Mathematical Modelling in Solid Mechanics

This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics:

• mathematical modelling in solid, fluid and contact mechanics

• nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics

• numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering

• numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools

• mechanics of fibre-reinforced materials

• behaviour of elasto-plastic materials accounting for the microstructural defects

• definition of structural defects based on the differential geometry concepts or on the atomistic basis
• interaction between phase transformation and dislocations at nano-scale

• energetic arguments

• bifurcation and post-buckling analysis of elasto-plastic structures

• engineering optimization and design, global optimization and related algorithms
  The book presents selected papers presented at ETAMM 2016. It includes new and original results written by internationally recognized specialists.

  Provides an excellent state of the art in the field of mathematical modelling in mechanics Offers new results, techniques and concepts Presents selected papers presented at ETAMM 2016 Includes supplementary material: sn.pub/extras

  Inhalt
  1 Convergence of Hencky-type discrete beam model to Euler inextensible Elastica in large deformation: rigorous proof.- 2 Analysis of the deformation of Cosserat elastic shells using the dislocation density tensor.- 3 Flow relations and yield functions for dissipative strain-gradient plasticity.- 4 Finite elasto-plastic models for lattice defects in crystalline materials.