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The elastic buckling of shell structures such as spherical shells subject to external pressure and cylindrical shells loaded in axial compression is highly sensitive to imperfections and often catastrophic. Recent studies of spherical shells have provided accurate quantitative results for the relation between the buckling pressure and the amplitude and shape of geometric imperfections and, additionally, quantitative results for the energy barrier that must be overcome to buckle the shell by extraneous loadings or disturbances when it is loaded to pressures below the buckling pressure. Results for the simultaneous interaction of imperfections and energy barriers for spherical shells under external pressure will be presented. Numerical studies for probing forces illustrate their use in determining the buckling energy barrier, and new experimental results on energy barriers obtained by others by probing spherical shells will be discussed and compared with predictions. It will be argued that while imperfections determine the buckling load of a shell, the energy barrier at loads below the buckling load supplies important additional information about the relative safety or precariousness of the shell to additional disturbances. Results for the energy barrier for perfect and imperfect spherical shells under external pressure provide important insights into the shell's robustness, or lack thereof, at pressures below the buckling pressure. In particular, the energy barrier trends provide critical insights into the low knockdown factor usually employed in establishing the design load of unstiffened spherical and cylindrical shells. These design loads are shown to correlate with conventional predictions provided that imperfection amplitudes scale as the shell radius. [ABSTRACT FROM AUTHOR]

Clamped-clamped compressed wide metal columns with length to thickness ratios such that they undergo plastic buckling are considered. Further, the thickness of the columns is assumed to be in the range of microns to tens of microns, typical of elements comprising some of the small-scale lattice materials currently being produced. The strengthening effects associated with plastic strain gradients are expected to influence buckling behavior, and the columns are analyzed using several versions of the available strain gradient plasticity theories. The columns are assumed to be infinitely wide and subject to plane strain deformations. Approximate one-dimensional and exact two-dimensional analyses are presented. The primary focus is the onset of plastic buckling as predicted by bifurcation from the state of uniform compression. However, a numerical post-buckling study is carried out for one class of strain gradient theories for columns with initial imperfections to ascertain if the buckling predictions stemming from this class of theory are realistic. The paper highlights the fact that one class of strain gradient theories does not appear to be adequate for analyzing plastic buckling. [ABSTRACT FROM AUTHOR]

The stability of lightweight space structures composed of longitudinal thin-shell elements connected transversely by thin rods is investigated, extending recent work on the stability of cylindrical and spherical shells. The role of localization in the buckling of these structures is investigated and early transitions into the post-buckling regime are unveiled using a probe that locally displaces the structure. Multiple probe locations are studied and the probe force versus probe displacement curves are analyzed and plotted to assess the structure's stability. The probing method enables the computation of the energy input needed to transition early into a post-buckling state, which is central to determining the critical buckling mechanism for the structure. A stability landscape is finally plotted for the critical buckling mechanism. It gives insight into the post-buckling stability of the structure and the existence of localized post-buckling states in the close vicinity of the fundamental equilibrium path. [ABSTRACT FROM AUTHOR]

Abstract: Cylindrical shells under uniaxial compression and spherical shells under equi-biaxial compression display the most extreme buckling sensitivity to imperfections. In engineering practice, the reduction of load carrying capacity due to imperfections is usually addressed by use of a knockdown factor to lower the critical buckling stress estimated or computed without accounting for imperfections. For thin elastic cylindrical shells under uniaxial compression and spherical shells under equi-biaxial compression, the knockdown factor is typically as small as 0.2. This paper explores the alleviation of imperfection-sensitivity for loadings with a reduced circumferential (transverse) membrane stress component. The analysis of on the effect of an axisymmetric imperfection on the elastic buckling of a cylindrical shell under uniaxial compression is extended to both cylinders and spheres for loadings that produce general combinations of biaxial membrane stresses. Increases in the knockdown factor due to a reduction of the transverse membrane component are remarkably similar for cylindrical and spherical shells. [Copyright &y& Elsevier]

