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Constitutive Modeling and Numerical Implementation of Anisotropic Plasticity of Metallic Lattice Materials using Stress Transformation Approach

Eynbeygui, Mehdi | 2024

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 57325 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Naghdabadi, Reza; Arghavani, Jamal; Akbarzadeh, Hamid
  7. Abstract:
  8. Lattice materials with periodic reticulated meso-truss architectures, frequently inspired by nature, are man-made materials offering outstanding stiffness-to-weight ratios which make them an excellent candidate for lightweight structures. Focusing on the metallic pyramidal lattice material for its remarkable applications especially in ultra-light energy absorbers, in the scale of representative volume element (RVE), an analytical framework using beam theory is presented to explore the anisotropic effective elastic properties of this lattice material. Utilizing hollow-tapered struts as the constituent of pyramidal lattices, superior effective stiffness as well as yield strength for the same weight as compared to solid-uniform struts are observed. Moreover, experimental studies are conducted over the pyramidal lattices with a wide range of relative density and various struts shape. The samples are made by a digital light processing (DLP) 3D printer, and are subjected to uniaxial compression tests to provide a partial experimental validation for effective elastic properties of pyramidal lattices. Beyond the elastic regime, using an analytical method considering plastic-hinge model, nonlinear elastic-plastic constitutive relations for a pyramidal lattice strut are determined. Along proportional loading paths, the initial and subsequent yield surfaces for metallic pyramidal lattices are investigated in the small deformation scope. Based on the Linear Stress Transformation (LST) approach, two anisotropic pressure-dependent yield functions with linear isotropic hardening model named Yld-13P and Yld-16P are presented. The initial and subsequent yield surfaces of pyramidal lattices under proportional biaxial loads reveal that phenomenological models have excellent predictive capabilities. In the finite deformation scope, 3D continuum finite element simulations are carried out to assess the yield surfaces evolution of metallic pyramidal lattices along proportional and non-proportional loading paths. The base material is assumed to have isotropic and strain-hardening behaviors. While in the tensile mode, the subsequent yielding of pyramidal lattices is associated with the strain hardening, in the compressive mode, local buckling of the lattice struts becomes a dominant phenomenon, and failure is associated with softening. In this case, collapse progresses at a roughly constant load (stress plateau) until the opposing struts meet and touch. In addition to the anisotropy, numerical experiments of pyramidal lattices, subjected to the various loading paths, disclose the asymmetry of yield behaviors. Moreover, under a cycle of loading, unloading, and reverse loading, Bauschinger effect is seen in the effective behavior of the lattice material. To deal with anisotropy, pressure-dependency, and asymmetry of the yield surface which evolves by a combination of expansion and translation, a yield function named Yldlrg-19P, based on the LST approach is proposed. In this function, a mixed isotropic-kinematic hardening model is utilized. Results confirm that the present model is capable of describing the post-yielding behaviors of pyramidal lattices along proportional and/or non-proportional loading paths
  9. Keywords:
  10. Experimental Method ; Analytical Closed Form Solution ; Phenomenological Property ; Finite Element Simulation ; Pyramidal Lattice Material ; Linear Stress Transformation Approach ; Anisotropic Effective Elastic-Plastic Properties

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