On residual stresses and homeostasis: an elastic theory of functional adaptation in living matter

Living matter can functionally adapt to external physical factors by developing internal tensions, easily revealed by cutting experiments. Nonetheless, residual stresses intrinsically have a complex spatial distribution, and destructive techniques cannot be used to identify a natural stress-free configuration. This work proposes a novel elastic theory of pre-stressed materials. Imposing physical compatibility and symmetry arguments, we define a new class of free energies explicitly depending on the internal stresses. This theory is finally applied to the study of arterial remodelling, proving its potential for the non-destructive determination of the residual tensions within biological materials

Wave propagation through periodic lattice with defects

International audienceThe discrete periodic lattice of masses and springs with line and point defects is considered. The matrix integral equations of a special form are solved explicitly to obtain the Floquet–Bloch dispersion spectra for propagative, guided and localised waves. Explicit form of the dispersion equations makes possible detailed analysis of the position and other characteristics of the spectra. For example in the case of the uniform lattice with one line inclusion along with one single defect we obtain the sharp explicit upper bound 34−12π for the mass of single defect for which there exist localised waves in the spectral gaps. The developed method can be applied to various problems in optics, solid-state physics, or electronics in which lattice defects play a major role