Mechanics of Strain Gradient Materials
- Albrecht Bertram (University of Magdeburg, Germany)
- 6 lectures on: Balance laws for gradient materials and finite elastoplasticity.
Starting with principle of virtual power, the balance laws and the boundary conditions for gradient materials can be derived. A format for a finite gradient elasticity is provided. Reduced forms and symmetry transformations are introduced.
Linear gradient elasticity. Hooke’s law is extended to the first strain gradient elasticity. After discussing the underlying principles, we examine the peculiarities that arise in this case. The appearance of odd-order elasticity tensors is a new feature absent in classical media.
- Lorenzo Bardella DICATAM (University of Brescia, Italy)
- 6 lectures on: Crystal plasticity.
A strain gradient crystal plasticity theory based on dislocation density tensor is presented, along with its isotropic counterpart, involving the plastic spin. A finite element framework to efficiently simulate both rate-dependent and rate-independent material responses is provided.
- Samuel Forest (Mines ParisTech, Evry, France)
- 6 lectures on: From micromorphic to gradient materials. Starting from Eringen ́s and Mindlin ́s higher order theory of materials with microstructure, elastic-plastic constitutive laws are presented at finite deformations. Internal constraints are enforced to recover the strain gradient theory. Applications deal with elasticity of nano-objects and strain localization phenomena in plasticity.
- Wolfgang H. Mueller (Technical University of Berlin, Germany)
6 lectures on: The experimental evidence of strain gradient elasticity from the micro perspective to macroscopic world including parameter analysis, theoretical basis for an experimental understanding of elastic strain gradient effects, experimental methods used to measure strain gradient elastic constants: Raman spectroscopy, atomic force microscopy, pantograph analysis.
- Christian Niordson (Technical University of Denmark, Lyngby, Denmark)
- 6 lectures on: Experimental results on size-effects in metals.
A general overview of plasticity size-effects in various experiments is given like indentation, torsion, and thin film deformation. Strain gradient plasticity theory is introduced together with numerical solution techniques.
- Pierre Seppecher (University of Toulon, France)
- 6 lectures on: Pantographs and graph-based structures.
Materials with pantographic microstructure and their generalization to graph-based structures are examples of materials with a clear microscopic interpretation of strain gradient effects. They also give an enlightening illustration of the concept of double forces.