For shape maintenance and migration of living organisms, bio-polymer materials play important roles for the redistribution of internal forces in the biological structures. A substantial amount of observations have been made over the past decades to show how the structures composed of bio-polymers deform and identify what the characteristics of the network materials are. For example, it has been revealed both experimentally and computationally that as macroscopic loading goes, the bio-polymer materials of the network type experience alterations from entropy-directed shape changes to structural deformations, such as filament bending and stretching. In addition, the transition point happens as the levels of macroscopic stress reach around 1% of the bulk modulus of the materials. Hence, here finite element formulations are developed to solve the large deformation problems for the bio-polymer materials in solutions by introducing fluid-solid interaction forces across the immersed boundaries of the materials. The formulations of mechanics which embrace conservation equations, kinematics descriptions and computing algorithms especially developed for elaborating fluid-solid interaction modeling are also the main theme of this research. The concept of the fluid-solid finite element formulations in this research is an adaptation of Peskin’s IB method. In this research proposal, we are further proposing that fluid-solid interaction forces acting on the neighboring fluid and solid particles are naturally action and reaction to each other satisfying Newton’s third law. For boundary value problems in solid mechanics, we consider a hyperelastic material model with the Neo-Hookean material description including nonlinear material behaviors and large shape changes for an isotropic solid to understand mechanical responses of biological soft materials under environmental loading related to possible physiological states. For model problems of viscous incompressible fluid in fluid dynamics, the Navier-Stoke equations of the incompressible Newtonian fluids are utilized by introducing 表 CM02 共 2 頁 第 2 頁 the finite difference operators and subjecting proper initial and boundary conditions. Upon the proposed algorithm above, a numerical experiment is designed to solve the oscillation in transverse direction of the cross section of the initially deformed collagen fibril in solutions with different NaCl concentrations. The computational results clearly illustrate that the collagen material becomes laxer along the transverse directions of its cross section while staying in the solutions with lower concentrations of sodium chloride. Finally, we anticipate that this technique will open doors for understanding more physiological states of biological specimens under environmental loading. 對於生物體結構之形態維持與其遷移，生物聚合物材料力學性質在生物結構體內力重分配具有相當大的影響性，且現今實驗技術已能觀察到生物聚合物材料組成結構之變形過程：當全域載重由零逐漸增加至其引致之應力大小為百分之一倍的材料體積彈性模量之時，材料的形變會由以溫度影響之熵主導的形狀改變機制轉為以結構體為單元的變形機制，如纖維彎曲或拉伸等形式。是故生物結構內力與其形態維持與遷移具有重要的關聯性，又生物體病理表徵與其形態變化與遷移能力亦為息息相關，因而可由各流體環境剌激下生物結構體內力分佈來透析生物體病理表徵背後之重大機理。但對於當今亟需創新與研發的生醫工程與科學領域而言，生物體材料所具有特殊之力學組成律往往不是一般商用分析軟體所能掌控，即對應於生物體重大病理表徵之微觀物理現象並不是簡易線彈性之材料力學模型即能描述，因此，開發創新流固耦合演算法與通用有限元素計算分析平台亟具必要性，是學術界與工業界急切需要的關鍵學理與技術，在符合不同的環境荷載條件設定之下，正確地分析非線性材料受力與變形行為，不僅能做為許多先進固體力學相關工程設計產出的基礎，更可提供科學家製藥以及醫生臨床投藥與新式療法開發之重要參考。
