In this work, several structure preserving and energy dissipative contact approaches are proposed and evaluated. The time integration schemes considered are general with regard to the version of constraint type, but here the emphasis was on mortar contact. The proposed mortar contact approach conserves both linear and angular momentum for mortar contact in a novel way. The proposed time integration scheme can conserve energy or provide strict contact dissipation. In addition, the proposed scheme enforces both gap constraints and gap velocity constraints (i.e., persistency). Using a midstep time integrator often causes energy dissipation during initial impact, here this energy can be recovered in a novel way. Enforcing the gap velocity constraint mitigates the contact chatter of the contact pressure and nodes in many problems. Whereas some approaches enforce the persistency condition and gap constraints simultaneously during the solution of the equations of motion (EOM) requiring multipliers for both constraints included in the equation set, here the gap constraint is solved through the equations of motion and the persistency condition is satisfied in the time integration scheme by the velocity update after the equations of motion. It is shown that this approach is strictly dissipative in that a plastic contact condition can be achieved. Analogous to a coefficient of restitution for rigid bodies, any dissipated energy can then be returned upon release if energy conservation is desired. Structure preserving methods are good for long-time dynamics simulations and energy conserving and strictly dissipative methods can overcome stability issues associated with standard time integration algorithms such as the Newmark method.

中文翻译：

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隐式动力学的结构保持和能量耗散接触方法

在这项工作中，提出并评估了几种结构保持和能量耗散的接触方法。所考虑的时间积分方案对于约束类型的版本来说是通用的，但这里的重点是迫击炮接触。所提出的迫击炮接触方法以一种新颖的方式保存了迫击炮接触的线性动量和角动量。所提出的时间积分方案可以节省能量或提供严格的接触耗散。此外，所提出的方案强制执行间隙约束和间隙速度约束（即持久性）。使用中步时间积分器通常会导致初始冲击期间的能量耗散，这里可以通过一种新颖的方式回收该能量。强制间隙速度约束可以减轻许多问题中接触压力和节点的接触颤振。尽管某些方法在求解运动方程 (EOM) 期间同时强制执行持久性条件和间隙约束，需要对方程组中包含的两个约束进行乘数，但这里间隙约束是通过运动方程求解的，并且满足持久性条件在时间积分方案中，通过运动方程之后的速度更新。结果表明，这种方法是严格耗散的，因为可以实现塑性接触条件。类似于刚体的恢复系数，如果需要能量守恒，任何耗散的能量都可以在释放时返回。结构保持方法适用于长时间动力学模拟和能量守恒，严格耗散方法可以克服与标准时间积分算法（例如 Newmark 方法）相关的稳定性问题。