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Evolutionary Solid Bodies - Growth and Remodelling of Biological Tissues


The Summer School shall address the issues of constitutive modelling of soft (such as arteries, ligaments and tendons) and hard biological tissues (typically bones) in stable and evolutive situations, covering growth and remodelling in relation to optimisation, which are hot topics in the mechanical community. The scientific idea behind the Summer School is then to work out the common fundamentals in both theory and computation of the two core topics.

1. Structural optimisation

Here, the engineer is used to designing optimal structures by modifying any of the above mentioned entities. In detail, different scalar valued design variables of different kinds can be introduced for parameter, thickness, shape and topology optimisation. Thus, every quantity has so far been considered as design variable. The computational approaches solve the application problems on the discrete level while neglecting the fundamental problem of a fixed solid body. The advantages of structural optimisation lie in the fact that every discrete quantity has already been considered as design variable. The main drawback of structural optimisation is due to the less developed theory of variations of all quantities in a continuum mechanical framework. Modifications by the engineer can be interpreted as design evolutions but they have not been  modelled as a time depending process.


2. Biological evolution

This scientific field entered the realm of continuum mechanics in the 1990’s. Time-dependent phenomena, basically consisting of a variation of material properties, mass and shape of the solid body, are attempted to be incorporated into the continuum description. One outstanding problem in developmental biology is the understanding of the factors that may promote the generation of biological form, involving the processes of growth (change of mass), remodelling (change of properties), and morphogenesis (shape changes). These three aspects of the development of a biological structure have tied mutual connections, and are due to a combination of chemical agents and mechanical factors, such as strains and stresses.


The challenge of linking both pillars

One main objective of the Summer School is then to (attempt to) unify the computational techniques known in structural optimisation (engineer has learned how to compute modifications of every quantity which, however, lie outside the physical time) and to combine them with rigorous mechanical models for open systems and modifications in material space. We shall then propose a classification of phenomena of biomechanics with respect to their a.) kinematical and b.) physical behaviour. This should be based on the classification mentioned above.



The Summer School is addressed to international PhD students and postdoctoral researchers in mechanical and civil engineering, applied mathematics, (bio)physics, biomedical engineering, physiology and material science who are interested in broadening their interests and knowledge in the area of growth and remodelling. The Summer School is equally open to Master students, senior scientists and engineers from relevant industries.



The Summer School will be held at the JugendGästehaus Aasee in Münster, Germany.