基于CS-FEM的可膨胀软材料三维增长模拟

Three-dimensional growth simulation of swellable soft materials based on CS-FEM

基于单元域光滑有限元方法建立了可膨胀软材料大变形增长的三维数值模拟框架,给出了变形梯度的乘法分解格式,选用第二P-K应力和格林应变张量作为功共轭对,推导了软材料刚度矩阵和几何刚度矩阵的数学表达式。基于MATLAB平台实现了所建立的数值方法,分别模拟了可膨胀软材料的各向同性、各向异性增长行为。结果显示,相比各向同性增长,各向异性增长会抑制可膨胀软材料的变形。模拟结果与已有文献计算结果进行比较,比较结果显示形态模式的变化特征和规律吻合较好,证明了该数值框架在模拟可膨胀软材料大变形增长行为方面的有效性,有助于揭示自然界植物生长现象背后的力学机制。

In this paper,a three-dimensional numerical framework for modeling growth of swellable soft materials at large deformation is established based on the cell-based smooth finite element method,and the multiplicative decomposition scheme of deformation gradient is given.The second P-K stress and Green′s strain tensor are selected as work conjugate pairs,and the corresponding mathematical expressions of stiffness matrix and geometric stiffness matrix are derived.The numerical method is implemented based on Matlab platform,and the isotropic and anisotropic growth behaviors of swellable soft materials are simulated respectively.The results show that anisotropic growth will inhibit the deformation of expandable soft materials compared with isotropic growth.The simulation results are compared with the calculation results in the existing literature.The comparison results show that the characteristics and the morphological mode are in good agreement,which proves the effectiveness of the numerical framework in simulating the growth behavior of expandable soft materials at large deformation,and is able to reveal the mechanical mechanism of the plant growth phenomenon in nature.