Development of interface based damage-plasticity constitutive model and its application in the simulation of masonry structures under monotonic and cyclic loads
Date
2022
Authors
Nie, Yu
Editors
Advisors
Sheikh, Abdul Hamid
Griffith, Michael
Visintin, Phillip
Griffith, Michael
Visintin, Phillip
Journal Title
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Thesis
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Abstract
Simulation of masonry structures at the mesoscale level to capture cracking failure is a challenging topic due to both the complexity of masonry materials and numerical difficulties in solving nonlinear problems. Within the framework of finite element method, cohesive elements with an interfacial constitutive model are commonly utilized as brick-mortar joints to simulate the nonlinear response of masonry structures, including simulation of mechanical behaviour and cracking patterns. This modelling strategy provides effective prediction of the strength-deformation relationship and failure modes of materials/structures, but is highly computationally expensive and convergence issues are frequently encountered during the numerical implementation process. In this thesis, interfacial constitutive models are proposed and developed in conjunction with advanced numerical implementation methods to avoid or overcome convergence difficulties. Constitutive criteria for masonry joints are established based on damage mechanics and plasticity principals which define the nonlinear behaviour of interface model in traction-separation scheme (stress-relative deformation relation). Another critical problem, divergence, is solved by improving numerical implementation method at both the global (FE solver) and local (material algorithm) level. The accuracy and robustness of the proposed interfacial models are validated at the elemental and structural level by comparing the load-displacement response and failure modes of finite element models with experimental results obtained from literature. Initially, the finite element method is investigated by using a general numerical software (Abaqus) which provides built-in interfacial models based on damage mechanics (cohesive zone model, CZM). A surface based cohesive technique is applied to model the connection between bricks and mortar joints. Since the built-in interfacial model can only determine the tension-shear mixed mode of joints, solid elements are defined with a continuum nonlinear material model (concrete damage plasticity model, CDP) to predict the compressive failure of bricks. To achieve most efficient and stable computational results, different numerical solvers are compared and the Implicit Dynamic solver with linear search option is adopted as the most proper numerical technique. After developing an understanding of the finite element modelling process, a plasticity based interfacial model is developed for the zero-thickness cohesive element. The plasticity model includes a hyperbolic yield surface which can define the tension-shear mix-mode failure of joints. An energy dissipation/plastic work based evaluation law is applied to determine the variation of internal variables, including strength softening, dilation and frictional change. Robustness of the numerical implementation is enhanced by subdividing large increments of deformation (relative displacements) into smaller sizes to increase the convergence of Newton-Raphson iteration in implicit integration. Regarding the cyclic behaviour of masonry structures, stiffness degradation of brick-mortar joints is often observed in experimental tests under unloading/reloading path. To improve the plasticity model, damage parameters are induced into the constitutive formula. In this way, a comprehensive interface model with inelastic deformation, strength reduction and stiffness degradation (considering the cracking closure) is presented in this study. A consistent tangent stiffness matrix for this coupled damage-plasticity model is also derived in a recursive format in sub-stepping scheme to achieve quadratic convergence rate. Despite the robustness and accuracy of the above described damage-plasticity model, it’s computational efficiency is limited by the complication of stress return mapping, thus application when simulating masonry structures under cyclic loadings requires significant computational resources. A simplified damage-plasticity model is proposed by using a similar constitutive formulation, but it is implemented in a more efficient numerical strategy where damage mechanics is separated from plasticity. By transferring stresses between effective and nominal stress spaces, the computation of damage mechanics and plasticity are completed in two individual progresses which are connected by the state dependent variable (plastic work). Furthermore, effects of the dilation coefficient on the constitutive behaviour and numerical modelling are investigated in the study by using a softening dilation function. Compared with the constant coefficient with a small magnitude, the proposed changeable dilation function can reflect physical phenomenon of masonry joints more realistically, and it is also helpful in enhancing the stress return mapping procedure. In addition to tension and shear failures, compressive crushing is another critical failure mode when masonry walls under in-plane loadings. By adding a compressive cap model into the interfacial based constitutive criteria, the crushing failure of masonry is represented by using cohesive elements. Therefore, all nonlinear behaviours are concentrated in the cohesive element with an interfacial multi-surface model and bricks are assumed as an elastic material. Even though this simplification has been widely accepted in mesoscale modelling of quasi-brittle materials, existing interfacial models usually ignore the compressive behaviour of cohesive element for convenience. To make the present interfacial model capable of simulating compressive failure, an elliptical yield surface is combined with the hyperbolic yield surface to form a multi-surface elastoplastic model. In effective stress space, tension-shear mixed hyperbolic yield surface follows a perfectly-plastic rule where no deformation or variation is allowed, while the compressive cap yield surface controlled by a hardening-plastic rule is allowed to extend in limited region until the interface reaches ultimate compressive strength of the masonry. In the aspect of damage mechanics, a series of polynomial equations relying on plastic work is adopted in the constitutive criteria to control the evaluation of internal variables, including the growth of damage parameters and the decrease of other internal variables (e.g. dilation effects). Configuration coefficients are considered in polynomial equations to help calibrate curves of internal variables along with plastic works/inelastic deformations. With the aid of a piecewise function, the hardening-softening relationship of the interface under monotonic/cyclic compressive loadings can be properly simulated, including the variation of normal stiffness which keeps constant during strength hardening stage but degrades in the strength softening process. Concerning the intricacy of numerical convergence in multi-surface model, a more advanced adaptive sub-stepping technique is adopted in the algorithm of numerical implementation where the sub-dividing size of large deformations can be automatically adjusted based on converging performance in each sub-steps.
School/Discipline
School of Civil, Environmental and Mining Engineering
Dissertation Note
Thesis (Ph.D.) -- University of Adelaide, School of Civil, Environmental & Mining Engineering, 2022
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