This volume originates from the INDAM Symposium on Trends on Applications of Mathematics to Mechanics (STAMM), which was held at the INDAM headquarters in Rome on 5¿9 September 2016. It brings together original contributions at the interface of Mathematics and Mechanics. The focus is on mathematical models of phenomena issued from various applications. These include thermomechanics of solids and gases, nematic shells, thin films, dry friction, delamination, damage, and phase-field dynamics. The papers in the volume present novel results and identify possible future developments. The book is addressed to researchers involved in Mathematics and its applications to Mechanics.

Presents state-of-the-art contributions from leaders in the field

1 E. Davoli and I. Fonseca, Relaxation of p-growth integral functionals under space-dependent differential constraints.- 2 A. Kalamajska et al., Weak lower semicontinuity by means of anisotropic parametrized measures.- 3 P. Pedregal, What does rank-one convexity have to do with viscosity solutions?.- 4 B. Schweizer, On Friedrichs inequality, Helmholtz decomposition, vector potentials, and the div-curl lemma.- 5 G. Canevari and A. Segatti, Variational analysis of nematic shells.- 6 M. Sabeel Khan and K. Hackl, Modeling of microstructures in a Cosserat continuum using relaxed energies.- 7 R. Rossi and M. Thomas, From nonlinear to linear elasticity in a coupled rate-dependent/independent system for brittle delamination.- 8 A. Mielke, Three examples concerning the interaction of dry friction and oscillations.- 9 S. Bartels et al., Numerical approach to a model for quasistatic damage with spatial BV - regularization.- 10 A. Braides, Rigidity effects for antiferromagnetic thin films: a prototypical example.- 11 P. Colli et al., Limiting problems for a nonstandard viscous CahnHilliard system with dynamic boundary conditions.- 12 H. Garcke and K.F. Lam, On a CahnHilliardDarcy system for tumour growth with solution dependent source terms.- 13 T. Ruggeri, Molecular extended thermodynamics of a rarefied polyatomic gas.- 14 J. Cyr, A comparison of two settings for stochastic integration with respect to Lévy processes in infinite dimensions.