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A mechanical model for dissolution-precipitation creep based on the minimum principle of the dissipation potential

S. Klinge, K. Hackl, J. Renner.

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, The Royal Society, 471, (2015)

Abstract
In contrast to previous approaches that consider dissolution-precipitation creep as a multi-stage process and only simulate its governing subprocess, the present model treats this phenomenon as a single continuous process. The applied strategy uses the minimum principle of the dissipation potential according to which a Lagrangian consisting of elastic power and dissipation is minimized. Here, the elastic part has a standard form while the assumption for dissipation stipulates the driving forces to be proportional to two kinds of velocities: The material-transport velocity and the boundary-motion velocity. A Lagrange term is included to impose mass conservation. Two ways of solution are proposed. The strong form of the problem is solved analytically for a simple case. The weak form of the problem is used for a finite-element implementation and for simulating more complex cases. © 2015 The Author(s) Published by the Royal Society. All rights reserved.


Keyword(s): variational principles, dissolution–precipitation creep, inelastic processes, finite-element method
Cite as: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84939832911&doi=10.1098%2frspa.2014.0994&partnerID=40&md5=2d33cf1cb81b06898b3d1e8643d9d1dc
DOI: 10.1098/rspa.2014.0994
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