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Linearization of finite-strain poro-visco-elasticity with degenerate mobility

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arxiv 2408.15151 v1 pith:J7TFDQI4 submitted 2024-08-27 math.AP

Willem J. M. van Oosterhout This is my paper · ORCID
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keywords finite-strainsolutionsdegenerateequationmobilitymodelnonlinearporo-visco-elasticity
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A quasistatic nonlinear model for finite-strain poro-visco-elasticity is considered in the Lagrangian frame using Kelvin-Voigt rheology. The model consists of a mechanical equation which is coupled to a diffusion equation with a degenerate mobility. Having shown existence of weak solutions in a previous work, the focus is first on showing boundedness of the concentration using Moser iteration. Afterwards, it is assumed that the external loading is small, and it is rigorously shown that solutions of the nonlinear, finite-strain system converge to solutions of the linear, small-strain system.

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  1. Linearization of quasistatic fracture evolution in brittle materials

    math.AP 2024-11 accept novelty 7.0 of 10

    Quasistatic fracture evolutions in nonlinear elasticity converge, after rescaling, to quasistatic crack growth in linear elasticity in two dimensions, without any a priori assumptions on the crack set.

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