Taehyo Park

The kinematics of damage for finite-strain elasto-plastic solids

In this paper the kinematics of damage for finite strain, elasto-plastic deformation is introduced using the fourth-order damage effect tensor through the concept of the effective stress within the framework of continuum damage mechanics. In the absence of the kinematic description of damage deformation leads one to adopt one of the following two different hypotheses for the small deformation problems. One uses either the hypothesis of strain equivalence or the hyphothesis of energy equivalence in order to characterize the damage of the material. The proposed approach in this work provides a general description of kinematics of damage applicable to finite strains. This is accomplished by directly considering the kinematics of the deformation field and furthermore it is not confined to small strains as in the case of the strain equivalence or the strain energy equivalence approaches. In this work, the damage is described kinematically in both the elastic domain and plastic domain using the fourth order damage effect tensor which is a function of the second-order damage tensor. The damage effect tensor is explicitly characterized in terms of a kinematic measure of damage through a second-order damage tensor. Two kinds of second-order damage tensor representations are used in this work with respect to two reference configurations. The finite elasto-plastic deformation behavior with damage is also viewed here within the framework of thermodynamics with internal state variables. Using the consistent thermodynamic formulation one introduces seperately the strain due to damage and the associated dissipation energy due to this strain.

Anisotropic Damage Effect Tensors for the Symmetrization of the Effective Stress Tensor

Based on the concept of the effective stress and on the description of anisotropic damage deformation within the framework of continuum damage mechanics, a fourth order damage effective tensor is properly defined. For a general state of deformation and damage, it is seen that the effective stress tensor is usually asymmetric. Its symmetrization is necessary for a continuum theory to be valid in the classical sense. In order to transform the current stress tensor to a symmetric effective stress tensor, a fourth order damage effect tensor should be defined such that it follows the rules of tensor algebra and maintains a physical description of damage. Moreover, an explicit expression of the damage effect tensor is of particular importance in order to obtain the constitutive relation in the damaged material. The damage effect tensor in this work is explicitly characterized in terms of kinematic measure of damage through a second-order damage tensor. In this work, tensorial forms are used for the derivation of such a linear transformation tensor which is then converted to a matrix form.

Vibration analysis of multi-delaminated beams

In the present study, free vibration analysis of multi-delaminated composite beams is performed. An analytical formulation is proposed and studied for the vibration analysis of the composite beams with arbitrary lateral, longitudinal, and both multiple delaminations. In order to investigate the effects of these multiple delaminations on the dynamic characteristics of composite beams, the general kinematics continuity conditions are derived from the assumption of constant curvature at the multi-delamination tip. Frequency equations of multi-delaminated composite beams are obtained by dividing the global delaminated beam into beam segments and by imposing recurrence relation from the continuity conditions on each sub-beam. Experiments are performed for the case of a single delamination and finite element analysis is conducted for multiple delaminations. It is shown that multiple delaminations significantly affect the dynamic characteristics of composite laminated beams.

Local and interfacial damage analysis of metal matrix composites using the finite element method

Abstract A micromechanical damage composite model is used here such that separate local evolution damage relations are used for each of the matrix and fiber. In addition, this is coupled with interfacial damage between the matrix and fiber exclusively. An overall response is linked to these damage relations through a certain homogenization procedure. A finite element analysis is used for quantifying each type of damage and predicting the failure loads of dog-bone shaped specimen and center-cracked laminate metal matrix composite plates. The development of damage zones and the stress-strain response are shown for two types of laminated layups, a (0/90) s layup and a (±45) s layup.

Local and interfacial damage analysis of metal matrix composites

Abstract Damage and plastic deformation is incorporated in the proposed model that is used for the analysis of fiber-reinforced metal matrix composite materials. The proposed micromechanical damage composite model used here is such that separate local constitutive damage relations are used for each of the matrix and the fiber. This is coupled with the interfacial damage between the matrix and the fiber exclusively. The damage relations are linked to the overall response through a certain homogenization procedure. Two local damage tensors are used M m and M f where M m accounts for the damage in the ductile matrix such as nucleation and growth of voids, while the tensor M f reflects the damage in the fibers such as fiber fracture. An additional tensor M d is incorporated in the overall formulation that represents interfacial damage between the matrix and the fiber. An overall damage tensor, M , is introduced that accounts for all these separate damage tensors M m , M f , and M d . For the undamaged matrix material, a von Mises type yield criterion with an associated flow rule, and a Ziegler-Prager kinematic hardening rule are used. However, the resulting overall yield function for the damaged composite system is a combination of the generalized Ziegler-Prager rule and a Phillips-type damaged composite system is a combination of the generalized Ziegler-Prager rule and a Phillips-type rule. The elasto-plastic stiffness tensor is derived for the damaged composite. Numerical solutions are obtained using the proposed theory for two types of laminate layups (0/90) s and (±45) s each consisting of four plies and compared with experimental results. A very good correlation is obtained between the experimental and numerical results.

