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Finite-deformation modeling of elastodynamics and smart materials with nonlinear electro-magneto-elastic coupling.

机译：具有非线性电磁磁耦合的弹性动力学和智能材料的有限变形建模。

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摘要

Eulerian formulations of the equations of finite-deformation solid dynamics are ideal for numerical implementation in modern high-resolution shock-capturing schemes. These powerful numerical techniques -- traditionally employed in unsteady compressible flow applications -- are becoming increasingly popular in the computational solid mechanics community. Their primary appeal is an exceptional ability to capture the evolution and interaction of nonlinear traveling waves. Currently, however, Eulerian models for the nonlinear dynamics of rods, beams, plates, membranes, and other elastic structures are currently unavailable in the literature.;The need for these reduced-order (1-D and 2-D) Eulerian structural models motivates the first part of this dissertation, where a comprehensive perturbation theory is used to develop a 1-D Eulerian model for nonlinear waves in elastic rods. The leading-order equations in the perturbation formalism are (i) verified using a control-volume analysis, (ii) linearized to recover a classical model for longitudinal waves in ultrasonic horns, and (iii) solved numerically using the novel space-time Conservation Element and Solution Element (CESE) method for first-order hyperbolic systems. Numerical simulations of several benchmark problems demonstrate that the CESE method effectively captures shocks, rarefactions, and contact discontinuities.;The second part of this dissertation focuses on another emerging area of finite-deformation mechanics: magnetoelectric polymer composites (MEPCs). A distinguishing feature of MEPCs is the tantalizing ability to electrically control their magnetization, or, conversely, magnetically control their polarization. Leveraging this magnetoelectric coupling could potentially impact numerous technologies, including information storage, spintronics, sensing, actuation, and energy harvesting. Most of the research on MEPCs to date, however, has focused on optimizing the magnitude of the magnetoelectric coupling through iterative design. Substantially less activity has occurred in the way of mathematical modeling and experimental characterization at finite strains, which are needed to advance fundamental understanding of MEPCs and encourage their technological implementation.;The aforementioned needs motivate the second part of this dissertation, where a finite-strain theoretical framework is developed for modeling soft magnetoelectric composites. Finite deformations, electro-magneto-elastic coupling, and material nonlinearities are incorporated into the model. A particular emphasis is placed on the development of tractable constitutive equations to facilitate material characterization in the laboratory. Accordingly, a catalogue of free energies and constitutive equations is presented, each employing a different set of independent variables. The ramifications of invariance, angular momentum, incompressibility, and material symmetry are explored, and a representative (neo-Hookean-type) free energy with full electro-magneto-elastic coupling is posed.
机译：有限变形固体动力学方程的欧拉公式非常适合现代高分辨率震动捕捉方案中的数值实现。这些强大的数值技术-传统上用于非定常可压缩流应用-在计算固体力学领域正变得越来越流行。它们的主要吸引力是捕获非线性行波的演化和相互作用的非凡能力。但是，目前在文献中尚无用于杆，梁，板，膜和其他弹性结构非线性动力学的欧拉模型;对这些降阶（1-D和2-D）欧拉结构模型的需求激发了本文的第一部分，在本文的第一部分中，使用了一种综合的扰动理论来为弹性杆中的非线性波建立一维欧拉模型。 （i）使用控制量分析验证（i）线性化以恢复超声喇叭中纵波的经典模型，以及（iii）使用新颖的时空守恒数值解法一阶双曲系统的元素和解元素（CESE）方法。几个基准问题的数值模拟表明，CESE方法可以有效地捕获冲击，稀疏作用和接触不连续性。本论文的第二部分着眼于有限变形力学的另一个新兴领域：磁电聚合物复合材料（MEPC）。 MEPC的一个显着特征是具有电控制其磁化或反之磁控制其极化的诱人能力。利用这种磁电耦合可能会影响众多技术，包括信息存储，自旋电子学，传感，致动和能量收集。但是，迄今为止，关于MEPC的大多数研究都集中在通过迭代设计优化磁电耦合的幅度上。在有限应变下进行数学建模和实验表征的活动大大减少，这是提高对MEPC的基本理解并鼓励其技术应用所必需的。上述需求激励了本文的第二部分，即有限应变建立了用于建模软磁电复合材料的理论框架。有限变形，电磁弹性耦合和材料非线性被纳入模型。特别强调发展易处理的本构方程，以促进实验室中的材料表征。因此，给出了一个自由能和本构方程的目录，每个目录都使用一组不同的自变量。探索了不变性，角动量，不可压缩性和材料对称性的结果，并提出了具有完全电磁弹性耦合的代表性（新胡克式）自由能。

著录项

  • 作者

    Lowe, Robert Lindsey.;

  • 作者单位

    The Ohio State University.;

  • 授予单位 The Ohio State University.;
  • 学科 Mechanical engineering.
  • 学位 Ph.D.
  • 年度 2015
  • 页码 327 p.
  • 总页数 327
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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