Digital materials are integral to the modern design methods for industrial components and structures, allowing mechanical properties to be predicted from a description of the microstructure and behavior laws of the constituent parts.

This book examines a wide range of material properties, from transport phenomena to the mechanics of materials and microstructure changes in physical metallurgy. The fundamental mechanisms of deformation, annealing and damage to materials involve complex atomic processes; these have been explored and studied by numerical simulations, such as molecular dynamics.

In contrast to this minutely detailed approach, Digital Materials explores how these mechanisms can instead be integrated into an approach that considers the continuum of the physics and mechanics of materials at the mesoscopic scale. The book thus focuses on the mechanics of continuous media and the continuum thermodynamics of irreversible processes. The models displayed take the myriad properties of different materials into account, in particular their polycrystalline and/or composite natures; this becomes an intermediate step toward establishing effective laws for engineers in the processes of structure calculation and manufacturing.

Digital materials are integral to the modern design methods for industrial components and structures, allowing mechanical properties to be predicted from a description of the microstructure and behavior laws of the constituent parts.

This book examines a wide range of material properties, from transport phenomena to the mechanics of materials and microstructure changes in physical metallurgy. The fundamental mechanisms of deformation, annealing and damage to materials involve complex atomic processes; these have been explored and studied by numerical simulations, such as molecular dynamics.

In contrast to this minutely detailed approach, Digital Materials explores how these mechanisms can instead be integrated into an approach that considers the continuum of the physics and mechanics of materials at the mesoscopic scale. The book thus focuses on the mechanics of continuous media and the continuum thermodynamics of irreversible processes. The models displayed take the myriad properties of different materials into account, in particular their polycrystalline and/or composite natures; this becomes an intermediate step toward establishing effective laws for engineers in the processes of structure calculation and manufacturing.

Over the past 50 years, strain gradient material theories have been developed for the continuum modeling of size effects in materials and structures in terms of their elasticity, plasticity and fracturing. This book puts forward a unifying perspective to combine existing theories involving the higher order gradient of the strain tensor, or of plastic strain. It begins by reviewing experimental findings on the existence (or non-existence) of size effects on the mechanics of materials. In turn, the book devises first, second and higher order strain gradient theories from general principles, and presents constitutive frameworks that satisfy thermodynamic requirements. The special case of strain gradient plasticity is then developed and illustrated via computational analyses of size effects on the plasticity of metals at small scales. In closing, the book explains the origin of gradient effects in the case of lattice structures by drawing on homogenization theory.

The present book contains the proceedings of the 14th International Symposium on Continuum Models and Discrete Systems (CMDS14) held in Paris in June 2023. It contains 21 contributions that cover a broad range of topics in the wide field of mechanics and physics of heterogeneous media for  discrete and continuous systems, from image analysis to models of random structures and to homogenization. The sessions in the CMDS conference series cover, in particular, the modeling of complex heterogeneous systems and metamaterials, structures and composites with extreme properties, deformable solids with microstructures, generalized continua, fracture and defect dynamics, fatigue, design of structured and architectured materials, micro and nanostructures, thermodynamics, transport theory and multiphysics coupling and methods ranging from homogenization theories to optimal design and machine-learning frameworks. Papers in the present volume are organized according to the following six main topics: probabilistic models, homogenization, solid mechanics, architectured materials, optics and metamaterials, machine learning methods.

This volume is devoted to an actual topic which is the focus world-wide of various research groups. It contains contributions describing the material behavior on different scales, new existence and uniqueness theorems, the formulation of constitutive equations for advanced materials. The main emphasis of the contributions is directed on the following items - Modelling and simulation of natural and artificial materials with significant microstructure,- Generalized continua as a result of multi-scale models, - Multi-field actions on materials resulting in generalized material models,- Theories including higher gradients, and  - Comparison with discrete modelling approaches 

In mechanical engineering and structural analysis there is a significant gap between the material models currently used by engineers for industry applications and those already available in research laboratories. This is especially apparent with the huge progress of computational possibilities and the corresponding dissemination of numerical tools in engineering practice, which essentially deliver linear solutions. Future improvements of design and life assessment methods necessarily involve non-linear solutions for inelastic responses, in plasticity or viscoplasticity, as well as damage and fracture analyses.

The dissemination of knowledge can be improved by software developments, data base completion and generalization, but also by information and training. With such a perspective Non-Linear Mechanics of Materials proposes a knowledge actualization, in order to better understand and use recent material constitutive and damage modeling methods in the context of structural analysis or multiscale material microstructure computations.

