Overview Abstracts
STAMM 2024
Thermodynamic modeling of curing polymers
Thermosetting polymers are hardened because of a chemical curing reaction that dissipates heat. Kinetic of curing reaction is needed to incorporate for applications where the curing takes a long time. In construction used adhesives, hours and even days are need to obtain a fully cured state depending on the environmental conditions that are not controlled. We discuss a thermodynamically sound modeling of thermo-mechano-chemical processes in many component auto-catalytic polymers, implement all governing equations in multiphysics simulations, and test the understanding by experimental analyses.
#070
B. E. Abali, J. Vorel, and R. Wan-Wendner. “Thermo-mechano-chemical modeling and compu- tation of thermosetting polymers used in post-installed fastening systems in concrete structures”. In: Continuum Mechanics and Thermodynamics 35 (2023), pp. 971–989.
#081 B. E. Abali, M. Y. Yardımcı, M. Zecchini, G. Daissè, F. H. Marchesini, G. De Schutter, and R. Wan-Wendner. “Experimental investigation for modeling the hardening of thermosetting polymers during curing”. In: Polymer Testing 102 (2021), p. 107310.
Variational models with Eulerian-Lagrangian formulation allowing for material failure
Variational models featuring Eulerian-Lagrangian formulations arise naturally in many multiphysics problems, where elasticity is coupled with other effects. In this talk, we focus on a model for nematic elastomers proposed by Barchiesi and DeSimone.
First, we investigate the purely elastic setting. We discuss both the existence of minimizers
and the existence of rate-independent quasistatic evolutions. In particular, we present recent
progresses concerning the case of nonstandard coervitiy assumptions. Eventually, we address the
extension of the existence theory for the static problem to a framework allowing for cavitation.
The talk is based on joint work with Bianca Stroffolini (Universit´a di Napoli Federico II),
Manuel Friedrich (FAU Erlangen-N¨urnberg), and Carlos Mora-Corral (Universidad Aut´onoma
de Madrid).
Global solutions and non-trivial long-time behaviour for fluid-elastic interaction with small data
We look at a geometrically linearized but non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid in 3d. We show that assuming no other damping but fluid viscosity, in the case of small initial data, the system admits a unique global strong solution that converges either to a steady state or a “pressure wave”-solution. We show the existence of non-trivial pressure waves for particular geometries of the elastic structure. The non-existence of pressure waves for a large class of domains follows from previous work of Avalos and Triggiani. The talk is based on joint work with Michelle Luckas (Universität Kassel).
Exploring the impact of thermal fluctuations on models of adhesion
Adhesion and de-adhesion processes at the interface between an object and a substrate are well-established phenomena in the realm of materials science and biophysics. These processes are profoundly influenced by thermal fluctuations, a phenomenon empirically validated through numerous experimental observations. We adopt discrete models comprising n elements, selected such that their physical parameters converge towards the continuum limit as n approaches infinity. This thoughtful scaling ensures that the discrete system retains its relevance in the context of continuous media. Leveraging principles from statistical mechanics, we employ this scaled discrete model to investigate the impact of temperature in adhesion phenomena. As result we obtain an analytical model to take care of the decreasing of the decohesion threshold depending on thermal (entropic) energy terms. Interestingly our approach shows that continuous adhesion models exhibit phase transitions, the critical temperatures of which can be derived through closed-form calculations.
Isometric and isoenergetic everting motions of elastic binormal scrolls with closed midlines
More information coming soon...
A model for lime consolidation of porous solids
We present the first mathematical 3D moel describing the process of filling the pores of a building material with a water-lime-mixture, with the goal to improve the consistency of the porous solid. Chemical reactions produce calcum carbonate which glues the solid particles together at some distance from the boundary and strengthens the whole structure. The model consists of a reaction-diffusion system with a nonlinear non-smooth boundary condition, coupled with the mass balance equations for the chemical reaction. The main result sonsists in proving that the system has a solution for each initial data from a physically relevant class. A 1D numerical test shows a qualitative agreement with experimental oberservations.
This is a joint work with B. Detmann (Universität Duisburg-Essen). P. Krejčí, J. Lamač and Y. Namlyeyeva (Czech Technical University Prague).
Non-Equilibrium Steady States for port gradient systems
The theory of gradient flows is a focus of applied mathematical research for decades, starting in the 1970s with Br´ezis’ Hilbert-space theory, followed by the Banach-space theory of doubly nonlinear equations of Colli-Visintin in the 1990s, and De Giorgi’s metric gradient flows developed by Ambrosio, Otto, and others after 2000. Many applications in mechanics and physics, like plasticity, phase-field models, or thermo-viscoelasticity, were developed in parallel. These theories describe closed systems where a free energy is a Liapunov function and the solutions follow a steepest descent with respect to a dissipation relation.
A port gradient system is a gradient systems coupled to the environment, e.g. via boundary conditions, in such a way that energy or mass can flow in and out according to certain rules. Thus, steady state solutions are no longer given as critical points of the free energy (and have zero dissipation), but arise by an interplay of dissipation and feeding from the environment.
We show that for port gradient systems so-called Non-Equilibrium Steady States (NESS) can be constructed as saddle points of a functional involving the state variable and the dual thermodynamical variable. This leads to a mathematical rigorous generalization of Prigogine’s principle of minimal dissipation. An application to the classicial Dirichlet problem for diffusion is given.
Moreover, we show that the saddle-point structure appears naturally in classical gradient systems with a two time scales. The fast variables stay in NESS where the slow variables act as environment. In such a way EDP-convergence of fast-slow gradient systems can be performed.
Thermomechanical models for finitely-strained viscoelastic solids and related mathematical aspects
Models of visco-elastodynamic solids at finite strains will be presented and the Lagrangian versus Eulerian formulation will be discussed. Also coupled thermomechanical problems will be presented, allowing for
heat capacity degenerating to zero at zero temperature, which is also a physically relevant attribute related with non-negativity of entropy. Mathematical analysis using some gradient theories will be outlined, too,
advantageously exploiting the mentioned degenerating heat capacity.
Mathematical analysis of models for ferronematics in two dimensions
More informations coming soon...
A model for an incompressible fluid of both viscoelastic and viscoplastic behavior is revisited, which is used in geodynamics, e.g., to describe the evolution of fault systems in the lithosphere on geological time
scales. The Cauchy stress of this fluid is composed of a viscoelastic Stokes-like contribution and of an additional internal stress. The model thus couples the momentum balance with the evolution law of this extra stress, which features the Zaremba-Jaumann time-derivative and a non-smooth viscoplastic dissipation mechanism. This model is augmented to the situation of a bi-phasic material that undergoes phase separation according to a Cahn-Hilliard-type evolution law. Suitable concepts of weak solutions are discussed for the coupled model.
This is joint work with Fan Cheng (FU Berlin) and Robert Lasarzik (WIAS and FU Berlin) within project C09 „Dynamics of rock dehydration on multiple scales“ of CRC 1114 „Scaling Cascades in Complex Systems“ funded by the German Research Foundation.
