Abstract-A constitutive approach is developed that predicts the critical stress for twinning as a function of external (temperature, strain rate) and internal (grain size, stacking-fault energy) parameters. Plastic deformation by slip and twinning are considered as competitive mechanisms. The twinning stress is equated to the slip stress based on the plastic flow by thermally assisted movement of dislocations over obstacles, which leads to successful prediction of the slip-twinning transition. The model is applied to body centered cubic, face centered cubic, and hexagonal metals and alloys: Fe, Cu, brasses, and Ti, respectively. A constitutive expression for the twinning stress in BCC metals is developed using dislocation emission from a source and the formation of pile-ups, as rate-controlling mechanism. Employing an Eshelby-type analysis, the critical size of twin nucleus and twinning stress are correlated to the twin-boundary energy, which is directly related to the stacking-fault energy (SFE) for FCC metals. The effects of grain size and SFE are examined and the results indicate that the grain-scale pile-ups are not the source of the stress concentrations giving rise to twinning in FCC metals. The constitutive description of the slip-twinning transition are incorporated into the Weertman-Ashby deformation mechanism maps, thereby enabling the introduction of a twinning domain. This is illustrated for titanium with a grain size of 100 µm. 

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Some fundamental issues in the formulation of constitutive theories of material response based on the multiplicative decomposition of the deformation gradient are reviewed, with focus on finite deformation thermoelasticity, elastoplasticity, and biomechanics. The constitutive theory of isotropic thermoelasticity is first considered. The stress response and the entropy expression are derived in the case of quadratic dependence of the elastic strain energy on the finite elastic strain. Basic kinematic and kinetic aspects of the phenomenological and single crystal elastoplasticity within the framework of the multiplicative decomposition are presented. Attention is given to additive decompositions of the stress and strain rates into their elastic and plastic parts. The constitutive analysis of the stress-modulated growth of pseudo-elastic soft tissues is then presented. The elastic and growth parts of the deformation gradient and the rate of deformation tensor are defined and used to construct the corresponding rate-type biomechanic theory. The structure of the evolution equation for growth-induced stretch ratio is discussed. There are 112 references cited in this review article.

Mechanics of Solids and Materials intends to provide a modern and integrated treatment of the foundations of solid mechanics as applied to the mathematical description of material behavior. The 2006 book blends both innovative (large strain, strain rate, temperature, time dependent deformation and localized plastic deformation in crystalline solids, deformation of biological networks) and traditional (elastic theory of torsion, elastic beam and plate theories, contact mechanics) topics in a coherent theoretical framework. The extensive use of transform methods to generate solutions makes the book also of interest to structural, mechanical, and aerospace engineers. Plasticity theories, micromechanics, crystal plasticity, energetics of elastic systems, as well as an overall review of math and thermodynamics are also covered in the book.