Abstract: A preliminary theoretical study is carried out of the role of micron-scale patterning on the interface toughness of bonded Cu-to-Cu nanometer-scale films. The work is motivated by the experimental studies of [Tadepalli, R., Turner, K.T., Thompson, C.V., 2008b. Effects of patterning on the interface toughness of wafer-level Cu–Cu bonds. Acta Materialia 56, 438–447; Tadepalli, R., Turner, K.T., Thompson, C.V., 2008c. Mixed-mode interface toughness of wafer-level Cu–Cu bonds using asymmetric chevron test. J. Mech. Phys. Solids 56, 707–718.] wherein 400nm Cu films were deposited in a variety of patterns on Si wafer substrates. Specimens were then produced by bringing the Cu surfaces into contact creating thermo-compression bonds. Interface toughness of these specimens was experimentally measured. The present study focuses on interface patterns comprised of bonded strips, called lines, alternating with lines of unbonded interface, all aligned parallel to the crack front. The interface toughness model employs a cohesive zone to represent separation of the interface and flow theory of plasticity to characterize the Cu films. Remote mode I loading is imposed on the elastic Si substrates. The computational model provides the resistance curve of macroscopic crack driving force versus crack advance as dependent on the work of separation and strength of the interface as well as the pattern geometry and the parameters controlling the plasticity of the Cu films. Plasticity in the Cu films makes a major contribution to the macroscopic interface toughness measured by Tadepalli, Turner and Thompson. Highlighted in this study is the difficulty of accurately representing plastic yielding in the thin films and the challenge of capturing the full range of scales in a computational model. [Copyright &y& Elsevier]

Abstract: Dynamic stretching of bilayer plates comprised of an elastomer layer bonded to a metal layer is studied with emphasis on neck development under plane strain. Neck retardation and multiple necks in the metal layer are promoted by the elastomer layer under quasi-static conditions and also by inertia in the all-metal layer under dynamic stretching. The present study explores the interaction of these two effects under the assumption that ductility is unlimited. The study reveals the roles of the elastomer modulus, the metal strength and the rate of stretching in giving rise to necking retardation. [Copyright &y& Elsevier]

Abstract: Recent results on fluid–structure interaction for plates subject to high intensity air shocks are employed to assess the performance of all-metal sandwich plates compared to monolithic solid plates of the same material and mass per area. For a planar shock wave striking the plate, the new results enable the structural analysis to be decoupled from an analysis of shock propagation in the air. The study complements prior work on the role of fluid–structure interaction in the design and assessment of sandwich plates subject to water shocks. Square honeycomb and folded plate core topologies are considered. Fluid–structure interaction enhances the performance of sandwich plates relative to solid plates under intense air shocks, but not as significantly as for water blasts. The paper investigates two methods for applying the loading to the sandwich plate—responses are contrasted for loads applied as a time-dependent pressure history versus imposition of an initial velocity. [Copyright &y& Elsevier]

Abstract: An extension of the Gurson model that incorporates damage development in shear is used to simulate the tension–torsion test fracture data presented in Faleskog and Barsoum (2013) (Part I) for two steels, Weldox 420 and 960. Two parameters characterize damage in the constitutive model: the effective void volume fraction and a shear damage coefficient. For each of the steels, the initial effective void volume fraction is calibrated against data for fracture of notched round tensile bars and the shear damage coefficient is calibrated against fracture in shear. The calibrated constitutive model reproduces the full range of data in the tension–torsion tests thereby providing a convincing demonstration of the effectiveness of the extended Gurson model. The model reinforces the experiments by highlighting that for ductile alloys the effective plastic strain at fracture cannot be based solely on stress triaxiality. For nominally isotropic alloys, a ductile fracture criterion is proposed for engineering purposes that depends on stress triaxiality and a second stress invariant that discriminates between axisymmetric stressing and shear dominated stressing. [Copyright &y& Elsevier]