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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.16072 |
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| _version_ | 1866917416085225472 |
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| author | Romero, Ignacio Ortiz, Michael |
| author_facet | Romero, Ignacio Ortiz, Michael |
| contents | We develop an operator-theoretic formulation of 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 modeling in computational mechanics. Selected numerical examples showcase optimal convergence of approximations with respect to rank and sampling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16072 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Identification of optimal history variables and corresponding hereditary laws in linear viscoelasticity Romero, Ignacio Ortiz, Michael Mathematical Physics We develop an operator-theoretic formulation of 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 modeling in computational mechanics. Selected numerical examples showcase optimal convergence of approximations with respect to rank and sampling. |
| title | Identification of optimal history variables and corresponding hereditary laws in linear viscoelasticity |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2604.16072 |