The viscoelastic paradox in a nonlinear Kelvin-Voigt type model of dynamic fracture
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908573890510848 |
|---|---|
| author | Caponi, Maicol Carbotti, Alessandro Sapio, Francesco |
| author_facet | Caponi, Maicol Carbotti, Alessandro Sapio, Francesco |
| contents | In this paper we consider a dynamic model of fracture for viscoelastic materials, in which the constitutive relation, involving the Cauchy stress and the strain tensors, is given in an implicit nonlinear form. We prove the existence of a solution to the associated viscoelastic dynamic system on a prescribed time-dependent cracked domain via a discretisation-in-time argument. Moreover, we show that such a solution satisfies an energy-dissipation balance in which the energy used to increase the crack does not appear. As a consequence, in analogy to the linear case this nonlinear model exhibits the so-called viscoelastic paradox. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_14250 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The viscoelastic paradox in a nonlinear Kelvin-Voigt type model of dynamic fracture Caponi, Maicol Carbotti, Alessandro Sapio, Francesco Analysis of PDEs 35L53, 35A01, 35Q74, 47H05, 74D10, 74R10 In this paper we consider a dynamic model of fracture for viscoelastic materials, in which the constitutive relation, involving the Cauchy stress and the strain tensors, is given in an implicit nonlinear form. We prove the existence of a solution to the associated viscoelastic dynamic system on a prescribed time-dependent cracked domain via a discretisation-in-time argument. Moreover, we show that such a solution satisfies an energy-dissipation balance in which the energy used to increase the crack does not appear. As a consequence, in analogy to the linear case this nonlinear model exhibits the so-called viscoelastic paradox. |
| title | The viscoelastic paradox in a nonlinear Kelvin-Voigt type model of dynamic fracture |
| topic | Analysis of PDEs 35L53, 35A01, 35Q74, 47H05, 74D10, 74R10 |
| url | https://arxiv.org/abs/2310.14250 |