无序纤维空间增强纤维材料非线性变形模型的建立

E. Shikula
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引用次数: 0

摘要

提出了一种含有定向不良纤维和物理非线性矩阵的多向增强纤维材料的非线性变形模型。空间增强纤维材料被认为是具有随机纤维排列的多组分材料。它基于物理非线性弹性理论的随机微分方程。用L.P.Khoroshun的条件矩方法构造了复合材料应力应变状态和有效性能问题的解。提出了一种确定具有物理非线性矩阵的空间增强材料有效变形性能的算法。利用迭代方法构造了考虑物理非线性的非线性方程组的解。建立了空间增强材料中宏观应力和宏观应变之间的联系规律,以及其基体中平均应变和应力对宏观应变的依赖性。绘制了纤维体积含量的各种值的材料变形曲线。研究了空间增强材料的有效变形性能与纤维体积含量的关系。研究了基体的非线性对空间增强复合材料变形的影响。研究表明,基体的非线性对空间增强材料的有效变形性能和应力-应变状态有显著影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
CONSTRUCTION OF A MODEL OF NONLINEAR DEFORMATION OF SPATIALLY-REINFORCED FIBER MATERIALS WITH DISORDERED FIBERS
A model of nonlinear deformation of fibrous materials of multidirectional reinforcement with misoriented fibers and a physically nonlinear matrix is proposed. A spatially reinforced fibrous material is regarded as a multicomponent material with a random arrangement of fibers. It is based on stochastic differential equations of the physically nonlinear theory of elasticity. The solution to the problem of the stress-strain state and the effective properties of the composite material is constructed by the method of conditional moments of L.P. Khoroshun. An algorithm for determining the effective deformative properties of a spatially reinforced material with a physically nonlinear matrix has been developed. The solution of nonlinear equations taking into account its physical nonlinearity is constructed by an iterative method. The law of connection between macrostresses and macrostrains in a spatially reinforced material and the dependence of average strains and stresses in its matrix on macrostrains have been established. Material deformation curves are plotted for various values of the fiber volumetric content. The dependence of the effective deformative properties of the spatially reinforced material on the volumetric content of fibers has been studied. The influence of the nonlinearity of the matrix on the deformation of a spatially reinforced composite material is investigated. It has been established that the nonlinearity of the matrix has a significant effect on the effective deformative properties and the stress-strain state of spatially reinforced materials.
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