Abstract
The developments reported in this paper relate to the concept of optimal evolutionary remodelling. A variational formulation is presented for the problem of optimal remodel of an arbitrary, given continuum structure, where the modification may be interpreted to represent a strengthening (growth) of or diminishing (resorbtion) from the starting structure. Modification variables have the form of an unrestricted material modulus tensor or a set (mixture) of such tensors. The argument of the isoperimetric constraint is expressed in generalized form, as is the objective. Evolution is simulated as a stepwise process, where each step is determined as an optimal remodel. Both local material properties and load configuration may vary with the process. Necessary and sufficient conditions for the optimal stepwise remodel are identified. Interpretations of the simulation model are compared to known methods for application to growth or degradation in bone.
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Taylor, J.E. (1999). Optimal Modification and Evolution of Elastic Continuum Structures. In: Pedersen, P., Bendsøe, M.P. (eds) IUTAM Symposium on Synthesis in Bio Solid Mechanics. Solid Mechanics and its Applications, vol 69. Springer, Dordrecht. https://doi.org/10.1007/0-306-46939-1_11
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DOI: https://doi.org/10.1007/0-306-46939-1_11
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