Foundations of Geometric Continuum Mechanics
Geometry and Duality in Continuum Mechanics
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Beschreibung
This monograph presents the geometric foundations of continuum mechanics. An emphasis is placed on increasing the generality and elegance of the theory by scrutinizing the relationship between the physical aspects and the mathematical notions used in its formulation. The theory of uniform fluxes in affine spaces is covered first, followed by the smooth theory on differentiable manifolds, and ends with the non-smooth global theory. Because continuum mechanics provides the theoretical foundations for disciplines like fluid dynamics and stress analysis, the author’s extension of the theory will enable researchers to better describe the mechanics of modern materials and biological tissues. The global approach to continuum mechanics also enables the formulation and solutions of practical optimization problems.
Foundations of Geometric Continuum Mechanics will be an invaluable resource for researchers in the area, particularly mathematicians, physicists, and engineers interested in the foundational notions of continuum mechanics.
This monograph presents the geometric foundations of continuum mechanics. An emphasis is placed on increasing the generality and elegance of the theory by scrutinizing the relationship between the physical aspects and the mathematical notions used in its formulation. The theory of uniform fluxes in affine spaces is covered first, followed by the smooth theory on differentiable manifolds, and ends with the non-smooth global theory. Because continuum mechanics provides the theoretical foundations for disciplines like fluid dynamics and stress analysis, the author’s extension of the theory will enable researchers to better describe the mechanics of modern materials and biological tissues. The global approach to continuum mechanics also enables the formulation and solutions of practical optimization problems.
Foundations of Geometric Continuum Mechanics will be an invaluable resource for researchers in the area, particularly mathematicians, physicists, and engineers interested in the foundational notions of continuum mechanics.
Provides a general framework for the geometric foundations of continuum mechanics Highlights the relationship between the physical aspects of continuum mechanics and the underlying mathematical notions Appeals to an audience of mathematicians, physicists, and engineers interested in the foundational problems of the area
Autor*in
Reuven Segev
Themen in »Foundations of Geometric Continuum Mechanics«
Continuum mechanics Classical field theories Uniform fluxes Smooth theory Differential geometry Smooth analysis Smooth fluxes Smooth manifolds Non-smooth manifolds Banach spaces Vector bundles Manifolds and bundles Configuration space Global analysis