A multilaminate constitutive model accounting for anisotropic small strain stiffness

Abstract

SUMMARY In this paper an extension of existing multilaminate soil models is presented, which can account for inherent and stress‐induced cross‐anisotropic elasticity in the small strain range and its dependency on the load history. In the multilaminate framework, material behaviour is formulated on a number of local planes in each stress point, and the macroscopic response of the material is obtained by integration of the local contributions. Strain‐induced anisotropy, which adds to the stiffness anisotropy inherently present in the material, is therefore intrinsically taken into account. Micro–macro relations between local parameters on plane level and global parameters on macroscopic level are obtained by the spectral decomposition of the global elastic compliance matrix. The model is implemented into a finite‐element code, and model predictions are compared with experimental data of triaxial tests on different soils involving small and large load cycles. The importance of cross‐anisotropic elasticity within the small strain range for predicting ground deformations in geotechnical boundary value problems is discussed at the example of an excavation problem. Copyright © 2012 John Wiley & Sons, Ltd.

Development of a new advanced elastoplastic constitutive model that considers soil behavior at small strains. The EPHYSS model

“…(A) Strain paths in the simulations of the biaxial tests, (B) degradation curves of $${G}_{t}^{\textit{ap}}$$ on Hochstetten sand with rotations of $$\beta = {0}^{\circ}$$, $$\beta = {90}^{\circ}$$, and $$\beta = {180}^{\circ}$$ in the hypoplastic model of Niemunis and Herle, 22 in HS‐SS model and in EPHYSS model, (C) $${G}_{t}^{\textit{ap}}/{G}_{t,\textit{ur}}-\beta $$ curves on Ticino sand in the model of Niemunis and Herle for values of $$\bm{L}({\bm{\sigma}}^{\prime},\mathrm{e}) = \mathbb{I}$$, $$\bm{N}({\bm{\sigma}}^{\prime},\mathrm{e}) = {\bm 0}$$, $${m}_{R} = 5$$, $${m}_{T} = 2$$ and values of $$\chi = 2.0$$ (from Benz 3 ), (D) $${G}_{t}^{\textit{ap}}/{G}_{t,\textit{ur}}-\beta $$ curves for different values of Π on Ticino sand in the multilaminated model of Schädlich and Schweiger (from Schädlich and Schweiger 29 ), (E) $${G}_{t}^{\textit{ap}}/{G}_{t,\textit{ur}}-\beta...$…”

“…{5}^{\circ}$ and $$\ \beta = {180}^{\circ}$$ are applied in the total strain paths in B. Figure 11 shows the curves $${G}_{t}^{\textit{ap}}/{G}_{t,\textit{ur}}-\beta $$ for different values of Π in the following models: (1) hypoplastic with intergranular strain (Figure 11C) 22 ; (2) multilaminated for small strains (Figure 11D) 29 ; (3) HS‐SS (Figure 11E); and (4) EPHYSS (Figure 11F).…”

“…Furthermore, rotations of 𝛽 = 0 • , 𝛽 = 22.5 • , 𝛽 = 45 • , 𝛽 = 67.5 • , 𝛽 = 90 • , 𝛽 = 112.5 • , 𝛽 = 135 • , 𝛽 = 157.5 • and 𝛽 = 180 • are applied in the total strain paths in B. Figure 11 shows the curves 𝐺 ap 𝑡 ∕𝐺 𝑡,ur − 𝛽 for different values of Π in the following models: (1) hypoplastic with intergranular strain (Figure 11C) 22 ; (2) multilaminated for small strains (Figure 11D) 29 ; (3) HS-SS (Figure 11E); and (4) EPHYSS (Figure 11F).…”

“…Nevertheless, in Niemunis and Herle model the reversals depend on the total strain rotations, thus giving place to a coupling between the variation of volumetric strains and the variation of the shear stiffness, 22,28 but it is possible to show that if εΔ𝑅 ∶ ε = 0 holds, then êΔ𝑅 ∶ ˆė = 0, provided that 𝜀 oct εoct = 0, so, in these cases, for the estimation of 𝐺 Toyoura sand 0.40 30 0.50 32 Komorany sand 0.50 31 Firoozkuh no. 161 sand 0.40 31 Undisturbed London Clay 0.50 28 (*) Schädlich and Schweiger 29,30 obtained a value of 0.44 for Hochstetten and Ticino sand in numerical simulations of biaxial compression tests using their multilaminated model. The state variable 𝒆 𝑅 , which stores the value of the total deviatoric strain tensor at the last reversal point that conforms the endpoint of the active strain cycle, appears, on the one hand, in the expression 𝛾 Δ𝑅 oct = √ 4∕3 (‖𝒆‖ − ‖𝒆 𝑅 ‖), which allows to know if the incremental constitutive equation that must be applied is the one corresponding to domain 1 or domain 2, and, on the other hand, in the expression 𝒆 Δ𝑅 = 𝒆 − 𝒆 𝑅 , with which it is possible to calculate the product êΔ𝑅 ∶ Δê that identifies the reversals in which the state variables 𝒆 𝑅 , 𝒆 𝑒,𝑅 , 𝑯 MEM , 𝑬 MEM and 𝑬 𝑒 MEM must be stored.…”

Erweiterte Anwendung der Barodesie für Finite‐Elemente‐Berechnungen

“…In einigen höherwertigen Mate rial modellen wird die Steifigkeit bei kleinen Dehnungen direkt berücksichtigt, z. B. in [11,12]. Es gibt auch Erweiterungen, um diese Effekte in vorhandenen Modellen, die für das Verhalten bei großen Verzerrungen konzipiert sind, zu berücksichtigen.…”