Non-Conventional Thermodynamics and Models of Gradient Elasticity

• Main Authors: Hans-Dieter Alber, Carsten Broese, Charalampos Tsakmakis, Dimitri E. Beskos
• Format: Article
• Language: English
• Published: MDPI AG 2018-03-01
• Series: Entropy
• Subjects: gradient elasticity; non-equilibrium thermodynamics; interstitial working; boundary conditions; energy transfer law
• Online Access: http://www.mdpi.com/1099-4300/20/3/179

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.