Plasticity Based Formulations for Pressure Sensitive Materials

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The dependency of the behavior of different materials with respect to the level of the pressure is addressed. Experimental results are accompanied with appropriate constitutive formulations to validate and reproduce the main features of the experimental results. Three types of materials have been studied. A simplified constitutive model has been introduced to simulate the behavior of concrete under high confinement. The multi-surface damage plasticity model combines the hyperbolic Drucker-Prager formulation in shear and tension regime and the modified cam-clay yield functions in the cap of the triaxial compression. The post yield behavior and the damage evolution of concrete are divided into the tensile, shear, and compressive regimes. Fracture energy based coefficients govern the hardening and softening behavior of concrete by altering a) the cohesion, b) the tension limit, and c) the compression cap limit. The non-associativity regulates the dilatancy of concrete. The bulk damage, which is activated at the point of transition from compaction to dilation is separated from the shear damage to capture the behavior of concrete subjected to cyclic loading. One advantage of the proposed formulation is the small number of material parameters. The performance of the material model has been verified using numerical examples under different load histories. Specifically, the response behavior of the model under high levels of confinement is investigated in the presentation. The constitutive formulation was validated using benchmark experiments from the literature. Some load cases of hydrostatic response, the proportional, and the oedometer benchmark test were used to calibrate the model. The pressure sensitivity of metals was addressed as a part of this research. It is stated that structural steel exhibits pressure sensitive behavior contrary to the common expectations. A series of experiments under different load scenarios were performed on steel specimens, which activates non-deviatoric stress tensor invariants. The load is applied to solid round bars in form of combinations of uniaxial tension/compression and torsion sequences, which will result in combined axial and shear stresses that maintain a constant ratio throughout the experiment. Digital Image Correlation (DIC) was used as a full-field measurement method of the displacement field and calculation of the strain distribution of the steel specimens to obtain plastic flow direction by integration of the plastic strain rate through the physical domain of the specimen and expressed it in terms of the first invariant of stress tensor and the second and third invariant of the stress deviator. Looking at the full strain tensor, a more accurate hardening rule was proposed as a function of all these three invariants of the plastic strain tensor. Using this method, the plastic flow rule was derived by integrating plastic strain rate through the physical domain of the specimen and expressing it in terms of the three invariant formulation of the stress tensor to activate the proposed hardening law. It has been observed that the pressure dependency plays a great role in the failure mechanism and strength of the interface layers between materials, such as masonry, that undergoes confined shear loads in the interface zones. The mechanical behavior of masonry heavily relies on the mechanical properties of the two constituents and especially their interaction and bonding in the interface layer of brick and mortar. Since the interface between two constituents is very important in behavior of masonry, the formulation should capture the interface behavior and predict the failure in the interface region. Parameter estimation and validation for interface behavior between mortar and brick in masonry triplet assemblies are being conducted. The data has been obtained using experiments performed in the materials laboratory facility at University of Houston on pre-compressed masonry triplets to establish the shear strength of the brick–mortar interface under variable pre-compression load level. The results of these experiments were used to propose a general plasticity based constitutive formulation for the behavior of zero-thickness interface layer between brick and mortar. This model takes into the account the shear resistance of the interface layer under confined conditions, and includes the frictional behavior of before and after failure of interface bond. A new element has been introduced using a combination of continuum solid formulation and a traction-separation based zero thickness interface formulation. The 2D sandwich element is used to incorporate inter-element displacement discontinuities for delamination and shear sliding in the case that the failure threshold of the interface is met.

Concrete, Steel, Interfaces, Masonry, Plasticity, Yield, Damages, Finite element, Lode angle, Stress, Strain, Inelastic, Constitutive formulation, Digital image correlation (DIC)
Portions of this document appear in: Willam, Kaspar, Amir Mohammadipour, Reza Mousavi, and Ashraf S. Ayoub. "Failure of unreinforced masonry under compression." In Structures Congress 2013: Bridging Your Passion with Your Profession, pp. 2949-2961. 2013. And in: Mousavi, R., Masoud D. Champiri, Mohammad S. Joshaghani, and Shahin Sajjadi. "A kinematic measurement for ductile and brittle failure of materials using digital image correlation." AIMS Materials Science 3, no. 4 (2016): 1759-1772. And in: Papadrakakis, M., V. Papadopoulos, G. Stefanou, and V. Plevris. "EFFICIENCY OF DAMAGE-PLASTICITY MODELS IN CAPTURING COMPACTION-EXPANSION TRANSITION OF CONCRETE UNDER DIFFERENT COMPRESSION LOADING CONDITIONS."