纺织复合材料和结构多尺度耦合的数值分析

研究了纺织复合材料和结构多尺度耦合的数值分析模型。建立了微、细观单胞,给出了纺织复合材料平均弹性常数的逐级分析方法,着重研究了由宏观结构、到细观纤维束、再到微观纤维三个尺度耦合的应力分析方案。对于常用的板壳状纺织复合材料结构,在面内载荷下,假设每层细观单胞的平均面内应变是一致的,在弯曲、横向剪切及扭曲等非面内载荷下,在内力等效条件下将沿厚度方向连续分布的宏观应力简化为阶梯状分布,忽略了每层细观单胞范围内宏观应力沿厚度方向的梯度变化,由此利用细观单胞模型实现宏观应力与细观应力之间的传递,再利用微观单胞可得到纤维尺度的微观应力。最后以一种三维机织复合材料为例,用上述多尺度耦合的模型逐级分析了材料的平均弹性常数,并沿相反方向,由宏观结构分析逐级计算出纤维束尺度和纤维尺度的细、微观应力的局部波动。

Multi-scale coupled numerical analysis of textile composites and structures

Multi-scale coupled numerical approaches for textile composites and structures were pursued. Firstly, micro- and meso-scale repeated unit cells (RUCs), which represent fiber packing in yarn and periodic braided architectures of textile composites, respectively, were built. The way of average elastic constants prediction of textile composites via multi-scale RUCs was presented. Then, strategy of stress analysis spanning scales of macro structure, meso- and micro RUCs was introduced in detail. To textile composite made panel or shell structures, under in-plane loads, the average in-plane strains of meso RUC is assumed identical. Under out-plane loads, e.g. bending, transverse shear and twisting, the continuous macro-scale stress distributions along thickness are simplified as ladder-like distributions which apply equivalent force and moment. The macro stress grads along thickness are ignored in range of a meso RUC layer. With meso- and micro-scale RUC models, stress transitions from structure to meso-RUC, and then to micro-RUC were achieved. Finally, this multi-scale model was applied to a fictitious square panel made of 3D woven composite. Average elastic constants of the material were calculated, and then, they were employed in structure analysis. By the opposite analysis process, meso- and then micro-scale stress concentrations in given local positions were obtained, respectively.