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880-01 Preface; Emerging Trends in Applied Mathematics and Mechanics (ETAMM 2016); Organizing Committee; International Scientific Committee; Plenary Lectures; Keynotes Lectures; Contents; Contributors; Convergence of Hencky-Type Discrete Beam Model to Euler Inextensible Elastica in Large Deformation: Rigorous Proof; 1 Introduction; 2 Convergence of Measure Functionals; 3 Micro-Model for Non-Linear Beams; 3.1 Discrete Configurations and Operators; 3.2 Left Hand Side Clamped Inextensible Beam; 3.3 Deformation Energy Associated with Three Points Interactions.

2 Geometry and Kinematics of Elasto-Plastic Body3 Energetic Assumptions; 3.1 Micro Balance Equations; 3.2 Free Energy Density Function; 4 The Postulate of the Free Energy Imbalance; 5 Viscoplastic Type Evolution Equations; 6 Concluding Remarks; References; Modeling Deformable Bodies Using Discrete Systems with Centroid-Based Propagating Interaction: Fracture and Crack Evolution; 1 Introduction; 1.1 Motivation and Basic Ideas; 1.2 A Summary of the Algorithm and of the Formalism Employed; 1.3 Short Summary of Preliminary Numerical Results; 1.4 Further Comparison with Finite Element Simulations.

2 Spontaneous Evolution and Discrete Energy Equivalent3 Fracture and Crack Formation and Evolution; 3.1 Introduction of the Fracture; 3.2 Basic Fracture and Crack Evolution; 3.3 Uniaxial External Action; 3.4 Almost-Steady State; 4 Conclusion and Further Objectives; References; A Review on Wave Propagation Modeling in Band-Gap Metamaterials via Enriched Continuum Models; 1 Introduction; 1.1 Notations; 1.2 The Fundamental Role of Micro-Inertia in Enriched Continuum Mechanics; 2 The Classical Relaxed Micromorphic Model.

3 Governing Equations for the Equilibrium of Cosserat Shells4 Variational Formulation and Existence of Minimizers; 5 Application: Isotropic Cosserat Shells; 6 Open Problems; References; Flow Relations and Yield Functions for Dissipative Strain-Gradient Plasticity; 1 Introduction; 2 Governing Equations and Inequalities; 3 Weak Form of Equilibrium and the Elastic -- Plastic Initial-Boundary Value Problem; 4 The Fully Discrete Problem; 5 Concluding Remarks; References; Finite Elasto-Plastic Models for Lattice Defects in Crystalline Materials; 1 Introduction.

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.