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Biomech Model Mechanobiol. 2007 Sep;6(5):289-96. Epub 2006 Nov 23.

On the definition and modeling of incremental, cumulative, and continuous growth laws in morphoelasticity.

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  • 1Program in Applied Mathematics and Department of Mathematics, University of Arizona, Building #89, Tucson, AZ 85721, USA.


In the theory of elastic growth, a growth process is modeled by a sequence of growth itself followed by an elastic relaxation ensuring integrity and compatibility of the body. The description of this process is local in time and only corresponds to an incremental step in the total growth process. As time evolves, these incremental growth steps are compounded and a natural question is the description of the overall cumulative growth and whether a continuous description of this process is possible. These ideas are discussed and further studied in the case of incompressible shells.

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