1. Non-Conventional Thermodynamics and Models of Gradient Elasticity
- Author
-
Alber, Hans-Dieter, Broese, Carsten, Tsakmakis, Charalampos, and Beskos, Dimitri
- Subjects
boundary conditions ,lcsh:QB460-466 ,interstitial working ,lcsh:Q ,lcsh:Astrophysics ,gradient elasticity ,lcsh:Science ,Article ,energy transfer law ,lcsh:Physics ,lcsh:QC1-999 ,non-equilibrium thermodynamics - Abstract
We consider material bodies exhibiting a response function for free energy, which depends on both the strain and its gradient. Toupin–Mindlin’s gradient elasticity is characterized by Cauchy stress tensors, which are given by space-like Euler–Lagrange derivative of the free energy with respect to the strain. The present paper aims at developing a first version of gradient elasticity of non-Toupin–Mindlin’s type, i.e., a theory employing Cauchy stress tensors, which are not necessarily expressed as Euler–Lagrange derivatives. This is accomplished in the framework of non-conventional thermodynamics. A one-dimensional boundary value problem is solved in detail in order to illustrate the differences of the present theory with Toupin–Mindlin’s gradient elasticity theory.
- Published
- 2018