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Author: Radszuweit, Markus ×

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    Modeling and simulation of non-isothermal rate-dependent damage processes in inhomogeneous materials using the phase-field approach
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Kraus, Christiane; Radszuweit, Markus
    We present a continuum model that incorporates rate-dependent damage and fracture, a material order parameter field and temperature. Different material characteristics throughout the medium yield a strong inhomogeneity and affect the way fracture propagates. The phasefield approach is employed to describe degradation. For the material order parameter we assume a Cahn Larché-type dynamics, which makes the model in particular applicable to binary alloys. We give thermodynamically consistent evolution equations resulting from a unified variational approach. Diverse coupling mechanisms can be covered within the model, such as heat dissipation during fracture, thermal-expansion-induced failure and elastic-inhomogeneity effects. We furthermore present an adaptive Finite Element code in two space dimensions that is capable of solving such a highly nonlinear and non-convex system of partial differential equations. With the help of this tool we conduct numerical experiments of different complexity in order to investigate the possibilities and limitations of the presented model. A main feature of our model is that we can describe the process of micro-crack nucleation in regions of partial damage to form macro-cracks in a unifying approach.
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    Cardiac contraction induces discordant alternans and localized block
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Radszuweit, Markus; Alvarez-Lacalle, Enrique; Bär, Markus; Echebarria, Blas
    In this paper we use a simplified model of cardiac excitation-contraction coupling to study the effect of tissue deformation on the dynamics of alternans, i.e. alternations in the duration of the cardiac action potential, that occur at fast pacing rates and are known to be pro-arrhythmic. We show that small stretch-activated currents can produce large effects and cause a transition from in-phase to off-phase alternations (i.e. from concordant to discordant alternans) and to conduction blocks. We demonstrate numerically and analytically that this effect is the result of a generic change in the slope of the conduction velocity restitution curve due to electromechanical coupling. Thus, excitation-contraction coupling can potentially play a relevant role in the transition to reentry and fibrillation.
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    An active poroelastic model for mechanochemical patterns in protoplasmic droplets of Physarum polycephalum
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Radszuweit, Markus; Engel, Harald; Bär, Markus
    Motivated by recent experimental studies, we derive and analyze a two-dimensional model for the contraction patterns observed in protoplasmic droplets of Physarum polycephalum. The model couples a description of an active poroelastic two-phase medium with equations describing the spatiotemporal dynamics of the intracellular free calcium concentration. The poroelastic medium is assumed to consist of an active viscoelastic solid representing the cytoskeleton and a viscous fluid describing the cytosol. The equations for the poroelastic medium are obtained from continuum force balance and include the relevant mechanical fields and an incompressibility condition for the two-phase medium. The reaction-diffusion equations for the calcium dynamics in the protoplasm of Physarum are extended by advective transport due to the flow of the cytosol generated by mechanical stress. Moreover, we assume that the active tension in the solid cytoskeleton is regulated by the calcium concentration in the fluid phase at the same location, which introduces a mechanochemical coupling. A linear stability analysis of the homogeneous state without deformation and cytosolic flows exhibits an oscillatory Turing instability for a large enough mechanochemical coupling strength. Numerical simulations of the model equations reproduce a large variety of wave patterns, including traveling and standing waves, turbulent patterns, rotating spirals and antiphase oscillations in line with experimental observations of contraction patterns in the protoplasmic droplets.