Digital materials are integral to the modern design methods for industrial components and structures, allowing mechanical properties to be predicted from a description of the microstructure and behavior laws of the constituent parts.

This book examines a wide range of material properties, from transport phenomena to the mechanics of materials and microstructure changes in physical metallurgy. The fundamental mechanisms of deformation, annealing and damage to materials involve complex atomic processes; these have been explored and studied by numerical simulations, such as molecular dynamics.

In contrast to this minutely detailed approach, Digital Materials explores how these mechanisms can instead be integrated into an approach that considers the continuum of the physics and mechanics of materials at the mesoscopic scale. The book thus focuses on the mechanics of continuous media and the continuum thermodynamics of irreversible processes. The models displayed take the myriad properties of different materials into account, in particular their polycrystalline and/or composite natures; this becomes an intermediate step toward establishing effective laws for engineers in the processes of structure calculation and manufacturing.

Digital materials are integral to the modern design methods for industrial components and structures, allowing mechanical properties to be predicted from a description of the microstructure and behavior laws of the constituent parts.

This book examines a wide range of material properties, from transport phenomena to the mechanics of materials and microstructure changes in physical metallurgy. The fundamental mechanisms of deformation, annealing and damage to materials involve complex atomic processes; these have been explored and studied by numerical simulations, such as molecular dynamics.

In contrast to this minutely detailed approach, Digital Materials explores how these mechanisms can instead be integrated into an approach that considers the continuum of the physics and mechanics of materials at the mesoscopic scale. The book thus focuses on the mechanics of continuous media and the continuum thermodynamics of irreversible processes. The models displayed take the myriad properties of different materials into account, in particular their polycrystalline and/or composite natures; this becomes an intermediate step toward establishing effective laws for engineers in the processes of structure calculation and manufacturing.

Over the past 50 years, strain gradient material theories have been developed for the continuum modeling of size effects in materials and structures in terms of their elasticity, plasticity and fracturing. This book puts forward a unifying perspective to combine existing theories involving the higher order gradient of the strain tensor, or of plastic strain. It begins by reviewing experimental findings on the existence (or non-existence) of size effects on the mechanics of materials. In turn, the book devises first, second and higher order strain gradient theories from general principles, and presents constitutive frameworks that satisfy thermodynamic requirements. The special case of strain gradient plasticity is then developed and illustrated via computational analyses of size effects on the plasticity of metals at small scales. In closing, the book explains the origin of gradient effects in the case of lattice structures by drawing on homogenization theory.

The present book contains the proceedings of the 14th International Symposium on Continuum Models and Discrete Systems (CMDS14) held in Paris in June 2023. It contains 21 contributions that cover a broad range of topics in the wide field of mechanics and physics of heterogeneous media for  discrete and continuous systems, from image analysis to models of random structures and to homogenization. The sessions in the CMDS conference series cover, in particular, the modeling of complex heterogeneous systems and metamaterials, structures and composites with extreme properties, deformable solids with microstructures, generalized continua, fracture and defect dynamics, fatigue, design of structured and architectured materials, micro and nanostructures, thermodynamics, transport theory and multiphysics coupling and methods ranging from homogenization theories to optimal design and machine-learning frameworks. Papers in the present volume are organized according to the following six main topics: probabilistic models, homogenization, solid mechanics, architectured materials, optics and metamaterials, machine learning methods.

This volume is devoted to an actual topic which is the focus world-wide of various research groups. It contains contributions describing the material behavior on different scales, new existence and uniqueness theorems, the formulation of constitutive equations for advanced materials. The main emphasis of the contributions is directed on the following items - Modelling and simulation of natural and artificial materials with significant microstructure,- Generalized continua as a result of multi-scale models, - Multi-field actions on materials resulting in generalized material models,- Theories including higher gradients, and  - Comparison with discrete modelling approaches 

In mechanical engineering and structural analysis there is a significant gap between the material models currently used by engineers for industry applications and those already available in research laboratories. This is especially apparent with the huge progress of computational possibilities and the corresponding dissemination of numerical tools in engineering practice, which essentially deliver linear solutions. Future improvements of design and life assessment methods necessarily involve non-linear solutions for inelastic responses, in plasticity or viscoplasticity, as well as damage and fracture analyses.

The dissemination of knowledge can be improved by software developments, data base completion and generalization, but also by information and training. With such a perspective Non-Linear Mechanics of Materials proposes a knowledge actualization, in order to better understand and use recent material constitutive and damage modeling methods in the context of structural analysis or multiscale material microstructure computations.