The initial stresses widely exist in elastic materials.While achieving a continuum stress-free configuration through compatible unloading is desirable,mechanical unloading alone frequently proves insufficient,posing c...The initial stresses widely exist in elastic materials.While achieving a continuum stress-free configuration through compatible unloading is desirable,mechanical unloading alone frequently proves insufficient,posing challenges in avoiding virtual stress-free configurations.In this paper,we introduce a novel concept of equivalent temperature variation to counteract the incompatible initial strain.Our focus is on initially stressed cylindrical and spherical elastomers,where we first derive the Saint-Venant,Beltrami-Michell,and Volterra integral conditions in orthogonal curvilinear coordinates using the exterior differential form theory.It is shown that for any given axially or spherically distributed initial stress,an equivalent temperature variation always exists.Furthermore,we propose two innovative initial stress forms based on the steady-state heat conduction.By introducing an equivalent temperature variation,the initial stress can be released through a compatible thermo-mechanical unloading process,offering valuable insights into the constitutive theory of initially stressed elastic materials.展开更多
We give a proof of an explicit formula for affine coodinates of points in the Sato’s infinite Grassmannian corresponding to tau-functions for the KdV hierarchy.
基金Project supported by the National Natural Science Foundation of China(Nos.12241205 and 12032019)the National Key Research and Development Program of China(No.2022YFA1203200)the Strategic Priority Research Program of Chinese Academy of Sciences(Nos.XDB0620101 and XDB0620103)。
文摘The initial stresses widely exist in elastic materials.While achieving a continuum stress-free configuration through compatible unloading is desirable,mechanical unloading alone frequently proves insufficient,posing challenges in avoiding virtual stress-free configurations.In this paper,we introduce a novel concept of equivalent temperature variation to counteract the incompatible initial strain.Our focus is on initially stressed cylindrical and spherical elastomers,where we first derive the Saint-Venant,Beltrami-Michell,and Volterra integral conditions in orthogonal curvilinear coordinates using the exterior differential form theory.It is shown that for any given axially or spherically distributed initial stress,an equivalent temperature variation always exists.Furthermore,we propose two innovative initial stress forms based on the steady-state heat conduction.By introducing an equivalent temperature variation,the initial stress can be released through a compatible thermo-mechanical unloading process,offering valuable insights into the constitutive theory of initially stressed elastic materials.
文摘We give a proof of an explicit formula for affine coodinates of points in the Sato’s infinite Grassmannian corresponding to tau-functions for the KdV hierarchy.
