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Multi-scale computation of plant tissue deformation using models for individual cell behavior

機譯：使用單個細胞行為模型對植物組織變形進行多尺度計算

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We present a micro-macro method for the simulation of large elastic deformations of plant tissue. At the microscopic level we use a discrete element model to describe the geometrical structure and basic properties of individual plant cells. The macroscopic domain is discretized using standard finite elements, in which the unknown macroscopic material properties (the stress-strain relation) are computed using the microscopic model in small sub-domains, called representative volume elements (RVEs), centered around the macroscopic quadrature points. The boundary conditions for these RVEs are derived from the macroscopic deformation gradient. The computation of the macroscopic stress tensor is based on the definition of virial stress, as defined in molecular dynamics. The anisotropic Eulerian elasticity tensor is estimated using a forward finite difference approximation for the Truesdell rate of the Cauchy stress tensor. We investigate the influence of the size of the RVE and the boundary conditions via numerical experiments. We show that the multi-scale method converges to the solution of the full microscopic simulation, both for globally and adaptively refined finite element meshes and achieves a significant speed-up compared with the full microscopic simulation.

機譯：我們提出了一種微宏方法，用于模擬植物組織的大彈性變形。在微觀層面上，我們使用離散元素模型來描述單個植物細胞的幾何結構和基本特性。宏觀域使用標準有限元離散化，其中使用微觀模型在小的子域（稱為代表體積元素（RVE））中，以宏觀正交點為中心，計算未知的宏觀材料屬性（應力-應變關系）。這些RVE的邊界條件是從宏觀變形梯度得出的。宏觀應力張量的計算基于在分子動力學中定義的虛擬應力的定義。使用柯西應力張量的Truesdell率的正向有限差分近似估計各向異性歐拉彈性張量。我們通過數(shù)值實驗研究了RVE大小和邊界條件的影響。我們表明，對于全局和自適應精煉的有限元網格，多尺度方法收斂于完整微觀仿真的解決方案，并且與完整微觀仿真相比，實現(xiàn)了顯著的加速。

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Ghysels Pieter; Samaey Giovanni; Tijskens Engelbert; Ramon Herman; Roose Dirk;
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年度 2008
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正文語種 en
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Multi-scale computation of plant tissue deformation using models for individual cell behavior

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