(2007) A mathematical representation of the multiaxial Bauschinger effect Materials at High Temperatures: Vol 24, No 1, pp 1-26

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A mathematical representation of the multiaxial Bauschinger effect

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Stress-strain relations, uniqueness and variational theorems for elastic-plastic materials with a singular yield surface

The virtual crack extension method for nonlinear material behavior

State-of-the-art report: Fracture mechanics of concrete: concepts, models and determination of material properties. Why fracture mechanics? Essential results from linear elastic fracture mechanics. Nonlinear fracture models with softening zone. Special nonlinear fracture models based on adaptions of LEFM. Size effect and brittleness of structures. Experimental or analytical determination of material fracture parameters. Factors influencing fracture parameters. Effect of reinforcement. Crack systems. Concluding remarks. References and bibliography. Appendix 1- derivations of some formulas. Conference papers. Material models for concrete fracture. Damage modelling. Numerical analysis of concrete fracture. Experimental methods and determination of fracture characteristics. Measurements of damage and size effect. Dynamic fracture. Fracture under shear. Fracture of reinforced concrete. Interaction between concrete and reinforcement. Fatigue and rate effects. Environment effects [temperature, shrinkage, corrosion]. Index.

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Fracture mechanics of concrete structures

The first part of this two-part study presents a new improved microplane constitutive model for concrete, representing the fourth version in the line of microplane models developed at Northwestern University. The constitutive law is characterized as a relation between the normal, volumetric, deviatoric, and shear stresses and strains on planes of various orientations, called the microplanes. The strain components on the microplanes are the projections of the continuum strain tensor, and the continuum stresses are obtained from the microplane stress components according to the principle of virtual work. The improvements include (1) a work-conjugate volumetric deviatoric split—the main improvement, facilitating physical interpretation of stress components; (2) additional horizontal boundaries (yield limits) for the normal and deviatoric microplane stress components, making it possible to control the curvature at the peaks of stress-strain curves; (3) an improved nonlinear frictional yield surface with plasticity asymptote; (4) a simpler and more effective fitting procedure with sequential identification of material parameters; (5) a method to control the steepness and tail length of postpeak softening; and (6) damage modeling with a reduction of unloading stiffness and crack-closing boundary. The second part of this study, by Caner and Bazant, will present an algorithm for implementing the model in structural analysis programs and provide experimental verification and calibration by test data.

Microplane Model M4 for Concrete. I: Formulation with Work-Conjugate Deviatoric Stress

Note presenting a theory of plasticity based on the concept of slip as proposed for the relationship between stress and strain for initially isotropic materials in the strain-hardening range. The theory is an extension to polyaxial stress conditions of the conventional uniaxial stress-strain relation, and time-dependent effects, such as creep and stress relaxation, are not considered.

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S. B. Batdorf

Papers

A Mathematical Theory of Plasticity Based on the Concept of Slip

Polyaxial Stress-Strain Relations of a Strain-Hardening Metal