The axiomatic introduction of arbitrary strain tensors by Hans Richter -- a commented translation of "Strain tensor, strain deviator and stress tensor for finite deformations"

Abstract

We provide a faithful translation of Hans Richter's important 1949 paper "Verzerrungstensor, Verzerrungsdeviator und Spannungstensor bei endlichen Formänderungen" from its original German version into English, complemented by an introduction summarizing Richter's achievements.

Polyconvex anisotropic hyperelasticity with neural networks

“…Moreover, Hencky deduced his material model from a number of simple axiomatic assumptions [32,33,61,63]. The applicability of his model to deformations not included in prior experiments can therefore be based on whether or not (or rather: to what degree) his postulates hold under the new circumstances.…”

Finite electro-elasticity with physics-augmented neural networks

“…[81]. Only for some analytical models, it is possible to arrive at even more interpretable formulations in the sense that the model parameters have a physical meaning, such as shear and compression modulus for the hyperelastic Hencky model [31,32,61,62].…”

“…They have in common that they reduce the epistemic uncertainty associated with analytical approaches, in the sense that they reduce their model uncertainty [37]: For analytical models, at some point an explicit choice for some functional relationship has to be made. While some explicit choices have a strong physical motivation, such as the hyperelastic Hencky model [31,32,61,62], most approaches are of a heuristic nature, e.g., the polynomial form of the hyperelastic Ogden model [63]. The reduced flexibility that often goes along with this human choice of functional relationship has no physical motivation, but purely stems from the necessity of an explicit form of the model.…”

Polyconvex anisotropic hyperelasticity with neural networks

“…Moreover, Hencky deduced his material model from a number of simple axiomatic assumptions [30,31,57,59]. The applicability of his model to deformations not included in prior experiments can therefore be based on whether or not (or rather: to what degree) his postulates hold under the new circumstances.…”