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Related Concept Videos

Factors Affecting Creep01:28

Factors Affecting Creep

132
In normal-weight aggregate concrete, the hardened cement paste is the primary contributor to creep, whereas the aggregates, being stiffer than the cement paste, are more resilient to stress-induced deformation. The stiffness of the aggregates is defined by their modulus of elasticity, and the more voluminous they are in the concrete, the less it will creep.
Further, the water/cement ratio is critical, as a lower ratio increases concrete strength, thus reducing creep. The strength of the...
132
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

263
Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
263
Effects of Creep01:25

Effects of Creep

129
Creep in concrete, the gradual deformation under prolonged stress, significantly impacts the integrity of structures. For reinforced concrete beams, it can be a vital design consideration, as it increases deflection, sometimes necessitating additional design measures. In columns, especially slender ones under eccentric loads, creep can cause buckling, compromising their stability. However, creep can be beneficial in indeterminate structures by mitigating stresses that arise from shrinkage,...
129
Creep in Concrete01:22

Creep in Concrete

206
Creep refers to the time-dependent increase in strain under a sustained load, excluding other time-dependent deformations associated with shrinkage, swelling, and thermal expansion in concrete. The primary mechanism behind creep involves the loss of physically adsorbed water from the calcium silicate hydrate within the hydrated cement paste. This process is further exacerbated by concrete's non-linear stress-strain relationship, microcrack development in the interfacial transition zone, and...
206
Dynamic Modulus of Elasticity of Concrete01:16

Dynamic Modulus of Elasticity of Concrete

302
The dynamic modulus of elasticity assesses how a concrete structure deforms under impact or dynamic loads. It is typically higher than the static modulus of elasticity, measured under slow, steady loading conditions.
The sonic test is a common method to determine the dynamic modulus. In this test, a concrete beam, sized either 6 x 6 x 30 inches or 4 x 4 x 20 inches, is clamped at its center. Vibrations are initiated at one end of the beam by an electromagnetic exciter unit powered by...
302
Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

182
As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
182

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Forward and inverse problems for creep models in viscoelasticity.

H Itou1, V A Kovtunenko2,3, G Nakamura4,5

  • 1Department of Mathematics, Tokyo University of Science , Tokyo 162-8601, Japan.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|July 15, 2024
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Summary

This study proves the existence of solutions for quasi-static viscoelastic problems using fixed-point theorems and constructs semi-analytic solutions for quasi-linear cases. It also addresses inverse problems by identifying design variables from measurements using Tikhonov regularization.

Keywords:
creepimplicit graphintegral equationinverse problemvariational methodviscoelasticity

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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Applied Mathematics

Background:

  • Viscoelastic materials exhibit time-dependent mechanical behavior under stress.
  • Nonlinear elasticity describes strain response using implicit, multi-valued functions.
  • Understanding viscoelasticity is crucial for designing structures and materials.

Purpose of the Study:

  • To analyze time-dependent constitutive equations for viscoelastic materials under creep.
  • To prove the existence and construct solutions for quasi-static and quasi-linear viscoelastic problems.
  • To address the inverse viscoelastic problem of identifying material properties from measurements.

Main Methods:

  • Application of the Browder-Minty fixed-point theorem for coercive and maximal monotone graphs.
  • Construction of semi-analytic formulas for quasi-linear viscoelastic problems.
  • Tikhonov regularization in the space of bounded measures and deformations for inverse problems.

Main Results:

  • Existence of solutions for quasi-static viscoelastic problems is proven.
  • Semi-analytic solutions are constructed for quasi-linear viscoelastic problems.
  • A non-empty set of optimal variables is obtained for inverse problems, with an example of isotropic kernel identification.

Conclusions:

  • The study provides a rigorous mathematical framework for analyzing viscoelastic behavior.
  • The methods developed are applicable to both forward and inverse viscoelastic problems.
  • This work contributes to the understanding of non-smooth variational problems in mechanics.