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Author: Krejčí, Pavel × Author: Sprekels, Jürgen × Type: Text ×

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Now showing 1 - 6 of 6
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    Small strain oscillations of an elastoplastic Kirchhoff plate
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Guenther, Ronald B.; Krejčí, Pavel; Sprekels, Jürgen
    The two dimensional equation for transversal vibrations of an elastoplastic plate is derived from a general three dimensional system with a single yield tensorial von Mises plasticity model in the five dimensional deviatoric space. It leads after dimensional reduction to a multiyield three dimensional Prandtl-Ishlinskii hysteresis model whose weight function is explicitly given. The resulting partial differential equation with hysteresis is solved by means of viscous approximations and a monotonicity argument.
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    Analysis of a tumor model as a multicomponent deformable porous medium
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Krejčí, Pavel; Rocca, Elisabetta; Sprekels, Jürgen
    We propose a diffuse interface model to describe tumor as a multicomponent deformable porous medium. We include mechanical effects in the model by coupling the mass balance equations for the tumor species and the nutrient dynamics to a mechanical equilibrium equation with phase-dependent elasticity coefficients. The resulting PDE system couples two Cahn--Hilliard type equations for the tumor phase and the healthy phase with a PDE linking the evolution of the interstitial fluid to the pressure of the system, a reaction-diffusion type equation for the nutrient proportion, and a quasistatic momentum balance. We prove here that the corresponding initial-boundary value problem has a solution in appropriate function spaces.
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    A nonlocal phase-field model with nonconstant specific heat
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Krejčí, Pavel; Rocca, Elisabetta; Sprekels, Jürgen
    We prove the existence, uniqueness, thermodynamic consistency, global boundedness from both above and below, and continuous data dependence for a strong solution to an integrodifferential model for nonisothermal phase transitions under nonhomogeneous mixed boundary conditions. The specific heat is allowed to depend on the order parameter, and the convex component of the free energy may or may not be singular.
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    Elastoplastic Timoshenko beams
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Krejčí, Pavel; Sprekels, Jürgen; Wu, Hao
    A Timoshenko type elastoplastic beam equation is derived by dimensional reduction from a general 3D system with von Mises plasticity law. It consists of two second-order hyperbolic equations with an anisotropic vectorial Prandtl--Ishlinskii hysteresis operator. Existence and uniqueness of a strong solution for an initial-boundary value problem is proven via standard energy and monotonicity methods.
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    The von Mises model vor one-dimensional elastoplastic beams and Prandtl-Ishlinskii hysteresis operators
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Krejčí, Pavel; Sprekels, Jürgen
    In this paper, the one-dimensional equation for the transversal vibrations of an elastoplastic beam is derived from a general three-dimensional system. The plastic behavior is modeled using the classical three-dimensional von Mises plasticity model. It turns out that this single-yield model without hardening leads after a dimensional reduction to a multi-yield one-dimensional hysteresis model with kinematic hardening, given by a hysteresis operator of Prandtl-Ishlinskii type whose density function can be determined explicitly. This result indicates that the use of Prandtl-Ishlinskii hysteresis operators in the modeling of elastoplasticity is not just a questionable phenomenological approach, but in fact quite natural. In addition to the derivation of the model, it is shown that the resulting partial differential equation with hysteresis can be transformed into an equivalent system for which the existence and uniqueness of a strong solution is proved. The proof employs techniques from the mathematical theory of hysteresis operators.
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    Unsaturated deformable porous media flow with phase transition
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Krejčí, Pavel; Rocca, Elisabetta; Sprekels, Jürgen
    In the present paper, a continuum model is introduced for fluid flow in a deformable porous medium, where the fluid may undergo phase transitions. Typically, such problems arise in modeling liquid-solid phase transformations in groundwater flows. The system of equations is derived here from the conservation principles for mass, momentum, and energy and from the Clausius-Duhem inequality for entropy. It couples the evolution of the displacement in the matrix material, of the capillary pressure, of the absolute temperature, and of the phase fraction. Mathematical results are proved under the additional hypothesis that inertia effects and shear stresses can be neglected. For the resulting highly nonlinear system of two PDEs, one ODE and one ordinary differential inclusion with natural initial and boundary conditions, existence of global in time solutions is proved by means of cut-off techniques and suitable Moser-type estimates.