The continuum theory of material separation (CTMS): An enrichment of continuum theory to achieve autonomous material separation

A framework is presented for material separation that operates within the setting of general Lagrangian continuum mechanics to yield autonomous surface separation. A key element of the theory is a novel regularization scheme that produces closing tractions on separating material surfaces. In contrast to the conventional cohesive theory, these closing tractions emerge in a natural way from the near-separation-front stress field. They are not the subject of a separate traction-separation constitutive postulate, as they are in the conventional theory. This construct facilitates the formulation of separation criteria that explicitly delineate the conditions under which a material point in the bulk continuum transitions to separation. This form of separation criterion represents the first central and unique element of the theory.This theory has been implemented in an existing quasi-static Lagrangian continuum code, and it is inherently compatible with any arbitrary bulk constitutive model. An explanation of the theory and its computational implementation will be presented, with a few verification exercises that demonstrate bounded stress fields at the crack front and convergence upon mesh refinement.In addition, a second central and unique element of the theory introduces the Separation Function which enables the CTMS to autonomously compute the criteria upon which a crack will extend, based on known limit states of materials. Computational theories for ductile, brittle, and shear fracture are presented for future development.The computational implementation of the theory involves a "Separation Element" consisting of a pair of separating finite-element facets. The opposing tractions acting on the facets are nonlocal, in the sense that they depend on the stress in the bulk continuum at all points within a distance that can be specified by a prefactor on the differential equation solved on the facet. This prefactor constitutes the material length scale related to separation. To impose nodal coincidence at the crack front, a consistency criterion is solved simultaneously with the closing traction differential equation at the crack front surfaces.