Mathematical Models of Stresses in Materials

This book presents original mathematical models of thermal/phase-transformation stresses, micro/macro-strengthening, inter/transcrystalline crack formation, and mathematical definitions of limit states with respect to the crack formation. The models (continuum mechanics) are determined for two types of two-component materials, which consist of isotropic ellipsoidal precipitates in isotropic crystalline grains (e.g., matrix-precipitate composites) or of two types of ellipsoidal isotropic crystalline grains (e.g., dual-phase steel). The strengthening and limit states represent important material phenomena. This monograph is applicable within basic research/engineering practice, suitable for university courses and for non-specialists in continuum mechanics. The appendix presents the mathematical topics required to perform the mathematical procedures in this book.