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Nonclassical Linear Theories of Continuum Mechanics
We present a brief survey of nonclassical linear theories of continuum mechanics. Thus, we give a concise characterization of the Eringen–Edelen...
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Principle of virtual action in continuum mechanics
We present the principle of virtual action as a foundation of continuum mechanics. Used mainly in relativity, the method has a useful application in...
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Foundations of Geometric Continuum Mechanics Geometry and Duality in Continuum Mechanics
This monograph presents the geometric foundations of continuum mechanics. An emphasis is placed on increasing the generality and elegance of the...
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Temetos Software Platform and Its Applications in Problems of Continuum Mechanics
AbstractThe Temetos platform is designed to conduct computational experiments at all stages of analysis and study of continuum mechanics models. A...
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“Algozit” Programming Environment for Continuum Mechanics Problem-Solving
The specific features of the “Algozit” programming environment for functional-object implementation of numerical experiment algorithms in continuum...
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Mathematical Tools for Continuum Mechanics
This chapter gives a number of definitions and mathematical results relating to the notions of trajectories in a regular velocity field. It then...
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A New Family of Thermodynamically Compatible Discontinuous Galerkin Methods for Continuum Mechanics and Turbulent Shallow Water Flows
In this work we propose a new family of high order accurate semi-discrete discontinuous Galerkin (DG) finite element schemes for the...
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Mathematical Models of Fluids in Continuum Mechanics
Fluids in continuum mechanics are described through a family of observable physical quantities called fields. Examples of fields are the mass density...
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Conservation Laws in Continuum Mechanics
A general fundamental mathematical framework at the base of the conservation laws of continuum mechanics is introduced. The notions of weak...
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Splitting Method for the Variational Phase Transition Problem in Two-Phase Continuum Media
For the multi-dimensional variational phase transition problem of continuum mechanics we propose a method for splitting the problem into two parts...
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Perspective on the description of viscoelastic flows via continuum elastic dumbbell models
Non-Newtonian fluid mechanics and computational rheology widely exploit elastic dumbbell models such as Oldroyd-B and FENE-P for a continuum...
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Optimal Control of the Behavior of Solutions to an Initial-Boundary Value Problem Arising in the Mechanics of Discrete-Continuum Systems
We consider an initial-boundary value problem for a system of two differential equations, one of which is ordinary and the other a partial...
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Nonlinear wave dispersion in monoatomic chains with lumped and distributed masses: discrete and continuum models
The main objective of this paper is to investigate the influence of inertia of nonlinear springs on the dispersion behavior of discrete monoatomic...
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Quantum mechanics, radiation, and the equivalence proof
This paper re-evaluates the formative year of quantum mechanics—from Heisenberg’s first paper on matrix mechanics to Schrödinger’s equivalence...
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General Relativistic Lagrangian Continuum Theories Part I: Reduced Variational Principles and Junction Conditions for Hydrodynamics and Elasticity
We establish a Lagrangian variational framework for general relativistic continuum theories that permits the development of the process of Lagrangian...
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Penguin Huddling: A Continuum Model
Penguins huddling in a cold wind are represented by a two-dimensional, continuum model. The huddle boundary evolves due to heat loss to the huddle...
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Introduction to Rigid Body Mechanics
The goal of this chapter is to introduce students to the rudiments of the theory of rigid bodies. Rigid bodies, sometimes also called solid bodies,...
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Modeling Problems of Dynamics and Development of Scientific Areas of Mechanics and Applied Mathematics
AbstractThe paper discusses the development of scientific areas of mechanics in the research by the honorary professor of St. Petersburg State...
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Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics
Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions....
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Mathematical Modelling of Continuum Physics
This monograph provides a comprehensive and self-contained treatment of continuum physics, illustrating a systematic approach to the constitutive...