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Micromagnetic simulations require the numerically challenging preservation of the Euclidean norm during the whole simulation. This can be accomplished by applying a priori length preserving methods, renormalization algorithms, or penalization strategies. The latter one includes both the penalty method and the Lagrangian multiplier. The penalty method requires the definition of a penalty parameter during the initiation of the simulation which, depending on its size, can lead to an unsatisfied constraint or stiff and difficult to solve systems of equations. The Lagrange multiplier always penalizes in problem-dependent intensity, hence, an additional degree of freedom is added to the system of equations to the drawback of higher computational costs. This paper proposes a method that utilizes a perturbed Lagrangian multiplier and an element level static condensation to condensate the additional degree of freedom. This guarantees fast simulations, and no parameter fitting in advance. Suitable numerical examples are conducted to prove the workability of the outlined scheme and to highlight the efficiency compared to the non-condensed formulation. [ABSTRACT FROM AUTHOR]

Viscoelastic phenomena are present in every‐day materials in engineering for example, polymers and bitumen. These materials usually present linear behavior for small deformations and small perturbations from the thermodynamic equilibrium. More generally, nonlinear behaviors may arise due to stress, temperature, ageing, and other drivers. In this work, the single‐integral Schapery model, derived from thermodynamic theory of irreversible processes including nonlinearities due to stress and temperature, is considered in this work. The aim is to collect data from experiments and simulate the nonlinear behavior with the material parameters, nonlinear functions and time scale shift factors. A finite element scheme for the Schapery model based on a stress‐update algorithm is proposed. For this, the decoupled deviatoric and volumetric responses and the strain tensor decomposition into instantaneous and hereditary parts are developed. The Schapery model depicts precisely the nonlinear viscoelastic phenomenon in creep and recovery strain tests, notably when all the nonlinear functions are considered. [ABSTRACT FROM AUTHOR]

As a modern method of contact free fusion, laser beam welding has gained importance in recent years. This is due to both the possibiliy of a high advance speed of the laser and low thermal distortion of the components compared to other welding processes, see Dal and Fabbro. These beneficial process properties follow from a focused laser, which thus results in a precise energy input. In addition, laser beam welding processes can be automated which makes the process attractive for a wide range of applications, cf. Dilthey. Nevertheless, various influences, like the temperature gradient, the chemical composition or process parameters, may have an effect on the occurrence of so‐called solidification cracks. Solidification cracks arise during solidification and occur in the area of the mushy zone, which is located behind the melt pool. The material behavior in the mushy zone is governed by a dendritic morphology. Due to this, liquid phase inclusions may occur in some parts of the mushy zone, see Hills et al. When these trapped areas solidify, no further liquid phase can follow and a negative pressure is created. The resulting stresses can then lead to solidification cracks. In further studies, the geometry of the dendritic morphology will be generated on the basis of previous phase field simulations. These describe the dendrite growth controlled by the chemical concentration. The resulting geometry will then be simulated using the possibilities of a thermo‐elastoplastic material model, which will enable temperature‐driven imitation of growth. This contribution addresses the evolving state of the dendritic microstructure in a simplified manner. Therefore, for the first study, a simplified morphology is used, that is, no secondary arms and an elliptical geometry of the dendrites is assumed. Thermal as well as elastoplastic effects are already taken into account, in order to represent the inherent stress and strain states in the microstructure. These may be related to critical states leading to failure in the future. [ABSTRACT FROM AUTHOR]

The seasonal growth and decay of the (Antarctic) sea ice has great impact on the local as well as the world's climate. Thus, the numerical analysis to forecast the sea ice dynamics with all its impact factors and the mutual influence on the climate is of great interest. This contribution studies the application of the least‐squares finite element method (FEM) to the coupled problem considering the ocean velocity, the stresses, the sea ice concentration, and the sea ice thickness. By using conforming and nonconforming approximation spaces for the stresses, their advantages and disadvantages are shown and discussed. [ABSTRACT FROM AUTHOR]