含韧性损伤结构钢在非欧流形中的力学状态

Mechanical State of Structural Steel with Ductile Damage in Non-Euclid Manifold

变形体内部含有微观缺陷时,变形将出现非协调,不能完全在经典理论范围内求解。文章针对结构钢韧性损伤进行几何拓扑,通过非完整标架建立该问题的非欧几何结构,确定受损材料在非欧流形中的力学状态,提出非欧流形中变形协调的韧性损伤模型。理论分析及算例表明:几何-拓扑后的模型形式统一,是在经典理论之外解决韧性损伤问题的一种途径。

The deformation becomes incompatible if there are micro-defects in plasmodium;so,the problem can not be solved with classical theory.We give the geometrical topology of the ductile damage theory of steel,establish its non-Euclid geometrical structure with non-completeness system,determine the mechanical state of damaged materials in non-Euclid manifold,and provide the ductile damage model in non-Euclid manifold.Complete details are given in sections 1 through 5,which are entitled：（1） definitions and basic assumptions,（2） the construction of Euclid material manifold,（3） the strain state of structural steel with ductile damage in non-Euclid manifold,（4） the stress state of structural steel with ductile damage in non-Euclid manifold,（5）example.Section 6 is entitled concluding remarks;it states the two advantages of the topologized damage model.