2019
DOI: 10.1063/1.5080333
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Brownian dynamics investigation of the Boltzmann superposition principle for orthogonal superposition rheology

Abstract: The most general linear equation describing the stress response at time t to a time-dependent shearing perturbation may be written as the integral over the past history t of a time dependent relaxation modulus, depending on t − t , multiplied by the perturbing shear rate at time t. This is in agreement with the Boltzmann superposition principle, which says that the stress response of a system to a time dependent shearing deformation may be written as the sum of responses to a sequence of stepstrain perturbatio… Show more

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Cited by 13 publications
(5 citation statements)
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References 52 publications
(75 reference statements)
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“…As the applied load intensity increases, the percentage difference between traction and compression displacement increases, and as the load speed increases, they increase. Based on the Boltzmann superposition principle, which describes the response of a material to different loading histories and fitting the deformations peaks for each cycle [ 21 , 22 ], in Figure 5 a–f are graphically represented the master curves covering the accumulated peak deformations in tensile ( Figure 5 a,c,e) and compression tests ( Figure 5 b,d,f). The behavior of the tested specimens differs in the two types of axial stresses.…”
Section: Resultsmentioning
confidence: 99%
“…As the applied load intensity increases, the percentage difference between traction and compression displacement increases, and as the load speed increases, they increase. Based on the Boltzmann superposition principle, which describes the response of a material to different loading histories and fitting the deformations peaks for each cycle [ 21 , 22 ], in Figure 5 a–f are graphically represented the master curves covering the accumulated peak deformations in tensile ( Figure 5 a,c,e) and compression tests ( Figure 5 b,d,f). The behavior of the tested specimens differs in the two types of axial stresses.…”
Section: Resultsmentioning
confidence: 99%
“…The long-term strength of rock and soil is an important parameter for assessing the stability of landslides [49,50]. At present, the main methods to obtain long-term strength through creep test curves include the isochronous curve method [3,51], which uses the creep test curve and the Boltzmann superposition principle [52] and states that the stress response of a system to a time dependent shearing deformation may be written as the sum of responses to a sequence of step strain perturbations in the past [53], to obtain the stress-strain isochronous curves corresponding to the different deviatoric stress at the same time [54]. Figure 10a-e show the isochronous curves corresponding to the creep curves of the samples after five kinds of dry-wet cycles (n = 0, 5,10,15,20).…”
Section: The Long-term Strength Of Loess Samples With Different Dry-w...mentioning
confidence: 99%
“…Establishing a model that has a time response that is consistent with or close to that of polymers is most important for solving the viscoelastic problem of polymers such as rubber. Commonly used models include the generalized Maxwell model, generalized Kelvin model, standard linear solid model, and standard linear three-parameter model [28][29]. In this study, the generalized Maxwell model was selected as the viscoelastic model, as shown in Figure4.…”
Section: Viscoelastic Model Modelingmentioning
confidence: 99%