Fatigue fracture characterization by cyclic material forces in viscoelastic solids at small strain

The study at hand introduces a new approach to characterize fatigue crack growth in small strain linear viscoelastic solids by configurational mechanics. In this study, Prony series with n-Maxwell elements are used to describe the viscoelastic behavior. As a starting point in this work, the local balance of energy momentum is derived using the free energy density. Moreover, at cyclic loading, the cyclic free energy substitutes the free energy. Using the cyclic free energy, the balance of cyclic energy momentum is obtained. The newly derived balance law at cyclic loading is appropriate for each cycle. In the finite element framework, nodal material forces and cyclic nodal material forces are obtained using the weak and discretized forms of the balance of energy momentum and cyclic energy momentum, respectively. The crack driving force and the cyclic crack driving force are determined by the nodal material forces and the cyclic nodal material forces, respectively. Finally, numerical examples are shown to illustrate path-independence of the domain integrals using material forces and cyclic material forces. The existence of the balance of energy momentum and cyclic energy momentum are also illustrated by numerical examples.

Small strain stiffness for granite residual soil: effect of stress ratio

Most previous studies have focused on the small strain stiffness of sedimentary soil while little attention has been given to residual soils with different properties. Most studies also neglected the effects of the deviator stress, which is extensively involved in civil engineering. This note considers the effects of the deviator stress on the small-strain stiffness of natural granite residual soil (GRS) as established from resonant column tests performed under various stress ratios. Although increasing the stress ratio results in a greater maximum shear modulus for both natural and remolded residual soils, remolded soil is more sensitive to changes in the stress ratio, which highlights the effects of soil cementation. The data herein offers new insights to understand the stiffness of residual soil and other weathered geomaterials.

Shallow Compaction Modeling and Upscaling: A One-Dimensional Analytical Solution and Upscaling

Natural depositional processes frequently give rise to the heterogeneous multilayer system, which is often overlooked but essential for the simulation of a geological process. The sediments undergo the large-strain process in shallow depth and the small-strain process in deep depth. With the transform matrix and Laplace transformation, a new method of solving multilayer small-strain (Terzaghi) and large-strain (Gibson) consolidations is proposed. The results from this work match the numerical results and other analytical solutions well. According to the method of transform matrix which can consider the integral properties of multilayer consolidation, a relevant upscaling method is developed. This method is more effective than the normally used weighted average method. Correspondingly, the upscaling results indicate that the upscaled properties of a multilayer system vary in the consolidation process.

On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems

In this work the finite element (FE) implementation of the small strain cyclic plasticity is discussed. The family of elastoplastic constitutive models is considered which uses the mixed, kinematic-isotropic hardening rule. It is assumed that the kinematic hardening is governed by the Armstrong–Frederick law. The radial return mapping algorithm is utilized to discretize the general form of the constitutive equation. A relation for the consistent elastoplastic tangent operator is derived. To the best of the author’s knowledge, this formula has not been presented in the literature yet. The obtained set of equations can be used to implement the cyclic plasticity models into numerous commercial or non-commercial FE packages. A user subroutine UMAT (User’s MATerial) has been developed in order to implement the cyclic plasticity model by Yoshida into the open-source FE program CalculiX. The coding is included in the Appendix. It can be easily modified to implement any isotropic hardening rule for which the yield stress is a function of the effective plastic strain. The number of the utilized backstress variables can be easily increased as well. Several validation tests which have been performed in order to verify the code’s performance are discussed.

Characterizing the Effect of Water Content on Small-Strain Shear Modulus of Qiantang Silt

Due to the impact of natural and artificial influence, such as waves, tides, and artificial dewatering, the small-strain shear modulus of soils may vary with the water content of soil, causing deformation of excavations and other earth structures. The present study used a resonant column device to investigate the effects of water content, void ratio, and confining pressure on the small-strain shear modulus of a silt extracted from an excavation site near Qiantang River in Hangzhou, China. The test results revealed that the effects of the three factors are not coupled and can be characterized by three individual equations. In particular, the small-strain shear modulus decreases with increasing water content under otherwise similar conditions, which can be characterized by a power function. The classical Hardin’s equation is modified to consider the effect of water content by introducing an additional function of water content.