Doctor of Philosophy (PhD)
Civil and Environmental Engineering
Structural materials display a strong size-dependence when deformed non-uniformly into the inelastic range: smaller is stronger. This effect has important implications for an increasing number of applications in structural failure, electronics, functional coatings, composites, micro-electro-mechanical systems (MEMS), nanostructured materials, micro/nanometer fabrication technologies, etc. The mechanical behavior of these applications cannot be characterized by classical (local) continuum theories because they incorporate no ‘material length scales’ and consequently predict no size effects. On the other hand, it is still not possible to perform quantum and atomistic simulations on realistic time and structures. It is therefore necessary to develop a scale-dependent continuum theory bridging the gap between the classical continuum theories and the atomistic simulations in order to be able to design the size-dependent structures of modern technology. Nonlocal rate-dependent and gradient-dependent theories of plasticity and damage are developed in this work for this purpose. We adopt a multi-scale, hierarchical thermodynamic consistent framework to construct the material constitutive relations for the scale-dependent plasticity/damage behavior. Material length scales are implicitly and explicitly introduced into the governing equations through material rate-dependency (viscosity) and coefficients of spatial higher-order gradients of one or more material state variables, respectively. The proposed framework is implemented into the commercially well-known finite element software ABAQUS. The finite element simulations of material instability problems converge to meaningful results upon further refinement of the finite element mesh, since the width of the fracture process zone (shear band) is determined by the intrinsic material length scale; while the classical continuum theories fail to address this problem. It is also shown that the proposed theory is successful for the interpretation of indentation size effects in micro/nano-hardness when using pyramidal and spherical indenters and gives sound interpretations of the size effects in micro-torsion of thin wires and micro-bending of thin beams. Future studies should be directed toward incorporation of the size effects into design procedures and code recommendations of modern engineering structures (e.g. for MEMS, NEMS, coatings, thin films), fiber composites (e.g. for aircrafts and ships), etc.
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Abu Al-Rub, Rashid Kamel, "Material length scales in gradient-dependent plasticity/damage and size effects: theory and computation" (2004). LSU Doctoral Dissertations. 3054.
George Z. Voyiadjis