A pure stress formulation for modeling elastic waves using central finite differences.

Area of Science:

• Solid Mechanics
• Computational Physics
• Materials Science

Background:

• Modeling elastic wave propagation is crucial for understanding material behavior.
• Existing methods often face challenges with spatial heterogeneity and computational cost.
• A pure stress-based formulation offers a novel approach to overcome these limitations.

Purpose of the Study:

• Introduce a pure stress-based finite difference (FD) formulation for elastic wave propagation.
• Model wave propagation in linear elastic solids with spatial heterogeneity.
• Enable efficient, large-scale simulations on modern hardware.

Main Methods:

• Derivation from the strong form of the elastodynamic equation of motion with stress as the sole dependent variable.
• Discretization using a standard second-order central difference scheme for space-time evolution of stress components.
• Numerical dispersion analysis for homogeneous materials and simulations for heterogeneous bimaterials.

Main Results:

• Successful modeling of stress component evolution in space and time.
• Validation against closed-form solutions for reflection/transmission coefficients in a heterogeneous bimaterial.
• Demonstration of large-scale 3D simulations exceeding 1 billion degrees of freedom on GPU architectures.

Conclusions:

• The stress-based FD formulation is promising for ultrasonic simulations in materials with stiffness heterogeneity.
• It offers an alternative for modeling wave propagation and scattering in heterogeneous media.
• Potential applications include nondestructive evaluation, materials characterization, biomedical ultrasound, and geosciences.