2018/07/02 by Tomáš Roubı́ček, Roubicek, Tomas, Ulisse Stefanelli +1
Computer Science · Engineering · #35Q74 #35Q79 #35Q86 #65M60 74A15 #74A30 #74C15 #74F10 #74J30 #74L05 #74R20 #76S05 #80A20 #86A17 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Elasticity and Material Modeling #FOS: Mathematics #Thermoelastic and Magnetoelastic Phenomena
paper · pdf · doi:10.48550/arxiv.1807.00910
openalex publication_date 2018/07/02 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28
A mathematical model for an elastoplastic porous continuum subject to large\nstrains in combination with reversible damage (aging), evolving porosity, water\nand heat transfer is advanced. The inelastic response is modeled within the\nframe of plasticity for nonsimple materials. Water and heat diffuse through the\ncontinuum by a generalized Fick-Darcy law in the context of viscous\nCahn-Hilliard dynamics and by Fourier law, respectively. This coupling of\nphenomena is paramount to the description of lithospheric faults, which\nexperience ruptures (tectonic earthquakes) originating seismic waves and flash\nheating. In this regard, we combine in a thermodynamic consistent way the\nassumptions of having a small Green-Lagrange elastic strain and nearly\nisochoric plastification with the very large displacements generated by fault\nshearing. The model is amenable to a rigorous mathematical analysis. Existence\nof suitably defined weak solutions and a convergence result for Galerkin\napproximations is proved.\n