New article: Identification of optimal history variables and corresponding hereditary laws in linear viscoelasticity
New article: Romero, I. and Ortiz, M. (2026). Identification of optimal history variables and corresponding hereditary laws in linear viscoelasticity, Computer Methods in Applied Mechanics and Engineering, 461, 119122. (link).
In this article, we develop an operator-theoretic formulation of linear hereditary constitutive models and characterize optimal finite-rank internal-variable approximations in the sense of Kolmogorov 𝑁-widths. The history operator is shown to be compact under natural assumptions on the relaxation kernel, thereby admitting optimal low-rank approximations. The resulting reduced models inherit thermodynamic consistency, stability, and provable approximation bounds. An analysis clarifies the structural relation between hereditary representations and internal-variable theories and provides a rigorous basis for reduced-order modelling in computational mechanics. Selected numerical examples showcase optimal convergence of approximations with respect to rank and sampling.