Mathematical Modelling in Solid Mechanics (Advanced Structured Materials (69))

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. Front Matter....Pages i-xv Convergence of Hencky-Type Discrete Beam Model to Euler Inextensible Elastica in Large Deformation: Rigorous Proof....Pages 1-12 Analysis of the Deformation of Cosserat Elastic Shells Using the Dislocation Density Tensor....Pages 13-30 Flow Relations and Yield Functions for Dissipative Strain-Gradient Plasticity....Pages 31-42 Finite Elasto-Plastic Models for Lattice Defects in Crystalline Materials....Pages 43-57 Modeling Deformable Bodies Using Discrete Systems with Centroid-Based Propagating Interaction: Fracture and Crack Evolution....Pages 59-88 A Review on Wave Propagation Modeling in Band-Gap Metamaterials via Enriched Continuum Models....Pages 89-105 A Continuous Model for the Wave Scattering by a Bounded Defective Domain....Pages 107-122 A History-Dependent Variational-Hemivariational Inequality in Contact Mechanics....Pages 123-134 Monolithic Algorithm for Dynamic Fluid-Structure Interaction Problem....Pages 135-146 Elastic-Plastic Rolling Contact Problems with Graded Materials and Heat Exchange....Pages 147-163 New Thoughts in Nonlinear Elasticity Theory via Hencky’s Logarithmic Strain Tensor....Pages 165-180 Continuum Physics with Violations of the Second Law of Thermodynamics....Pages 181-192 An Inverse Method to Get Further Analytical Solutions for a Class of Metamaterials Aimed to Validate Numerical Integrations....Pages 193-210 Identification of Two-Dimensional Pantographic Structures with a Linear D4 Orthotropic Second Gradient Elastic Model Accounting for External Bulk Double Forces....Pages 211-232 Models of Debonding Caused by Vibrations, Heat and Humidity....Pages 233-250 A Variational-Hemivariational Inequality in Contact Mechanics....Pages 251-264 Truncation and Indirect Incremental Methods in Hencky’s Perfect Plasticity....Pages 265-284 Can a Hencky-Type Model Predict the Mechanical Behaviour of Pantographic Lattices?....Pages 285-311 Back Matter....Pages 313-316