Journal of Engineering Mechanics

Based on the damage ratio strength theory, a dimensionless damage ratio strength criterion for fiber-reinforced concrete (FRC) under true triaxial stress states was established under the assumption of small strains. Based on the experimental data of steel fiber–reinforced concrete (SFRC), polypropylene fiber–reinforced concrete (PFRC), hybrid fiber–reinforced concrete (HFRC), and steel fiber–reinforced high-performance lightweight concrete (SFRHLC), parameters for the damage ratio criterion were recommended. The damage ratio values were verified by SFRC experimental results under uniaxial, biaxial, and triaxial loading conditions, and the damage ratio values of SFRC under uniaxial tension, uniaxial compression, and biaxial equal compression stress conditions were compared with those of plain concrete. The true triaxial damage ratio strength criterion can be reduced to the conventional triaxial criterion and biaxial criterion, and the corresponding simplified strength criteria were proposed. The proposed dimensionless six-parameter criterion agrees well with the experimental results of the aforementioned materials for true triaxial, conventional triaxial, and biaxial loading conditions. Compared with the strength criteria in other studies, the proposed criterion can accurately represent the strength characteristics of FRC.

In this research, size effects on the mode I notch fracture toughness of polymeric specimens weakened by a rounded-tip V-shaped (RV) notch are investigated experimentally and theoretically. For this purpose, multiple fracture tests are performed on the RV-notched Brazilian disk (RVNBD) and RV-notched semicircular bend (RVNSCB) polymeric samples with four different scales. Then, the fracture loads measured from the experiments are converted to the notch fracture toughness using finite element analysis. The experimental results show that the mode I notch fracture toughness is significantly dependent on the nominal dimension (radius) of RVNBD and RVNSCB samples, so by increasing the sample radius, the mode I notch fracture toughness increases. In order to justify the size dependency of notch fracture toughness, a modified form of the point stress criterion is proposed. The value of critical distance $r_c$ in the modified point stress (MPS) criterion is considered to be size-dependent. Subsequently, a semiempirical relation is used for describing this size dependency. It is revealed that the MPS criterion is able to predict the size-dependent value of notch fracture toughness for both RVNBD and RVNSCB samples made of polymeric materials well.

Dispersion is studied for the two-dimensional propagation of elastic waves in transversely isotropic media using the Lagrange spectral element method. Spectral element matrices are derived as the tensor product of elementary second-order tensors. Gauss-Lobatto-Legendre points are used for the interpolation of Lagrange-type shape functions as well as for the numerical integration to obtain elementary matrices. The Rayleigh quotient approximation technique is employed to find the solution of the eigenvalue problem, which is obtained from the semidiscretized form of the elastic wave equation for propagation of plane harmonic waves. Variations of errors in the phase/group velocities of bulk waves are depicted graphically with the order of interpolation polynomial, angle with the symmetry axis, and the time discretization. Error analysis clearly demonstrated the effectiveness of the Lagrange spectral element method for wave simulation in a transversely isotropic medium.

The cavity expansion approach has been a popular tool to interpret a wide range of geotechnical problems over the last several decades. Most previous research focused on the expansion of cylindrical and/or spherical cavities, whereas nonstandard cavities have received much less attention. To address this shortcoming, this paper presents a general theoretical framework for two-dimensional (2D) displacement-controlled undrained noncircular cavity expansion (N-CCE) in undrained soil. The new approach combines strain path method (SPM) concepts and conformal mapping to determine the soil velocity and strain rate fields analytically. The soil displacement and strain subsequently are determined by integrating the soil velocities and strain rates along the strain path using a series of transformed ordinary differential equations. In this study, the modified Cam Clay (MCC) effective stress constitutive model was used to determine the soil stress–strain relationship, and consolidation effects were captured using finite-difference calculations. The proposed methodology was validated by comparing the reduced solution for a circular cavity with traditional circular cavity expansion theory. A parametric analysis subsequently was undertaken to explore the influence of three noncircular cavity shapes on expansion-induced soil deformation mechanisms, shear strains, effective stresses, and pore-water pressure development and consolidation. The proposed solution can be implemented with any critical state–based soil model and can be applied to arbitrary noncircular cavity problems.

Substructure identification with the idea of divide and conquer has played a significant role in the identification of large-scale structures. Nevertheless, most existing substructure identification methods are only used for linear structures. In addition, it is often required that the information of substructural interface forces are available or the interface responses are measured, which limits the application of substructure identification approaches in practice. In this paper, an improved substructure identification algorithm is proposed to identify linear/nonlinear structures and unknown inputs using only partial measurements of structural responses. In the proposed algorithm, the identification of substructural states and parameters including the parameters of the nonlinear models, unknown external excitations, and the substructural interface forces can be achieved without the measurement of substructural interface responses based on the generalized extended Kalman filter with unknown inputs, which was recently proposed by the authors. The proposed algorithm can identify each substructure in parallel because no information needs to be transferred between the adjacent substructures. Some numerical identifications of linear and nonlinear structures were conducted to demonstrate the proposed substructure identification algorithm and verify the efficiency for the identification of the large-scale structures.