Variational Views in Mechanics

This volume provides a timely survey of interactions between the calculus of variations and theoretical and applied mechanics. Chapters have been significantly expanded since preliminary versions appeared in a special issue of the Journal of Optimization Theory and Applications (184(1), 2020) on Calculus of Variations in Mechanics and Related Fields. The variety of topics covered offers researchers an overview of problems in mechanics that can be analyzed with variational techniques, making this a valuable reference for researchers in the field. It also presents ideas for possible future areas of research, showing how the mastery of these foundational mathematical techniques can be used for many exciting applications. Specific topics covered include:

• Topology optimization
• Identification of material properties
• Optimal control
• Plastic flows
• Gradient polyconvexity
• Obstacle problems
• Quasi-monotonicity Variational Views in Mechanics will appeal to researchers in mathematics, solid-states physics, and mechanical, civil, and materials engineering.

Provides a survey of interactions between the calculus of variations and theoretical and applied mechanics Presents future research ideas, connecting foundational mathematical techniques to exciting potential applications Teaches a multidisciplinary audience how real-world phenomena can be seen through the lens of the calculus of variations

Contenu
Numerical study of microstructures in multiwell problems in linear elasticity.- Surface shear waves in a functionally graded half-space.- Modeling of microstructures in a Cosserat continuum using relaxed energies - analytical and numerical aspects.- The polar-isogeometric method for the simultaneous optimization of shape and material properties of anisotropic shell structures.- Gradient polyconvexity and modeling of shape memory alloys.- Placement of an obstacle for optimizing the fundamental eigenvalue of divergence form elliptic operators.- Quasi-monotonicity formulas for classical obstacle problems with Sobolev coefficients and applications.- Optimal feedback for structures controlled by hydraulic semi-active dampers.- Multi-displacement requirement in a topology optimization algorithm based on non-uniform rational basis spline hyper-surfaces.- Anti-plane shear in hyperelasticity.- Identification of diffusion properties of polymer-matrix composite materials with complex texture.