A Dissipative Model for Hydrogen Storage: Existence and Regularity Results

We prove global existence of a solution to an initial and boundary value problem for a highly nonlinear PDE system. The problem arises from a thermomechanical dissipative model describing hydrogen storage by use of metal hydrides. In order to treat the model from an analytical point of view, we formulate it as a phase transition phenomenon thanks to the introduction of a suitable phase variable. Continuum mechanics laws lead to an evolutionary problem involving three state variables: the temperature, the phase parameter and the pressure. The problem thus consists of three coupled partial differential equations combined with initial and boundary conditions. Existence and regularity of the solutions are here investigated by means of a time discretization-a priori estimates-passage to the limit procedure joined with compactness and monotonicity arguments

Shape memory and elastoplastic materials: from constitutive and numerical to fatigue modeling

Shape memory materials (SMMs) represent an important class of smart materials that have the ability to return from a deformed state to their original shape. Thanks to such a property, SMMs are utilized in a wide range of innovative applications. The increasing number of applications and the consequent involvement of industrial players in the field have motivated researchers to formulate constitutive models able to catch the complex behavior of these materials and to develop robust computational tools for design purposes. Such a research field is still under progress, especially in the prediction of shape memory polymer (SMP) behavior and of important effects characterizing shape memory alloy (SMA) applications. Moreover, the frequent use of shape memory and metallic materials in biomedical devices, particularly in cardiovascular stents, implanted in the human body and experiencing millions of in-vivo cycles by the blood pressure, clearly indicates the need for a deeper understanding of fatigue/fracture failure in microsize components. The development of reliable stent designs against fatigue is still an open subject in scientific literature. Motivated by the described framework, the thesis focuses on several research issues involving the advanced constitutive, numerical and fatigue modeling of elastoplastic and shape memory materials. Starting from the constitutive modeling, the thesis proposes to develop refined phenomenological models for reliable SMA and SMP behavior descriptions. Then, concerning the numerical modeling, the thesis proposes to implement the models into numerical software by developing implicit/explicit time-integration algorithms, to guarantee robust computational tools for practical purposes. The described modeling activities are completed by experimental investigations on SMA actuator springs and polyethylene polymers. Finally, regarding the fatigue modeling, the thesis proposes the introduction of a general computational approach for the fatigue-life assessment of a classical stent design, in order to exploit computer-based simulations to prevent failures and modify design, without testing numerous devices

Damage of nonlinearly elastic materials at small strain --- Existence and regularity results

In this paper an existence result for energetic solutions of rate-independent damage processes is established and the temporal regularity of the solution is discussed. We consider a body consisting of a physically nonlinearly elastic material undergoing small deformations and partial damage. The present work is a generalization of [Mielke-Roubicek 2006] concerning the properties of the stored elastic energy density as well as the suitable Sobolev space for the damage variable: While previous work assumes that the damage variable z satisfies z \∈ W^{1,r} (\Omega) with r>d for \Omega \⊂ \R^d, we can handle the case r>1 by a new technique for the construction of joint recovery sequences. Moreover, this work generalizes the temporal regularity results to physically nonlinearly elastic materials by analyzing Lipschitz- and Hölder-continuity of solutions with respect to time

