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We present an efficient model for the simulation of polycrystalline materials undergoing solid to solid phase transformations. As a basis, we use a one-dimensional, thermodynamically consistent phase-transformation model. This model is embedded into a micro-sphere formulation in order to simulate three-dimensional boundary value problems. To solve the underlying evolution equations, we use a newly developed explicit integration scheme which could be proved to be unconditionally A-stable. Besides the investigation of homogeneous deformation states, representative finite element examples are discussed. It is shown that the model nicely reflects the overall behaviour. IntroductionThe development of so-called 'smart materials' like shape memory alloys, TRIP-steels, piezoceramics, electro active polymers, and so forth offers a great potential for innovative industrial applications; for an overview, the reader is referred to the monography [60], the articles in [18], and -with application to piezoceramics -the references cited in [8,44]. The growing need of a reliable manufacturing and application of such components gives rise to an increasing demand of accurate material models to predict the material's response by means of simulations as well as in view of material design purposes. In this context, micromechanical models may be regarded as most appropriate in the sense that they are directly based on physically bound and well-motivated quantities.Micromechanical models are mainly characterized by the consideration of the material's microstructure and its stress-or temperature-driven evolution, respectively. Following [10,21], in particular the kinematics of martensitic (i.e. diffusionless) solid-solid phase transformations can be sufficiently described by homogeneous deformations of the crystal lattice. Thus, the transformation kinematics is captured by so-called Bain-strains which can for example be represented by the right Cauchy-Green stretch tensor U tr in a continuum mechanical sense (see for example [19,39]). The change of the cristalline structure in going from, e.g., austenite to martensite is always accompanied by a reduction of the crystallographic symmetry. Thus, several martensite variants have to be taken into account at the microscopic material scale. The coexistence of these phases is restricted to certain kinematical compatibility conditions which are reflected in rank-one connections between the deformations of each phase. Fundamental studies concerning this matter are provided in [12]. One major conclusion to be drawn from these investigations is the occurence of so-called martensite twins in order to form compatible or, in other words, coherent interfaces between austenite and martensite. This is exemplified in the so-called twinning equation from which exact solutions for the geometry of the microstructure and the respective volume fractions can be derived. This concept is frequently used for the modeling of martensitic phase transformations as for example shown in [20,29,37,55].The material's micr...

The simulation of complex engineering components and structures under loads requires the formulation and adequate calibration of appropriate material models. This work introduces an optimisation-based scheme for the calibration of viscoelastic material models that are coupled to gradient-enhanced damage in a finite strain setting. The parameter identification scheme is applied to a self-diagnostic poly(dimethylsiloxane) (PDMS) elastomer, where so-called mechanophore units are incorporated within the polymeric microstructure. The present contribution, however, focuses on the purely mechanical response of the material, combining experiments with homogeneous and inhomogeneous states of deformation. In effect, the results provided lay the groundwork for a future extension of the proposed parameter identification framework, where additional field-data provided by the self-diagnostic capabilities can be incorporated into the optimisation scheme.

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