@article {2021, title = {A dynamic model for viscoelasticity in domains with time-dependent cracks}, volume = {28}, year = {2021}, month = {2021/10/01}, pages = {67}, abstract = {

In this paper, we prove the existence of solutions for a class of viscoelastic dynamic systems on time-dependent cracking domains.

}, isbn = {1420-9004}, url = {https://doi.org/10.1007/s00030-021-00729-0}, author = {Francesco Sapio} } @article {2021, title = {An existence result for the fractional Kelvin{\textendash}Voigt{\textquoteright}s model on time-dependent cracked domains}, year = {2021}, month = {2021/06/04}, abstract = {

We prove an existence result for the fractional Kelvin{\textendash}Voigt{\textquoteright}s model involving Caputo{\textquoteright}s derivative on time-dependent cracked domains. We first show the existence of a solution to a regularized version of this problem. Then, we use a compactness argument to derive that the fractional Kelvin{\textendash}Voigt{\textquoteright}s model admits a solution which satisfies an energy-dissipation inequality. Finally, we prove that when the crack is not moving, the solution is unique.

}, isbn = {1424-3202}, url = {https://doi.org/10.1007/s00028-021-00713-2}, author = {Maicol Caponi and Francesco Sapio} } @article {2021, title = {Quasistatic Limit of a Dynamic Viscoelastic Model with Memory}, year = {2021}, month = {2021/11/30}, abstract = {

We study the behaviour of the solutions to a dynamic evolution problem for a viscoelastic model with long memory, when the rate of change of the data tends to zero. We prove that a suitably rescaled version of the solutions converges to the solution of the corresponding stationary problem.

}, isbn = {1424-9294}, url = {https://doi.org/10.1007/s00032-021-00343-w}, author = {Gianni Dal Maso and Francesco Sapio} } @article {2020, title = {A dynamic model for viscoelastic materials with prescribed growing cracks}, volume = {199}, year = {2020}, month = {2020/08/01}, pages = {1263 - 1292}, abstract = {

In this paper, we prove the existence of solutions for a class of viscoelastic dynamic systems on time-dependent cracked domains, with possibly degenerate viscosity coefficients. Under stronger regularity assumptions, we also show a uniqueness result. Finally, we exhibit an example where the energy-dissipation balance is not satisfied, showing there is an additional dissipation due to the crack growth.

}, isbn = {1618-1891}, url = {https://doi.org/10.1007/s10231-019-00921-1}, author = {Maicol Caponi and Francesco Sapio} }