particle methods to handle severe distortions and complex phenomena. Copyright © 2004 John Wiley & Sons, Ltd.     

Three‐dimensional finite element computations for frictional contact problems with non‐associated sliding rule

This paper presents an algorithm for solving anisotropic frictional contact problems where the sliding rule is non‐associated.The algorithm is based on a variational formulation of the complex interface model that combine the classical unilateral contact law and an anisotropic friction model with a non‐associated slip rule. Both the friction condition and the sliding potential are elliptical and have the same principal axes but with different semi‐axes ratio. The frictional contact law and its inverse are derived from a single non‐differentiable scalar‐valued function, called a bi‐potential. The convexity properties of the bi‐potential permit to associate stationary principles with initial/boundary value problems. With the present formulation, the time‐integration of the frictional contact law takes the form of a projection onto a convex set and only one predictor–corrector step addresses all cases (sticking, sliding, no‐contact). A solution algorithm is presented and tested on a simple example that shows the strong influence of the slip rule on the frictional behaviour. Copyright 2004 John Wiley & Sons, Ltd.     

Exact static element stiffness matrices of non‐symmetric thin‐walled curved beams

An evaluation procedure of exact static stiffness matrices for curved beams with non‐symmetric thin‐walled cross section are rigorously presented for the static analysis. Higher‐order differential equations for a uniform curved beam element are first transformed into a set of the first‐order simultaneous ordinary differential equations by introducing 14 displacement parameters where displacement modes corresponding to zero eigenvalues are suitably taken into account. This numerical technique is then accomplished via a generalized linear eigenvalue problem with non‐symmetric matrices. Next, the displacement functions of displacement parameters are exactly calculated by determining general solutions of simultaneous non‐homogeneous differential equations. Finally an exact stiffness matrix is evaluated using force–deformation relationships. In order to demonstrate the validity and effectiveness of this method, displacements and normal stresses of cantilever thin‐walled curved beams subjected to tip loads are evaluated and compared with those by thin‐walled curved beam elements as well as shell elements. Copyright © 2004 John Wiley & Sons, Ltd.