Variational Methods for Crystalline Microstructure - Analysis and Computation
Dolzmann, Georg.
Variational Methods for Crystalline Microstructure - Analysis and Computation [electronic resource] / by Georg Dolzmann. - XI, 217 p. online resource. - Lecture Notes in Mathematics, 1803 0075-8434 ; . - Lecture Notes in Mathematics, 1803 .
Introduction -- Semiconvex Hull of Compact Sets -- Macroscopic Energy for Nematic Elastomers -- Uniqueness and Stability of Microstructure -- Applications to Martensitic Transformations -- Algorithmic Aspects -- Bibliographic Remarks -- A. Convexity Conditions and Rank-one Connections -- B. Elements of Crystallography -- C. Notation -- References -- Index.
Phase transformations in solids typically lead to surprising mechanical behaviour with far reaching technological applications. The mathematical modeling of these transformations in the late 80s initiated a new field of research in applied mathematics, often referred to as mathematical materials science, with deep connections to the calculus of variations and the theory of partial differential equations. This volume gives a brief introduction to the essential physical background, in particular for shape memory alloys and a special class of polymers (nematic elastomers). Then the underlying mathematical concepts are presented with a strong emphasis on the importance of quasiconvex hulls of sets for experiments, analytical approaches, and numerical simulations.
9783540361251
10.1007/b10191 doi
Mathematics.
Differential equations, partial.
Numerical analysis.
Mathematical physics.
Mechanics.
Mathematics, general.
Condensed Matter Physics.
Partial Differential Equations.
Numerical Analysis.
Mathematical Methods in Physics.
Classical Mechanics.
QA1-939
510
Variational Methods for Crystalline Microstructure - Analysis and Computation [electronic resource] / by Georg Dolzmann. - XI, 217 p. online resource. - Lecture Notes in Mathematics, 1803 0075-8434 ; . - Lecture Notes in Mathematics, 1803 .
Introduction -- Semiconvex Hull of Compact Sets -- Macroscopic Energy for Nematic Elastomers -- Uniqueness and Stability of Microstructure -- Applications to Martensitic Transformations -- Algorithmic Aspects -- Bibliographic Remarks -- A. Convexity Conditions and Rank-one Connections -- B. Elements of Crystallography -- C. Notation -- References -- Index.
Phase transformations in solids typically lead to surprising mechanical behaviour with far reaching technological applications. The mathematical modeling of these transformations in the late 80s initiated a new field of research in applied mathematics, often referred to as mathematical materials science, with deep connections to the calculus of variations and the theory of partial differential equations. This volume gives a brief introduction to the essential physical background, in particular for shape memory alloys and a special class of polymers (nematic elastomers). Then the underlying mathematical concepts are presented with a strong emphasis on the importance of quasiconvex hulls of sets for experiments, analytical approaches, and numerical simulations.
9783540361251
10.1007/b10191 doi
Mathematics.
Differential equations, partial.
Numerical analysis.
Mathematical physics.
Mechanics.
Mathematics, general.
Condensed Matter Physics.
Partial Differential Equations.
Numerical Analysis.
Mathematical Methods in Physics.
Classical Mechanics.
QA1-939
510