Recall that f: X→Y is a homotopy epimorphism (monomorphism) if given u, v: Y→W(u, v:W→X), u(?)of(?)v(?)f implies u(?)v(f(?)u(?)f(?)v implies u(?)v). In ref. [1], Lin and Shen
The thermal expansion strain is considered as a special case of eigenstrain.The authors proved the theorem on decomposition of eigenstrain existing in a body into two constituents:Impotent eigenstrain(not causing stre...The thermal expansion strain is considered as a special case of eigenstrain.The authors proved the theorem on decomposition of eigenstrain existing in a body into two constituents:Impotent eigenstrain(not causing stress in any point of a body)and nilpotent eigenstrain(not causing strain in any point of a body).According to this theorem,the thermal stress can be easily found through the nilpotent eigenstrain.If the eigenstrain is an impotent one,the thermal stress vanishes.In this case,the eigenstrain must be compatible.The authors suggest a new approach to measure of eigenstrain incompatibility and hence to estimate of thermal stresses.展开更多
文摘Recall that f: X→Y is a homotopy epimorphism (monomorphism) if given u, v: Y→W(u, v:W→X), u(?)of(?)v(?)f implies u(?)v(f(?)u(?)f(?)v implies u(?)v). In ref. [1], Lin and Shen
文摘The thermal expansion strain is considered as a special case of eigenstrain.The authors proved the theorem on decomposition of eigenstrain existing in a body into two constituents:Impotent eigenstrain(not causing stress in any point of a body)and nilpotent eigenstrain(not causing strain in any point of a body).According to this theorem,the thermal stress can be easily found through the nilpotent eigenstrain.If the eigenstrain is an impotent one,the thermal stress vanishes.In this case,the eigenstrain must be compatible.The authors suggest a new approach to measure of eigenstrain incompatibility and hence to estimate of thermal stresses.
