This study presents comprehensive numerical modeling methods for simulating early-age stress (EAS) relaxation in cementitious materials, based on the autogenous deformation (AD), elastic modulus, creep, and stress continuously tested by a mini temperature stress testing machine (Mini-TSTM) and a mini AD testing machine from a very early age (i.e., from a few hours to a week). Four methods for converting creep compliance to relaxation modulus were discussed in detail and used for the one-dimensional (1D) and three-dimensional (3D) simulation of stress evolution in the Mini-TSTM test. Furthermore, virtual creep and relaxation tests were conducted using an exponential algorithm with either the Kelvin or Maxwell chains to show their applicability in simulating the viscoelastic behavior of early-age cementitious materials. The results showed that the exponential algorithm with the Maxwell chain using an exponential conversion function from creep to relaxation obtains good prediction accuracy of EAS in 3D analysis. The numerical solutions of the Volterra integral of creep compliance can lead to a negative relaxation modulus, thus introducing stress calculation errors in both 1D and 3D analysis.

中文翻译：

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使用从蠕变到松弛的指数转换对水泥材料的早期应力演化进行实验建模

本研究提出了模拟水泥材料早期应力（EAS）松弛的综合数值模拟方法，该方法基于微型温度应力试验机（Mini-TSTM）连续测试的自生变形（AD）、弹性模量、蠕变和应力）和从很小的时候（即从几个小时到一周）的迷你AD测试机。详细讨论了将蠕变柔度转换为松弛模量的四种方法，并将其用于 Mini-TSTM 测试中应力演化的一维 (1D) 和三维 (3D) 模拟。此外，使用开尔文链或麦克斯韦链的指数算法进行虚拟蠕变和松弛测试，以显示其在模拟早期水泥材料粘弹性行为方面的适用性。结果表明，利用从蠕变到松弛的指数转换函数的麦克斯韦链指数算法在3D分析中获得了良好的EAS预测精度。蠕变柔度的 Volterra 积分的数值解可能会导致负松弛模量，从而在 1D 和 3D 分析中引入应力计算误差。