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Degenerating Cahn-Hilliard systems coupled with mechanical effects and complete damage processes

Christian Heinemann, Christiane Kraus (2014)

Mathematica Bohemica

This paper addresses analytical investigations of degenerating PDE systems for phase separation and damage processes considered on nonsmooth time-dependent domains with mixed boundary conditions for the displacement field. The evolution of the system is described by a degenerating Cahn-Hilliard equation for the concentration, a doubly nonlinear differential inclusion for the damage variable and a quasi-static balance equation for the displacement field. The analysis is performed on a time-dependent...

Determination of the initial stress tensor from deformation of underground opening in excavation process

Josef Malík, Alexej Kolcun (2022)

Applications of Mathematics

A method for the detection of the initial stress tensor is proposed. The method is based on measuring distances between pairs of points located on the wall of underground opening in the excavation process. This methods is based on solving twelve auxiliary problems in the theory of elasticity with force boundary conditions, which is done using the least squares method. The optimal location of the pairs of points on the wall of underground openings is studied. The pairs must be located so that the...

Determination of the Thickness and Composition Profiles for a Film of Binary Mixture on a Solid Substrate

L. Fraštia, U. Thiele, L. M. Pismen (2010)

Mathematical Modelling of Natural Phenomena

We determine the steady-state structures that result from liquid-liquid demixing in a free surface film of binary liquid on a solid substrate. The considered model corresponds to the static limit of the diffuse interface theory describing the phase separation process for a binary liquid (model-H), when supplemented by boundary conditions at the free surface and taking the influence of the solid substrate into account. The resulting variational problem...

Development of three dimensional constitutive theories based on lower dimensional experimental data

Satish Karra, Kumbakonam R. Rajagopal (2009)

Applications of Mathematics

Most three dimensional constitutive relations that have been developed to describe the behavior of bodies are correlated against one dimensional and two dimensional experiments. What is usually lost sight of is the fact that infinity of such three dimensional models may be able to explain these experiments that are lower dimensional. Recently, the notion of maximization of the rate of entropy production has been used to obtain constitutive relations based on the choice of the stored energy and rate...

Dislocation dynamics - analytical description of the interaction force between dipolar loops

Vojtěch Minárik, Jan Kratochvíl (2007)

Kybernetika

The interaction between dislocation dipolar loops plays an important role in the computation of the dislocation dynamics. The analytical form of the interaction force between two loops derived in the present paper from Kroupa’s formula of the stress field generated by a single dipolar loop allows for faster computation.

Driver's influence on kinematics of articulated bus rear axle

Bartoň, Stanislav, Krumphole, Tomáš (2013)

Programs and Algorithms of Numerical Mathematics

This paper studies kinematic properties of the rear axle of the particle coach as function of driver’s activity. The main goals are the prediction of the trajectory, the computation of the vector of velocity of each wheel of the rear axle as a function of the real velocity vector of the front coach axle and the real curvature of the bus trajectory. The computer algebra system MAPLE was used for all necessary computations.

Entropy flux far from equilibrium in solids and in non viscous gases

M. S. Mongiovì, R. A. Peruzza (2004)

Bollettino dell'Unione Matematica Italiana

One of the main question arising in Extended Thermodynamics concerns the physical meaning of the temperature far from equilibrium. Some authors define thermodynamic temperature T t ⁢ h the inverse of the coefficient linking the entropy flux with the heat flux. Other authors, instead, define non-equilibrium temperature θ the inverse of the partial derivative of entropy with respect to energy, at density and heat flux constant. The aim of this paper is to determine the expression of entropy flux in some...

Equazioni di bilancio della meccanica dei continui nell’ambito della teoria geometrica della misura

Alessandro Musesti (2004)

Bollettino dell'Unione Matematica Italiana

Si dà una presentazione della formulazione delle equazioni di bilancio della Meccanica dei Continui tramite l'approccio insiemistico (flussi e interazioni di Cauchy) e quello distribuzionale (potenze virtuali), illustrando i progressi ottenuti nell'indebolimento delle ipotesi, fino a comprendere campi tensoriali a divergenza misura. Si mostra poi come l'approccio attraverso il Principio delle potenze virtuali permetta di individuare il tensore degli sforzi anche nel caso di un corpo continuo dotato...

Estensione a leggi costitutive a variabili interne dei teoremi di inadattamento in dinamica strutturale elastoplastica

Alberto Corigliano, Claudia Comi (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si considera il problema del mancato adattamento in campo dinamico per strutture elasto-plastiche incrudenti. Si dimostrano una condizione necessaria ed una sufficiente per il verificarsi di fenomeni di inadattamento (plasticità alternata o collasso incrementale) estendendo risultati precedenti ad un'ampia classe di modelli costitutivi a variabili interne in grado di rappresentare comportamenti incrudenti non lineari.

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