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首頁> 中文期刊> 《三峽大學(xué)學(xué)報(bào)（自然科學(xué)版）》 >變分?jǐn)?shù)階微積分在描述材料力學(xué)性質(zhì)演變方面的應(yīng)用

變分?jǐn)?shù)階微積分在描述材料力學(xué)性質(zhì)演變方面的應(yīng)用

     
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材料在受力和變形過程中,力學(xué)性質(zhì)是不斷變化的,而現(xiàn)有的整數(shù)階本構(gòu)模型只能定性描述材料從彈性變?yōu)樗苄?變?yōu)榱黧w,不能定量地描述力學(xué)性質(zhì)的演變.在常分?jǐn)?shù)階本構(gòu)模型的基礎(chǔ)上,提出一個(gè)新的變分?jǐn)?shù)階本構(gòu)模型.從理論上講,該模型可以通過階數(shù)的變化來展示材料力學(xué)性質(zhì)的變化、用該模型,對(duì)銅、鋁合金以及低碳鋼在等應(yīng)變率拉伸過程中的力學(xué)性質(zhì)進(jìn)行分析,發(fā)現(xiàn)其變化過程均可分為3個(gè)階段:第1階段為線彈性階段,第2階段力學(xué)性質(zhì)發(fā)生突變,第3階段為線性變化階段,而這與實(shí)驗(yàn)中所得現(xiàn)象是符合的,從而得出該模型可以描述力學(xué)性質(zhì)演變.因?yàn)殡A數(shù)的變化范圍為0到1,所以該模型可用于其他粘彈性材料在具有時(shí)間效應(yīng)的受力及變形過程中力學(xué)性質(zhì)演變的分析,如巖土及高分子材料的應(yīng)力松弛與蠕變,等應(yīng)變率加載等.%The mechanical properties of materials are changing when they are under loading, the existing integer models only can depict the properties as from elasticity to plasticity and fluid, and cannot represent the process quantitatively. Based on fractional constitutive model, a new variable-order fractional constitutive model is proposed. Theoretically, the change of the order can show the evolution of mechanical properties of materials. When the tensile tests of copper, low carbon steel and alloy aluminum are simulated using the variable-order model, it is found that the changing process of mechanical properties of these ductile metals has three stages in the changing process. The first stage is linear elastics the second one is a transient mutation phase; and the last one is an approximately uniform (linear) changing phase of material feature. These conclusions are consistent with the phenomenon, which shows that this model can be used to trace the evolution of mechanical properties of materials. Because the value of the order change from 0 to 1, so this model can be used for the analysis of the evolution of mechanical properties of other viscoelastic materials in the deformation and loading process with time effect, such as the rock and high polymer material in the stress relaxation , creep or constant strain rate loading process.

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