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Continuum mechanics
About: Continuum mechanics is a research topic. Over the lifetime, 5042 publications have been published within this topic receiving 181027 citations.
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TL;DR: The governing PDE system is symmetric hyperbolic and satisfies the first and second principle of thermodynamics, hence it belongs to the so-called class of symmetricHyperbolic thermodynamically compatible systems (SHTC), which have been studied for the first time by Godunov in 1961.
76 citations
TL;DR: The convergence of a class of finite-differences numerical schemes is studied and an appropriate concept of consistency with the continuous problem is introduced.
Abstract: Conservative linear equations arise in many areas of application, including continuum mechanics or high-frequency geometrical optics approximations. This kind of equations admits most of the time solutions which are only bounded measures in the space variable known as duality solutions. In this paper, we study the convergence of a class of finite-differences numerical schemes and introduce an appropriate concept of consistency with the continuous problem. Some basic examples including computational results are also supplied.
76 citations
TL;DR: A method able to avoid the identification of the constitutive equations of complex systems and rather work in a purely numerical manner by employing experimental data that is able to identify both the Hamiltonian and dissipative parts of the dynamics while satisfying fundamental laws such as energy conservation or positive production of entropy.
Abstract: In the paradigm of data-intensive science, automated, unsupervised discovering of governing equations for a given physical phenomenon has attracted a lot of attention in several branches of applied sciences. In this work, we propose a method able to avoid the identification of the constitutive equations of complex systems and rather work in a purely numerical manner by employing experimental data. In sharp contrast to most existing techniques, this method does not rely on the assumption on any particular form for the model (other than some fundamental restrictions placed by classical physics such as the second law of thermodynamics, for instance) nor forces the algorithm to find among a predefined set of operators those whose predictions fit best to the available data. Instead, the method is able to identify both the Hamiltonian (conservative) and dissipative parts of the dynamics while satisfying fundamental laws such as energy conservation or positive production of entropy, for instance. The proposed method is tested against some examples of discrete as well as continuum mechanics, whose accurate results demonstrate the validity of the proposed approach.
76 citations
TL;DR: In this paper, a thermo-mechanical constitutive model for the prediction of fatigue in structures using the finite element method is formulated based on the damage mechanics of the continuous medium and allows the treatment in a unified way of coupled phenomena such as fatigue with damage, plasticity, viscosity and temperature effects.
76 citations
76 citations