Matematické modelování tenkých filmů z martenzitických materiálů

The aim of the thesis is the mathematical and computer modelling of thin films of martensitic materials. We derive a thermodynamic thin-film model on the meso-scale that is capable of capturing the evolutionary process of the shape-memory effect through a two-step procedure. First, we apply dimension reduction techniques in a microscopic bulk model, then enlarge gauge by neglecting microscopic interfacial effects. Computer modelling of thin films is conducted for the static case that accounts for a modified Hadamard jump condition which allows for austenite--martensite interfaces that do not exist in the bulk. Further, we characterize $L^p$-Young measures generated by invertible matrices, that have possibly positive determinant as well. The gradient case is covered for mappings the gradients and inverted gradients of which belong to $L^\infty$, a non-trivial problem is the manipulation with boundary conditions on generating sequences, as standard cut-off methods are inapplicable due to the determinant constraint. Lastly, we present new results concerning weak lower semicontinuity of integral functionals along (asymptotically) $\mathcal{A}$-free sequences that are possibly negative and non-coercive. Powered by TCPDF (www.tcpdf.org)Cílem této práce je matematické a počítačové modelování tenkých filmů martenzitických materiálů. Dvoustupňovém postupem odvodíme mezoskopický termodynamický model pro tenké filmy, jenž umí zachytit evoluční proces efektu tvarové paměti. Nejprve provedeme redukci dimenze v mikroskopickém 3D modelu, pak zvětšíme měřítko zanedbáním mikroskopických mezifázových vlivů. Počítačové modelování tenkých filmů je provedeno v statickém případě zahrnutím modifikované Hadamardovy podmínky skoku, jež dává slabší podmínku na kompatibilitu fází ve srovnání s 3D modelem. Dále jsou popsány $L^p$-Youngovy míry generované regulárními maticemi, popř. maticemi s kladným determinantem. Gradientní případ je vyřešen pro zobrazení, kde gradient a inverze gradientu jsou v $L^\infty$, netriviálním problémem byla manipulace s okrajovými podmínkami u generující posloupnosti, neboť standardní "ořezávací metody" nelze v našem případě aplikovat kvůli podmínce na determinant. V poslední kapitole zmíníme nové výsledky týkající se slabé zdola polospojitosti integrálních funkcionálů podél tzv. (asymptoticky) $\mathcal{A}$-free posloupností, jež mohou být záporné i nekoercivní. Powered by TCPDF (www.tcpdf.org)Matematický ústav UKMathematical Institute of Charles UniversityFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Multiscale thermo-hydro-mechanical-chemical coupling effects for fluid-infiltrating crystalline solids and geomaterials: theory, implementation, and validation

Extreme climate change and demanding energy resources have led to new geotechnical engineering challenges critical for sustainable development and resilient infrastructure of our society. Applications such as geological disposal of nuclear waste and carbon dioxide, artificial ground freezing, and hydraulic fractures all require an in-depth understanding of the thermo-hydro-mechanical coupling mechanisms of geomaterials subjected to various environmental impact. This dissertation presents a multiphysical computational framework dedicated to address the issues related to those unconventional applications. Our objective is not only incorporating multiphysical coupling effects at the constitutive laws, but also taking into account the nonlocal effects originated from the flow of pore-fluid, thermal convection and diffusion among solid and fluid constituents, and crystallization and recrystallization of crystals in the pore space across length scales. By considering these coupling mechanisms, we introduce a single unified model capable of predicting complex thermo-hydro-mechanical responses of geological and porous media across wide spectra of temperature, confining pressure and loading rate. This modeling framework applies to two applications, i.e., the freezing and thawing of frozen soil and the modeling of anisotropic crystal plasticity/fracture response of rock salt. Highlights of the key ingredients of the models cover the stabilization procedure used for the multi-field finite element, the return mapping algorithm for crystal plasticity, the micromorphic regularization of the Modified Cam-Clay model, and the strategy for enhancing computational efficiency of solvers, such as pre-conditioner, adaptive meshing, and internal variable mapping. By introducing the multiphysical coupling mechanisms explicitly, our computational geomechanics model is able to deliver more accurate and consistent results without introducing a significant amount of additional material parameters. In a parallel effort, we analyze the impact of thermo-hydro-mechanical (THM) coupling effects on the dynamic wave propagation and strain localization in a fully saturated softening porous medium. The investigation starts with deriving the characteristic polynomial corresponding to the governing equations of the THM system. The theoretical analysis based on the Abel–Ruffini theorem reveals that the roots of the characteristic polynomial for the THM problem cannot be expressed algebraically. Our analysis concludes that the rate-dependence introduced by multiphysical coupling may not regularize the THM governing equations when softening occurs