In this study, we propose a non-iterative boundary element method (BEM) of highly nonlinear viscoelasticity in time domain. The computationally attractive iteration-free algorithmic structure is achieved by the linearization of a power-type evolution equation. Supplementing the consistent linearization about every solution step with a semi-implicit update scheme, we obtain a robust boundary element framework for nonlinear viscoelasticity. The domain integrals emerging in the proposed approach are calculated using truly mesh-free integration techniques. To our best knowledge, this is the first work on a non-iterative time-domain BEM of nonlinear viscoelasticity. The proposed approach is critically assessed through a comprehensive numerical study that involves representative boundary-value problems (BVPs). The analyses of BVPs are also conducted by the corresponding fully implicit nonlinear finite element method (FEM). The rate of loading, the degree of nonlinearity, and the level of spatial non-uniformity are the primary variables considered in the numerical analyses. The quantitative comparisons made in terms of global force-displacement curves and the local contour plots of a viscous strain measure suggest that the proposed non-iterative time-domain BEM formulation is capable of accurately solving nonlinear viscoelasticity problems in nonstandard domains.

中文翻译：

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非线性粘弹性的非迭代边界元公式

在这项研究中，我们提出了一种时域高度非线性粘弹性的非迭代边界元方法（BEM）。通过幂型演化方程的线性化实现了计算上有吸引力的无迭代算法结构。通过半隐式更新方案补充每个求解步骤的一致线性化，我们获得了非线性粘弹性的鲁棒边界元框架。所提出的方法中出现的域积分是使用真正的无网格积分技术来计算的。据我们所知，这是第一个关于非线性粘弹性非迭代时域边界元法的工作。通过涉及代表性边值问题（BVP）的全面数值研究对所提出的方法进行了严格评估。BVP 的分析也通过相应的全隐式非线性有限元方法（FEM）进行。加载速率、非线性程度和空间不均匀程度是数值分析中考虑的主要变量。根据全局力-位移曲线和粘性应变测量的局部轮廓图进行的定量比较表明，所提出的非迭代时域边界元方程能够准确解决非标准域中的非线性粘弹性问题。