Free vibration analysis of axially compressed laminated composite beam-columns with multiple delaminations

In this work free vibration analysis is performed for multi-delaminated composite beam-columns subjected to axial compression load. In order to investigate the effects of multi-delaminations on the natural frequency and the elastic buckling load of multi-delaminated beam-columns, the general kinematic continuity conditions are derived from the assumption of constant slope and curvature at the multi-delamination tip. The characteristic equation of multi-delaminated beam-column is obtained by dividing the global multi-delaminated beam-columns into segments and by imposing recurrence relation from the continuity conditions on each sub-beam-column. The natural frequency and the elastic buckling load for multi-delaminated beam-columns are obtained in this work. The latter is based on the incremental load of axial compression, which is limited to the maximum elastic buckling load of the sound laminated beam-column. To verify the results of the present models, experimental results are obtained for isotropic single delaminated beam-columns. Comparisons are conducted between these experimental results and the present analysis. Good agreement is obtained from this comparison of results. It is found that the sizes, locations and numbers of multi-delaminations have significant effect on the natural frequency and the elastic buckling load, specifically the latter ones.

The behavior of concrete cylinders confined by shape memory alloy wires

The purpose of this study was to propose a new method to confine concrete cylinders or reinforced concrete columns using martensitic or austenitic shape memory alloy (SMA) wires. The prestrained martensitic SMA wire was wrapped around a concrete cylinder then heated by a heating jacket. In the process, the confining stress around the cylinder was developed in the SMA wire due to the shape memory effect, which can increase the strength and ductility of the cylinder under axial compressive load. For austenitic shape memory wires, the wires were prestrained as they were wrapped around the concrete cylinders on which post-tensioning stress was generated. In this study, martensitic and austenitic SMA wires of 1.0 mm in diameter were used for the confinement. Recovery tests were conducted on the martensitic wire to assess the recovery stress. Also, a superelastic behavior test was performed for the austenitic wire. The confinement by martensitic SMA wires increased the strength slightly and greatly increased the ductility compared to the strength and ductility of plain concrete cylinders. The austenitic SMA wires showed a similar effect on concrete cylinders to that of the martensitic wires. This study showed the potential of the SMA wire jacketing method to retrofit reinforced concrete columns and protect them from seismic risks.

Seismic design, performance, and behavior of composite-moment frames with steel beam-to-concrete filled tube column connections

Concrete filled steel tube (CFT) columns have been widely used in composite-moment frames (C-MFs) both in non-seismic and in high seismic zones. The objective of this research is to develop a design methodology of such moment resisting frame structures designed with CFT columns in achieving ductile behavior and high strength. These composite-moment frames mostly constructed around the perimeter of the building provide the enough stiffness to withstand the lateral displacement due to wind or seismic loads. In this research, three sets of prototype composite frame models were designed on the basis of the proposed design examples as 3-, 9-, and 20-story post-Northridge SAC buildings with composite-special moment frame (C-SMF) systems designed for the western US area. The exact moment-rotational behavior of steel beam-to-CFT column connections including the strength degradation was simulated using the 2D joint model with the rigid boundary element. Nonlinear pushover analyses were conducted on the numerical frame models so as to evaluate the over-strength, inelastic deformation, and P-Delta effect for the entire structure. The statistical investigation was introduced to nonlinear dynamic analyses under 40 SAC ground motions corresponding to a seismic hazard level of 2% probability of exceedence in 50 years in order to efficiently examine seismic performance and behavior of entire composite frame structures. All frame models meet the allowable limit for safe designs. In addition, the entire frame design becomes conservative as the number of stories increases. The distribution of interstory drift ratios (ISDRs) as well as the over-strength ratio also demonstrates this conservative design of low to high-rise CMF structures.

Kinematic Description of Damage

In this paper the kinematics of damage for finite elastic deformations is introduced using the fourth-order damage effect tensor through the concept of the effective stress within the framework of continuum damage mechanics. However, the absence of the kinematic description of damage deformation leads one to adopt one of the following two different hypotheses. One uses either the hypothesis of strain equivalence or the hypothesis of energy equivalence in order to characterize the damage of the material. The proposed approach in this work provides a relation between the effective strain and the damage elastic strain that is also applicable to finite strains. This is accomplished in this work by directly considering the kinematics of the deformation field and furthermore it is not confined to small strains as in the case of the strain equivalence or the strain energy equivalence approaches. The proposed approach shows that it is equivalent to the hypothesis of energy equivalence for finite strains. In this work, the damage is described kinematically in the elastic domain using the fourth-order damage effect tensor which is a function of the second-order damage tensor. The damage effect tensor is explicitly characterized in terms of a kinematic measure ofdamage through a second-order damage tensor. The constitutive equations of the elastic-damage behavior are derived through the kinematics of damage using the simple mapping instead of the other two hypotheses.

Effect of wall roughness on fluid transport resistance in nanopores.

Using non-equilibrium molecular dynamics simulations, we investigate the effect of wall roughness on the transport resistance of water molecules inside modified carbon nanotubes. The effective shear stress, which characterizes the strong interaction between liquid molecules and solid wall, is a quantity that dominates the nanofluidic transport resistance. Both the effective shear stress and nominal viscosity arise with the increase of the amplitude or the decrease of the wavelength of roughness. The effect of roughness is also relatively more prominent in smaller nanotubes. The molecular mechanism is elucidated through the study of the radial density profile, hydrogen bonding, and velocity field of the confined water molecules.