What is it about?

We deal with a mathematical description of a solid which grows over time and is elastically deformed. We prove that such a model admits solutions. The growth of the solid can be controlled by providing a nutrient. By assuming this nutrient to diffuse in the body, we are able to prove that the combined growth-diffusion process admits a solution.

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Why is it important?

Mechanical systems experiencing growth are common in applications in biological and technological systems. Growth is often influenced by the mechanical state of the solid, calling for the study of both effects. This seems to be a first result in this setting (finite deformations, hyperelasticity, quasistatic equilibria).

Perspectives

The mathematical analysis of mechanical problems with growth offers a wealth of challenging problems and relates to a variety of interesting applications, from tumor growth to additive manufacturing. We believe that there is still much to do in this direction.

Ulisse Stefanelli
University of Vienna

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This page is a summary of: Existence results for a morphoelastic model, ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, May 2022, Wiley, DOI: 10.1002/zamm.202100478.
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