SUMMARYThe FE-simulation of inhomogeneous structures, such as composite materials, biological tissues or foams, requires the generation of respective finite element meshes. With increasing complexity of the inner architecture of such structures, this becomes a time-consuming and laborious task. Additionally, the risk of forming bad-shaped elements that may lead to ill-conditioned numerical problems grows significantly. A solution to this problem provides the extended finite element method (XFEM). Thereby, the interface between different materials is represented by a local enrichment of the displacement approximation. As a consequence of this, the element boundary need not be aligned to the interface.In order to improve the accuracy of the interface approximation, the development of a plane element based on the XFEM and quadratic shape functions will be presented. This element allows for the description of curved material interfaces. The computation of the element stiffness matrix requires a numerical integration process that accounts for discontinuous fields. Regarding a linear element formulation, this can be achieved by an adapted triangulation of the element domain. However, in the case of a curved interface this solution is not applicable. Hence, non-uniform rational B-Spline (NURBS) surfaces are used to evaluate the integrals numerically.Finally, the results of different examples will show the general properties such as the accuracy of the numerical integration procedure and the convergence behavior of this element formulation.

In this study, DAMASK was used to model and elucidate the microstructural deformation behavior of sintered X3CrMnNi16-7-6 TRIP steel. The recently developed TRIP-TWIP material model was used within the DAMASK framework. Material optimization was performed using the least computationally expensive method, which yielded the desired results. The physical parameters of the material model were identified and tuned to fit the experimental observations. This tuned material model was used to run simulations utilizing 2D EBSD data. The local deformation, transformation, and twinning behaviors of the material under quasi-static tensile and compressive loads were analyzed. The results of this are in good agreement with previous experimental observations. The phenomena of dislocation glide, twinning, martensitic transformation, stress evolution, and dislocation pinning in different deformation stages are discussed.

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A material model is presented that accounts for strain rate dependent inelastic deformation and strain‐induced phase transformation in TRIP‐steels. Modifications for the kinetics equations of the strain‐induced phase transformation, introduced by Stringfellow, are proposed to overcome a drawback of Stringfellow's model. A parameter identification strategy that relies on Gauss‐Markov estimates is used to determine the model parameters from experimental data of a recently developed cast TRIP‐steel. Good agreement is observed between experimental results of the compression test and the corresponding finite element simulation employing the proposed model. This forms the basis for future applications of the material model in the design of composites and structures.

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