复合材料激光辐照下热力耦合效应的多尺度分析

With the development of laser technology and composites science,it becoming urgent to study the interaction of laser and composite material in the field of defence and mechanical industries.When composite material irradiated by laser beam,there will be two kinds of response come into being. The first one is thermal decomposition and thermal-mechanical damage by long laser pulse,and the second effct is the stress wave that induced by ultra-short laser pulse.Currently,there are many mature research results about interaction of laser and homogeneous material.But most of them focus on macroeffect.Furthermore,in the numerical simulation for model of composites,the homogeneous model under idealized assumptions were often adopted.Actually,we should also foucus on local coupling effect between different components of composite material besides the macroeffect between the laser and composites.However,the model that can describe the thermal-mechanical coupling effect in Macro-Meso scales of composites is evolution systems that have oscillating coefficients. It's very inefficient to solve the systems by traditional numerical method.Base on above reasons,we'll study the multi-scale finite element method that can solve this evolution systems efficiently in this project.Firstly,we'll select proper thermo-elastic model that can describe the thermal-mechanical coupling effect of composites irradiated by laser.Secondly,by thoroughly considering all options of periodic composite,we'll design homogenization method and multi-scale method that can efficiently compute the general transient coupling thermo-elastic response ofcomposites.Then we'll settle our research results to multi-scale computational software kits.At last,we'll apply our results to study the time threshold value of structural failure that induced by laser beam.

随着激光技术和复合材料科学的发展，在国防、机械工业等领域亟待解决激光与复合材料的相互作用问题。当激光辐照复合材料时，其效应包括长脉冲激光引起的热分解和热力破坏效应，及超短脉冲激光引起的冲击波效应。当前，激光辐照均匀材料的研究结果较为成熟，但大都侧重于宏观效应；并且，在复合材料问题数值模拟中常采用理想假设下的均匀化模型。实际上，除了分析复合材料与激光的宏观相互作用，还应该研究复合材料不同组分间的局部耦合效应。然而，描述复合材料热力宏-细观耦合效应的模型是具震荡系数的发展方程组,用传统数值方法求解时计算量巨大。因而,本项目将研究能高效求解此问题的多尺度有限元方法。首先，选择能准确描述激光辐照下复合材料热力耦合效应的偏微分方程模型；其次，针对具有拟周期细观构造复合材料的偏微分方程问题，设计高效的多尺度有限元方法并进行数值模拟和理论分析；最后，将此结果用于激光辐照下复合材料结构失效时间阈值的分析。

描述激光辐照下复合材料热力宏-细观耦合效应的模型是具周期震荡系数的发展方程组，用传统数值方法求解时需要处处加密网格。需要对此类问题研究有效的数值方法。. 主要研究内容：(1)复合材料激光辐照下热力耦合模型的确立。(2)多尺度有限元算法及软件实现 。(3解的性质及多尺度解的误差估计。(4)典型复合材料和激光相互作用时的结构失效阈值研究。. 重要结果：(1)对具有小周期细观构造的复合材料，建立了基于傅里叶定律的抛物模型、经典热-力耦合模型、和基于非傅里叶定律的双曲模型、G-L广义热弹性模型。(2)以上问题的解有周期奇性。给出了它们的均匀化算法，均匀化材料的等效参数；构造了它们的双尺度有限元算法。用C++/Matlab等开发了SPSCMFEM软件包。该软件包实现了一个均匀化有限元、双尺度有限元计算的通用架构。进行大量数值试验，验证了双尺度有限元解计算时间远少于常规有限元，解决了周期奇性计算需要处处网格加密的问题。(3)对抛物模型二阶双尺度有限元算法和经典热-力耦合二阶双尺度有限元算法，分析了渐近解的收敛阶。(4)对具有小周期构造的铝基碳化硅增强复合材料、氰酸酯树脂基碳纤维增强复合材料进行了数值实验。分析了铝外壳圆柱状层叠结构在强激光辐照下的热损伤和失效阈值。. 关键数据：(1)SPSCMFEM软件包代码约26000行。(2)多尺度有限元解在达到和传统有限元解同样精度的同时，计算时间远远少于后者。（目前观察到约为后者的1/10）(3)混合边界条件下，抛物模型和经典热-力耦合模型的二阶双尺度解的收敛阶为ef的1/2阶，其中ef为微尺度尺寸。(4)对铝外壳圆柱状层叠结构的辐照实验结果，与已有文献计算结果对比，相对误差在7%左右。. 科学意义：(1)建立多尺度渐近误差分析的理论架构，将丰富多尺度理论的内容。(2)注重数值计算软件的开发，使数值算法和软件平台紧密结合， 有较高的CAE工程价值。