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Thermomechanics of damageable materials under diffusion: modelling and analysis

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Abstract

We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat generation/consumption/transfer is considered. Damage is modelled as rate-independent. The applications include metal-hydrogen systems with metal/hydride phase transformation, poroelastic rocks, structural and ferro/para-magnetic phase transformation, water and heat transport in concrete, and if diffusion is neglected, plasticity with damage and viscoelasticity, etc. For the ensuing system of partial differential equations and inclusions, we prove existence of solutions by a carefully devised semi-implicit approximation scheme of the fractional-step type.

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Authors and Affiliations

  1. Mathematical Institute, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

    Tomáš Roubíček

  2. Institute of Thermomechanics of the Czech Academy of Sciences, Dolejškova 5, 182 00, Praha 8, Czech Republic

    Tomáš Roubíček

  3. Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università di Roma “Tor Vergata”, Via Politecnico, 00133, Roma, Italy

    Giuseppe Tomassetti

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  1. Tomáš Roubíček
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Correspondence to Tomáš Roubíček.

Additional information

This research has been supported by GA ČR through the projects 201/10/0357 “Modern mathematical and computational models for inelastic processes in solids”, 13-18652S “Computational modeling of damage and transport processes in quasi-brittle materials”, 14-15264S “Experimentally justified multiscale modelling of shape memory alloys”, by the CENTEM Project No. CZ.1.05/21.00/03.0088 (cofounded from ERDF within the OP RDI programme, MŠMT ČR) at New Technologies Research Centre (Univ. of West Bohemia, Plzeň), and by INdAM-GNFM through projects “Mathematical Modeling of Morphing Processes” and “Mathematical Modeling of Shape Changes in Soft Tissues”.

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Roubíček, T., Tomassetti, G. Thermomechanics of damageable materials under diffusion: modelling and analysis. Z. Angew. Math. Phys. 66, 3535–3572 (2015). https://doi.org/10.1007/s00033-015-0566-2

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  • DOI: https://doi.org/10.1007/s00033-015-0566-2

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