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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.
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Upon subjecting concrete to moderate or high uniaxial compressive or tensile stresses, the strain response is non-linear relative to the stress applied. As the stress is removed, the resulting stress-strain curve deviates from the original path traced during loading, creating a hysteresis loop, indicative of the concrete's non-linear and non-elastic properties. Typically, a material's modulus of elasticity, which is a measure of the material's stiffness, is inferred from the linear...
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Updated: Feb 25, 2026

Stress Distribution During Cold Compression of Rocks and Mineral Aggregates Using Synchrotron-based X-Ray Diffraction
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Concrete wave dispersion interpretation through Mindlin's strain gradient elastic theory.

Sokratis N Iliopoulos1, Fabian Malm2, Christian U Grosse2

  • 1Department of Mechanics of Materials and Constructions, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium Sokratis.Iliopoulos@vub.ac.be.

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Area of Science:

  • Materials Science
  • Solid Mechanics
  • Civil Engineering

Background:

  • Elastic wave features like pulse velocity and attenuation are established methods for concrete characterization.
  • Concrete exhibits dispersive behavior, with phase velocity changing with frequency, particularly below 200 kHz.
  • A unified theory to model this dispersion and phase velocity change is currently lacking.

Purpose of the Study:

  • To investigate Mindlin's strain gradient elastic theory as a model for concrete's dispersive behavior.
  • To explore the role of micro-stiffness and micro-inertia parameters in elastic wave propagation.
  • To validate the theory using experimental data from cementitious materials with controlled microstructures.

Main Methods:

  • Application of Mindlin's strain gradient elastic theory, incorporating micro-stiffness and micro-inertia.
  • Experimental generation of cement paste with specific glass bead diameters to dictate microstructure.
  • Measurement and analysis of elastic wave propagation characteristics (velocity, attenuation, dispersion).

Main Results:

  • Mindlin's theory successfully models the dispersive behavior of concrete.
  • The theory provides insights into the material's microstructure.
  • Observed dispersion is accurately described across various length scales, from millimeters (mortar) to centimeters (concrete).

Conclusions:

  • Mindlin's strain gradient elastic theory offers a viable alternative to multiple scattering theory for modeling concrete.
  • The theory effectively explains the frequency-dependent phase velocity changes in concrete.
  • This approach enhances the understanding and characterization of concrete at different scales.