A mixture-compatible theory of chemothermal deposition and expansion in n-constituent finitely deforming composite materials with initially circularly cylindrical microstructures. (February 2015) - Hall, Richard B
A multiscale approach to growth and recession is adopted that is compatible with the theory of mixtures. The growth may result from chemical reactions or infiltrations, or combinations thereof. The emphasis of the work is on the construction of approximate constituent elastic deformation gradients, associated with an arbitrary overall deformation, that reflect an initially circularly cylindrical geometry relative to which growth occurs. A decomposition of the deformation into cylindrical and non-cylindrical parts is employed. A cylindrically symmetric reference configuration for a given constituent is adopted in which chemical growth, chemothermal (and/or equivalently moisture) expansion, and appearance or disappearance of the constituent may occur; the reference configuration of a constituent thus possesses evolving spatial dimensions but fixed geometric and material symmetries. The traditional composite micromechanics assumption of common radial stress is adopted, in combination with the assumptions of either common axial deformation rate or common axial deformation, for the cylindrical component of deformation. Elastic deformations of constituents are obtained through comparison, of the actual deformation, to the assumed stress-free deposition configurations and subsequent chemothermal stress-free expansions. The requirement that the local and homogenized cylindrical deformations (or rates) match in the axial and outermost radial directions is used to define a homogenized non-cylindrical component that is applied across the local constituents to couple the cylindrical deformation to the overall deformation. The general objective of the study may be stated as incorporating ordered microstructure-based stresses incorporating growth, chemothermal expansion, inhomogeneous natural states, and applied deformations into a mixture theory-compatible framework to provide an important refinement to the assessments of constituent states. The model is intended to enable a new efficiency of multiscale representation in the modeling of composite materials with evolving microstructures, considering both manufacturing processes and environmental influences.