Rice’s Internal Variables Formalism and Its Implications for the Elastic and Conductive Properties of Cracked Materials, and for the Attempts to Relate Strength to Stiffness

Rice’s internal variables formalism [1975, “Continuum Mechanics and Thermodynamics of Plasticity in Relation to Microscale Deformation Mechanisms,” in Constitutive Equations in Plasticity, edited by A. Argon, MIT Press, Cambridge, MA, pp. 23–75] is one of the basic tools in the micromechanics of materials. One of its implications is the possibility to relate the compliance/resistivity contributions of cracks—the key quantities in the problem of effective elastic/conductive properties—to the stress intensity factors (SIFs) and thus to utilize a large library of available solutions for SIFs. Examples include configurations that are common in materials science applications: branched and intersecting cracks, cracks with partial contact between crack faces, and cracks emanating from pores. The formalism also yields valuable physical insights of a qualitative character, such as the impossibility to correlate, in a quantitative way, the strength of microcracking materials and their stiffness reduction.