Nonlinear Mechanics of Strain-Stiffening Elastomers and Biomaterials

应变硬化弹性体和生物材料的非线性力学 摘要研究目的和方法：本研究主要是对橡胶类材料或生物软组织在大应变下的力学行为进行连续介质力学建模。与通常采用的经典非线性弹性模型相比，开发的新材料模型在大应变下表现出严重的应变硬化。主要关注的是本构模型，反映在分子水平上的限制链延伸性。这些具有在极限应变处发生应力奇异性的特征，并且因此捕获非结晶橡胶、软生物组织和生物材料的实验观察到的突然应变硬化。提出用非线性连续介质力学的基本概念来模拟和分析这些材料的一些基本问题。特别强调的是断裂，压痕和渗透问题。 社会影响：这里提出的关于橡胶和橡胶类材料的机械行为的工作对国家至关重要？此外，该公司还为美国的基础设施以及汽车、航空航天、国防和生物技术行业提供服务。该研究也适用于生物软组织和生物材料的行为。在工业实践中，大型商用有限元计算机代码主要基于经典模型，因此它们对橡胶类材料在大应变下的预测值得重新评估。特别是，断裂，压痕和渗透的弹性体是重要的当前技术领域，拟议的工作将作出贡献。这项工作是跨学科的，涉及工程力学，物理学和应用数学的现代方法。研究生的教育将有助于未来的科学和工程劳动力。这里提出的类型的基础研究是必要的，以确保安全可靠地利用橡胶类材料和工程生物材料在现代技术。

NONLINEAR MECHANICS OF STRAIN-STIFFENING ELASTOMERS AND BIOMATERIALS Abstract Research Objectives and Approaches:This research is concerned with continuum mechanics modeling of the mechanical behavior of rubber-like materials or soft biological tissues undergoing large strains. The new material models that are developed exhibit severe strain-stiffening at large strains, in contrast to the classical nonlinear elastic models usually employed. Of primary concern are constitutive models that reflect limiting chain extensibility at the molecular level. These have the feature that a stress singularity occurs at the limiting strain and thus capture the abrupt strain-stiffening observed experimentally for non-crystallizing rubber, soft biological tissues and biomaterials. It is proposed to use basic concepts of nonlinear continuum mechanics to model and analyze some fundamental problems for these materials. Particular emphasis is given to fracture, indentation and penetration problems. Societal Impact :The work proposed here on the mechanical behavior of rubber and rubber-like materials is of critical importance to the nation?s infrastructure as well as to the automotive, aerospace, defense and bio-technological industries. The research also is applicable to the behavior of biological soft tissues and biomaterials. In industrial practice, large scale commercial finite element computer codes are based primarily on classical models and so their predictions for rubber-like materials at large strains warrant critical reassessment. In particular, fracture, indentation and penetration of elastomers are important current technological areas to which the proposed work will contribute. The work is interdisciplinary involving modern methods of engineering mechanics, physics and applied mathematics. The education of graduate students will contribute to the future science and engineering workforce. Fundamental studies of the type proposed here are necessary to ensure the safe reliable utilization of rubber-like materials and engineered biomaterials in modern technology.