Perspectives on biological growth and remodeling

The continuum mechanical treatment of biological growth and remodeling has attracted considerable attention over the past fifteen years. Many aspects of these problems are now well-understood, yet there remain areas in need of significant development from the standpoint of experiments, theory, and computation. In this perspective paper we review the state of the field and highlight open questions, challenges, and avenues for further development.     

Stress-induced crystal preferred orientation in the poromechanics of in-pore crystallization

A non-hydrostatic stress field affects the orientation of crystals growing in the pore network of an elastic porous medium. The hypothesis of a hydrostatic state of stress within the crystal has been implicitly made in the recent extension of poromechanics to in-pore crystalization (Coussy, 2006). This underlying hypothesis is revisited on a small-scale conceptual model based on Eshelby's problem and shows that chemo-mechanical equilibrium requires that the crystal adapts its shape and orientation to the far-field stress, therefore resulting at equilibrium in a hydrostatic state of stress within the crystal. The optimum crystal shape as a function of the far-field stress is consistently investigated, highlighting limiting cases. The small scale model allows to understand the macroscopic effects associated with deviatoric stresses in the poromechanics of in-pore crystallization. Moreover, it provides the building block for an up-scaling of the macroscopic tangent poroelastic properties, which depend on both the current crystal saturation and the state of stress. A dilute micromechanical scheme illustrates the variation of the macroscopic Biot's coefficient tensor as a function of deviatoric stresses. A simple configuration akin to a potential laboratory experiment finally illustrates the strong induced anisotropy of the crystallization induced macroscopic strain when deviatoric stresses are applied to the material prior to crystallization.     

A path-independent integral for fracture of solids under combined electrochemical and mechanical loadings

In this study, we first demonstrate that the J-integral in classical linear elasticity becomes path-dependent when the solid is subjected to combined electrical, chemical and mechanical loadings. We then construct an electro-chemo-mechanical J-integral that is path-independent under such combined multiple driving forces. Further, we show that this electro-chemo-mechanical J-integral represents the rate at which the grand potential releases per unit crack growth. As an example, the path-independent nature of the electro-chemo-mechanical J-integral is demonstrated by solving the problem of a thin elastic film delaminated from a thick elastic substrate.