Leonard R. Herrmann

Development of a plasticity bond model for steel reinforcement

The development of an interface, non-associative, plasticity model for bond between ribbed, steel bars and concrete is discussed. The model relates average local slip and radial dilation to average bond shear stress and radial confinement stress. The model partially accounts for the response of the damaged, finite-thickness region around the bar—the bond zone. The model is developed for standard steel bars that are initially unstrained. With simplifying assumptions, data for the components of a plasticity law are extracted from a key set of experimental results. In this paper, we emphasize the development of an expression for the yield surface for monotonic loading. While the forms of the models components are empirically derived, they qualitatively reflect the mechanics of the mechanical interaction of ribbed bars with the adjacent concrete. A characteristic length, related to the rib pattern, helps quantify this interaction. The mechanics of the bond are difficult to characterize in a simple form, but the calibrated model only requires four physical properties and reproduces with acceptable accuracy experimental results with various levels of radial confinement stress. Model refinements are suggested for future work.

Response of Reinforcing Wires to Compressive States of Stress

A theoretical investigation of the compressive response of a wire embedded in an elastic matrix is reported. In the first section con sideration is given to the beam-column behavior of an initially crooked wire embedded in a matrix which is subjected to a state of uniaxial stress. A plot of the effective stiffness of the wire as a function of the wires initial crookedness is given. Secondly, con sideration is given to the possibility of buckling, within the matrix, of a compressively loaded straight wire. A plot of the buckling load of the wire as a function of the ratio of the wires and matrixs shear moduli is given. Two procedures are developed for the pre diction of the lateral support offered to the wire by the matrix. Both procedures are developed by treating the matrix as a three- dimensional elastic solid, however, only the first of the two meth ods completely satisfies the displacement continuity requirements between the wire and the matrix. This research was supported under subcontract to the Stanford Research Institute, Menlo Park, California, under prime contract no. N123 ( 60530)-55641A with the U. S. Naval Ordinance Test Station, China Lake, California.

On a variational theorem for incompressible and nearly-incompressible orthotropic elasticity

Abstract A mixed variational theorem for linear orthotropic thermoelastic solids is presented. The mechanical state variables are taken to be the displacement vector and a scalar stress variable. The Euler equations of the variational principle are the displacement equations of equilibrium and a condition relating the stress variable to strain and temperature change. An important feature of the principle is that the field equations for both compressible and incompressible solids may be generated. In connection with applications to the development of finite element computer algorithms for the solution of boundary value problems a well-conditioned system of equations is obtained for nearly-incompressible solids.

Validation of a plasticity bond model for steel reinforcement

The validation of a plasticity model for bond between ribbed, steel bars and concrete is discussed. The model relates local slip and radial dilation to bond stress and radial confinement stress, i.e. it provides an interface characterization of the behaviour of a finite-thickness region around the bar—the bond zone. The validation study considers experimental results from six independent investigations. The specimens are all pull-out specimens but differ significantly in size and configuration. Models for each specimen, based on a single bond model calibration, reproduce the experimental results with acceptable accuracy. The response over the full range of slip and the mode of failure are examined. Some of the models strengths, weaknesses, and potential improvements are discussed. For the most part, the models predicts the experimental bond strength within 20 per cent and exhibits the potential to predict both pull-out and splitting failures. Copyright

Efficiency evaluation of a two-dimensional incompatible finite element

Abstract An incompatible plane elasticity finite element is developed and its computational efficiency is compared to that of related compatible elements. The efficiency study includes the consideration of a plane stress bending problem and the extensional behavior of a thin slotted sheet. Finally the desirability of investigating the use of the Richardsons extrapolation procedure to improve the accuracy of finite element results is briefly considered.

Three-dimensional finite element analysis of Legg-Calve-Perthes disease.

We studied the theoretical stress distribution in the proximal femoral epiphysis by means of a three-dimensional finite element model that allowed simulation of the central epiphyseal necrosis found in Legg-Calve-Perthes disease. The model was altered to study effects of age, extent of necrosis, portion of gait cycle, and effects of osteotomy on containment. It was found that small infarcts were less likely to exhibit collapse because of stress shielding, which decreased when the infarct was extensive or the area was not contained. There was little difference in stresses regardless of age or portion of the gait cycle. Femoral and pelvic osteotomies did little to modify mechanical stresses, and specifically failed to stimulate stress shielding in the case of extensive necrosis. This study suggests that basic mechanical behavior of the femoral epiphysis is similar in younger and older children, and good results in the former may be due to remodelling and low body weight. Although containment may have a place in less extensive lesions, there is no obvious mechanical support for the practice of performing osteotomies in the face of extensive epiphyseal necrosis.

A nonlinear, semi-analytical finite element analysis for nearly axisymmetric solids

Abstract The presented research is concerned with the development of the theory and accompanying computer program for a semi-analytical finite element analysis of non axisymmetrically loaded, nearly axisymmetric solids. The theoretical basis of the method together with numerical procedures for handling boundary conditions, rigid body motion and the iterative solution process are described. A finite element program for evaluating the analysis is discussed, evaluated for effectiveness and applied to several examples. The range of application of the analysis for inhomogeneous, orthotropic, nonlinear and nearly axisymmetric bodies is demonstrated by a series of examples. The substantial savings in computer time and memory as compared to a conventional finite element analysis is discussed.

Improved stress calculations for simple quadrilateral elements

Abstract An interpolation procedure is developed for calculating node point stresses for plane four node quadrilateral elements. The procedure is applied to three sample problems and the results compared to other finite element results and to analytical results. Particular attention is given to the accuracy of stresses for node points lying on the boundaries of the bodies.

Mechanical Property Tests for Cylindrically Orthotropic Materials

Experiments for the determination of the elastic properties of cylindrically orthotropic materials are suggested. Analyses, which neglect end effects, are presented for the tests, consideration is given to the importance of this approximation. Because of the cylindrical orthotropy two of the tests even in the absence of end effects result in very complicated strain states; a special procedure is presented for the interpretation of the results of these tests. Lastly, for a particular cylin drically orthotropic material an example of the application of the interpretation procedure is presented.

Effect of edge conditions on test results for concrete

Abstract A study was conducted to determine what theoretical statements can be made concerning the relative magnitudes of experimentally measured properties of concrete (measured on relatively small samples) and the actual properties. The bulk of the paper is concerned with results obtained from triaxial tests with zero surface shear stresses and either uniform normal stresses or uniform normal displacements.