When crawling on a flat substrate, living cells exert forces on it via adhesive contacts, enabling them to build up tension within their cytoskeleton and to change shape. The measurement of these forces has been made possible by traction force microscopy (TFM), a technique which has allowed us to obtain time-resolved traction force maps during cell migration. This cell 'footprint' is, however, not sufficient to understand the details of the mechanics of migration, that is how cytoskeletal elements (respectively, adhesion complexes) are put under tension and reinforce or deform (respectively, mature and/or unbind) as a result. In a recent paper, we have validated a rheological model of actomyosin linking tension, deformation and myosin activity. Here, we complement this model with tentative models of the mechanics of adhesion and explore how closely these models can predict the traction forces that we recover from experimental measurements during cell migration. The resulting mathematical problem is a PDE set on the experimentally observed domain, which we solve using a finite-element approach. The four parameters of the model can then be adjusted by comparison with experimental results on a single frame of an experiment, and then used to test the predictive power of the model for following frames and other experiments. It is found that the basic pattern of traction forces is robustly predicted by the model and fixed parameters as a function of current geometry only.
International audienceThis paper deals with a method to evaluate and optimize the design of railway wheels subjected to multiparameter variable fatigue loading. The fatigue loads are statistically evaluated from in-service measurements. Representative realistic loading paths are built from the knowledge of the influence of various factors (such as train speed and track curvature). Using these paths, the method combines finite element computations and the fatigue equivalence method for damage evaluation in the structure. An extension of the Dang Van fatigue criterion in the high-cycle fatigue finite life domain associated with a damage accumulation law is adopted. The probability of failure of the structure is directly obtained from the interference between a local fatigue equivalent stress and fatigue strength distributions (based on the stress-strength interference approach). The result is useful for the optimization during the design stage or the validation of the fatigue strength of structures
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