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Linear elasticity
About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.
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TL;DR: In this paper, the authors presented a cyclic stress-strain relationship of reinforcing bars and verified the cyclic behavior of the reinforcing bars including the post-buckling loops by combining the equations representing the two monotonic envelopes and cyclic loops.
135 citations
TL;DR: The flat state is shown to become unstable to oscillations above a critical swelling rate and the computed wavelengths are in quantitative agreement with the experiment.
Abstract: The patterns arising from the differential swelling of gels are investigated experimentally and theoretically as a model for the differential growth of living tissues. Two geometries are considered: a thin strip of soft gel clamped to a stiff gel, and a thin corona of soft gel clamped to a disk of stiff gel. When the structure is immersed in water, the soft gel swells and bends out of plane leading to a wavy periodic pattern whose wavelength is measured. The linear stability of the flat state is studied in the framework of linear elasticity using the equations for thin plates. The flat state is shown to become unstable to oscillations above a critical swelling rate and the computed wavelengths are in quantitative agreement with the experiment.
135 citations
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30 Nov 1990
TL;DR: In this paper, the authors proposed an energy balance model for a semi-infinite crack and showed that the model can be used to detect cracks in bending plates and shells in concrete.
Abstract: 1. Introductory chapter.- 1.1. Conventional failure criteria.- 1.2. Characteristic brittle failures.- 1.3. Griffith's work.- 1.4. Fracture mechanics.- References.- 2. Linear elastic stress field in cracked bodies.- 2.1. Introduction.- 2.2. Crack deformation modes and basic concepts.- 2.3. Eigenfunction expansion method for a semi-infinite crack.- 2.4. Westergaard method.- 2.5. Singular stress and displacement fields.- 2.6. Method of complex potentials.- 2.7. Numerical methods.- 2.8. Experimental methods.- 2.9. Three-dimensional crack problems.- 2.10. Cracks in bending plates and shells.- References.- 3. Elastic-plastic stress field in cracked bodies.- 3.1. Introduction.- 3.2. Approximate determination of the crack-tip plastic zone.- 3.3. Small-scale yielding solution for antiplane mode.- 3.4. Complete solution for antiplane mode.- 3.5. Irwin's model.- 3.6. Dugdale's model.- 3.7. Singular solution for a work-hardening material.- 3.8. Numerical solutions.- References.- 4. Crack growth based on energy balance.- 4.1. Introduction.- 4.2. Energy balance during crack growth.- 4.3. Griffith theory.- 4.4. Graphical representation of the energy balance equation.- 4.5. Equivalence between strain energy release rate and stress intensity factor.- 4.6. Compliance.- 4.7. Critical stress intensity factor fracture criterion.- 4.8. Experimental determination of KIc.- 4.9. Crack stability.- 4.10. Crack growth resistance curve (R-curve) method.- 4.11. Mixed-mode crack propagation.- References.- 5. J-Integral and crack opening displacement fracture criteria.- 5.1. Introduction.- 5.2. Path-independent integrals.- 5.3. J-integral.- 5.4. Relationship between the J-integral and potential energy.- 5.5. J-integral fracture criterion.- 5.6. Experimental determination of the J-integral.- 5.7. Stable crack growth studied by the J-integral.- 5.8. Mixed-mode crack growth.- 5.9. Crack opening displacement (COD) fracture criterion.- References.- 6. Strain energy density failure criterion.- 6.1. Introduction.- 6.2. Volume strain energy density.- 6.3. Basic hypotheses.- 6.4. Two-dimensional linear elastic crack problems.- 6.5. Uniaxial extension of an inclined crack.- 6.6. Three-dimensional linear elastic crack problems.- 6.7. Bending of cracked plates.- 6.8. Ductile fracture.- 6.9. Failure initiation in bodies without pre-existing cracks.- 6.10. Other criteria based on energy density.- References.- 7. Dynamic fracture.- 7.1. Introduction.- 7.2. Mott's model.- 7.3. Stress field around a rapidly propagating crack.- 7.4. Strain energy release rate.- 7.5. Transient response of cracks to impact loads.- 7.6. Standing plane waves interacting with a crack.- 7.7. Crack branching.- 7.8. Crack arrest.- 7.9. Experimental determination of crack velocity and dynamic stress intensity factor.- References.- 8. Fatigue and environment-assisted fracture.- 8.1. Introduction.- 8.2. Fatigue crack propagation laws.- 8.3. Fatigue life calculations.- 8.4. Variable amplitude loading.- 8.5. Mixed-mode fatigue crack propagation.- 8.6. Nonlinear fatigue analysis based on the strain energy density theory.- 8.7. Environment-assisted fracture.- References.- 9. Engineering applications.- 9.1. Introduction.- 9.2. Fracture mechanics design philosophy.- 9.3. Design example problems.- 9.4. Fiber-reinforced composites.- 9.5. Concrete.- 9.6. Crack detection methods.- References.- Author Index.
134 citations
TL;DR: A stress is an equilibrating application of force to a body as discussed by the authors, and a strain is any definite alteration of form or dimensions experienced by a solid, i.e., a force that causes a change in the shape of the body.
Abstract: Def. A Stress is an equilibrating application of force to a body. Cor. The stress on any part of a body in equilibrium will thus signify the force which it experiences from the matter touching that part all round, whether entirely homogeneous with itself or only so across a portion of its bounding surface. Def. A strain is any definite alteration of form or dimensions experienced by a solid.
133 citations
TL;DR: In addition to the Dahlquist criterion requiring a low modulus, two additional rheological predictors of the adhesive properties were proposed in this paper, which can be used to fine tune the adhesive performance of a PSA.
Abstract: The major objective of this article is to present recent advances in the methodology to fine tune the adhesive performance of a PSA. In addition to the so-called Dahlquist criterion requiring a low modulus, we propose two additional rheological predictors of the adhesive properties. The first one is derived from the description of the detachment of a linear elastic layer from a rigid substrate. We made an approximate extension of this analysis to the viscoelastic regime and showed that the transition from interfacial cracks to cavitation and fibrillation can be quantitatively predicted from the easily measurable ratio tan(δ)/G′(ω). If a fibrillar structure is formed, the nonlinear large strain properties become important. We showed that the ability of the fibrils to be stretched before final debonding can be predicted from the analysis of simple tensile tests. The softening, which occurs at intermediate strains, and, more importantly, the hardening which occurs at large strains, can be used to predict the...
133 citations