0566662 20250218172327.020230110235959.9 85143582510 000896227200001 10.3390/math10234412 17 s. E cav_un_epca*04536012227-739010MDPI vectorized FEM implementation incremental minimization principle dissipative solids shape memory alloys cav_un_auth*0255186 Frost Miroslav UT-L D 5 - Ultrazvukové metody D 5 - Ultrasonic Methods D5 – Ultrasonic Methods CZ Ústav termomechaniky AV ČR, v. v. i. cav_un_auth*0292941 Valdman Jan UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. pdf https://mdpi-res.com/d_attachment/mathematics/mathematics-10-04412/article_deploy/mathematics-10-04412.pdf?version=1669191552 GA22-20181S GA ČR CZ cav_un_auth*0435651 LTAUSA18199 GA MŠk CZ cav_un_auth*0371955 GF21-06569K GA ČR cav_un_auth*0412957 The incremental energy minimization principle provides a compact variational formulation for evolutionary boundary problems based on constitutive models of rate-independent dissipative solids. In this work, we develop and implement a versatile computational tool for the resolution of these problems via the finite element method (FEM). The implementation is coded in the MATLAB programming language and benefits from vector operations, allowing all local energy contributions to be evaluated over all degrees of freedom at once. The monolithic solution scheme combined with gradient-based optimization methods is applied to the inherently nonlinear, non-smooth convex minimization problem. An advanced constitutive model for shape memory alloys, which features a strongly coupled rate-independent dissipation function and several constraints on internal variables, is implemented as a benchmark example. Numerical simulations demonstrate the capabilities of the computational tool, which is suited for the rapid development and testing of advanced constitutive laws of rate-independent dissipative solids. WOS JG 20000 20300 20302 2023 2 UTIA-B 10000 10100 10102 4 O 4o 20250218172328.0 UTIA-B BD RVO:61388998 RVO:67985556 https://hdl.handle.net/11104/0338138 S 4412 n.a. Article Mathematics A MATHEMATICS 2.3 1 1.8 0.02342 0.369 21851 0.446 2.000 4790 Q1 93.2 Q3 Q3 2.08 Q1 93.2 2022 Soubory v repozitáři: 0566662_Vectorized MATLAB Implementation _Frost_Valdman_2022.pdf 85143582510 SCOPUS PUBMED 000896227200001 WOS pdf cav_un_epca*0453601 Mathematics 2227-7390 2227-7390 Roč. 10 č. 23 2022 MDPI ONLINE