How can a strain rate dependent damage model be used to evaluate the dynamic response of CFRTP laminates?5 answersA strain rate dependent damage model can be used to evaluate the dynamic response of CFRP laminates by considering the effect of strain rate on the failure process and damage evolution. This model consists of three parts: a modified stress-strain relationship for composites under dynamic stress states, a strain-rate-dependent progressive damage model to evaluate intra-laminar damage, and a cohesive zone model to examine inter-laminar delamination. By incorporating the strain rate effect, the model can accurately capture the failure process of composite laminates under low velocity impact (LVI). Experimental validation of the model has shown that the numerical results are highly consistent with the experimental outcomes, with the contact force history curves, intra- and inter-laminar damage evolution process being strain rate dependent. This strain rate dependent damage model is crucial for accurately predicting the dynamic stress state and damage evolution of CFRP laminates under LVI, especially for high impact energies.
What are the different methods used to calculate the dynamic crack velocity in concrete?5 answersDifferent methods used to calculate the dynamic crack velocity in concrete include the PeriDynamics (PD) model, finite-difference time-domain (FDTD) method, and the rocking spalling test. The PD model combines the advantages of multi-scale modeling and the finite element method (FEM) to simulate crack initiation and propagation in concrete. The FDTD method utilizes electromagnetic waves to simulate cracks, defects, and geometry in concrete, and compares the simulation results with nondestructive measurements. The rocking spalling test is an experimental method that uses double-notched specimens and high-speed cameras to characterize crack speed in concrete under dynamic tensile loading. These methods provide insights into the behavior of cracks in concrete and contribute to the understanding of fracture mechanics in this material.
What are the different experimental methods used to calculate the dynamic crack velocity in concrete?5 answersDifferent experimental methods have been used to calculate the dynamic crack velocity in concrete. One method involves analyzing the crack resistance performance of steel fibre-reinforced concrete (SFRC) under coupled loads, such as dynamic loads at relatively high temperatures. This method measures the variation in the beam's dynamic response parameters, including modal amplitude and frequency, and compares them with experimental results for regular and reinforced concrete beams. Another method utilizes the PeriDynamics (PD) model of material fracture, which can simulate the nucleation and propagation of cracks naturally. This model combines the PD-FEM method to reduce calculation costs and accurately describe crack initiation and propagation in concrete. Additionally, electromagnetic (EM) waves are used for numerical simulation to identify cracks in concrete. The finite-difference time-domain (FDTD) method with Gaussian pulse wave excitation is employed to validate the reflection and transmission coefficients obtained from measurements.
How to generate damage vs plastic strain curve?4 answersTo generate a damage vs plastic strain curve, a constitutive model that combines plasticity with damage mechanics can be used. This model captures the postpeak strain-softening behavior of materials such as dense sand and stiff clay. The total strain increment is composed of an elasto-damage strain increment and a plastic strain increment, which are determined using the elasto-damage formulation and either the Drucker-Prager classical plasticity model or as a function of damage strain. Experimental programs can be conducted to determine the physical and mechanical properties of the materials, and triaxial tests and hydrostatic tests can be performed under different confining pressures to obtain the model parameters. The model can then be calibrated and coded in computer programs to simulate the stress-strain behavior of the materials. By analyzing the results of these simulations, the damage vs plastic strain curve can be generated.
How to calculate mode-1 strain energy release rate by area method?5 answersThe mode-1 strain energy release rate can be calculated using the area method. This method involves determining the energy release rate by integrating the strain energy density over the crack front area. The virtual crack-closure method is commonly used to obtain accurate strain energy release rates for crack growth in isotropic materials. This method has been applied to various types of finite elements, including non-singular and singularity elements, and has been shown to give accurate results. Additionally, the crack closure integral method combined with a 3-D finite element model can be employed to obtain strain energy release rates for stitched composites. The energy release rate can also be estimated using an approximation based on the theory of small deformations superposed on a finite deformation. Overall, there are multiple methods available to calculate the mode-1 strain energy release rate, depending on the specific material and crack configuration.
What is the effect of delamination size on the wave amplitude in a composite laminate?5 answersThe size of delamination in a composite laminate has an effect on the wave amplitude. Small variations in delamination shape significantly affect the interference pattern on top of the delamination, but have limited effect on the scattered wave outside the delamination. The amplitude of the delamination signal decreases first, then starts to increase after reaching the minimum value. The minimum is reached when the waves from the two sub-laminates are 180° out of phase. The effective elastic properties of laminated composites decrease as the delamination extension increases due to the increase in delamination area. The effects of delamination on the propagation of guided waves in composite beams are investigated using a spectral element model. The weak transverse tensile and interlaminar shear strengths of laminated composites make them susceptible to delamination damage.