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Incremental finite element method for thermomechanical contact part II: application to elastomeric seals

机译：热机械接触部分的增量有限元法II：应用于弹性体密封

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In Part I, an incremental finite element formualtion was introduced to model thermomechanical contact, which is a type of boundary condition which occurs widely in pressure vessel applications, for example at supports. A new gap function was introduced and a compact expression was derived for the contribution of contact to the tangent stiffness matrix, which serves as the Jacobian matrix for solution by Newton iteration. Part II applies the formualtion to elastomeric seals, which are essential components of pressure vessel systems. Of particular concern is the accuracy with which high pressures ensuing from confinement are modeled. A three field formulation is adopted, combing a displacement field, a temperature field, and a pressure field introduced to satisfy the constraint of nearincompressibility. Typically, commerical finite element codes model elastomers using a hyperelastic element, which is not coupled to the thermal field. Here, a thermohyperelastic constitutive model for nearincompressible elastomers, introduced by the authors, is used. The tangent modulus matrix ensuing from the constitutive model is derived in compact form using Kronecker product notation. An application of great interest is seals. A special purpose finite element code implementing the general formulation has been written and applied to a natural rubber seal which is subject to thermal and mechanical loading and confinement, say by being pressed into a well. The computations have been validated in various ways, and are illustrated in graphical form. In particular, pressure contours in the seal are shown as a function of degree of compression and of time. The great amplification of pressure due to confinement is captured.
机译：在第一部分中，引入增量有限元形式化来模拟热机械接触，这是一种边界条件，广泛出现在压力容器应用中，例如在支架上。引入了新的间隙函数，并导出了接触对切线刚度矩阵的贡献的紧凑表达式，该矩阵用作牛顿迭代求解的雅可比矩阵。第二部分将形式化应用于弹性体密封件，弹性体密封件是压力容器系统的基本组成部分。特别要关注的是对限制产生的高压进行建模的准确性。采用三场公式，将引入的位移场，温度场和压力场进行组合以满足近不可压缩性的约束。通常，商业有限元代码使用不与热场耦合的超弹性元件对弹性体进行建模。在这里，使用了由作者介绍的几乎不可压缩的弹性体的热超弹性本构模型。本构模型产生的切线模量矩阵使用Kronecker乘积符号以紧凑形式导出。密封件引起了人们极大的兴趣。已经编写了实现通用配方的特殊用途的有限元代码，并将其应用于天然橡胶密封件，该密封件会受到热，机械载荷和约束，例如通过压入井中。计算已通过各种方式进行了验证，并以图形形式进行了说明。特别地，密封件中的压力轮廓被示出为压缩程度和时间的函数。由于限制，压力的极大放大被捕获。

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