incompatibility

Dear colleagues,

In this manuscript with Lev Truskinovsky, we developed a new nonlinear theory of large-strain incompatible surface growth. Surface growth is a crucial component of many natural and artificial processes from cell proliferation to additive manufacturing. In elastic systems, surface growth is usually accompanied by the development of geometrical incompatibility leading to residual stresses and triggering various instabilities. Here we developed a nonlinear theory of incompatible surface growth which quantitatively linkes deposition protocols with post-growth states of stress.

Chiqun Zhang            Amit Acharya

The utility of the notion of generalized disclinations in materials science is discussed within the physical context of modeling interfacial and bulk line defects like defected grain and phase boundaries, dislocations and disclinations. The Burgers vector of a disclination dipole in linear elasticity is derived, clearly demonstrating the equivalence of its stress field to that of an edge dislocation. We also prove that the inverse deformation/displacement jump of a defect line is independent of the cut-surface when its g.disclination strength vanishes. An explicit formula for the displacement jump of a single localized composite defect line in terms of given g.disclination and dislocation strengths is deduced based on the Weingarten theorem for g.disclination theory at finite deformation. The Burgers vector of a g.disclination dipole at finite deformation is also derived.

(to appear in International Journal of Fracture; Proceedings of the 5th Intl. Symposium on Defect andMaterial Mechanics)

Amit Acharya and Claude Fressengeas