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Conducting Elevated Temperature Normal and Combined Pressure-Shear Plate Impact Experiments Via a Breech-end Sabot Heater System

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Converging shocks in elastic-plastic solids.

A López Ortega¹, M Lombardini, D J Hill

¹Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, California 91125, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|December 21, 2011

Summary

This study applies Whitham's shock dynamics to elastic-plastic solids, revealing how material properties influence converging shock behavior. Strong shocks are dominated by compression, with Mach number depending on constitutive laws and geometry.

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Area of Science:

Solid Mechanics
Continuum Mechanics
Shock Wave Physics

Background:

Whitham's shock dynamics theory, successful in gas dynamics, is extended to elastic-plastic solid media.
Understanding material behavior under extreme conditions like converging shocks is crucial for various engineering applications.

Purpose of the Study:

To develop an approximate description of elastic-plastic material behavior under cylindrically or spherically symmetric converging shocks.
To analyze the influence of different constitutive laws on shock dynamics and strong-shock limits.
To characterize the elastic-plastic transition in converging shock scenarios.

Main Methods:

Application of Whitham's shock dynamics theory to elastic-plastic solids.
Derivation of exact solutions for shock dynamics equations.
Analysis of compressible neo-Hookean constitutive laws for internal energy.
Investigation of isothermal and nonisothermal constitutive models.

Main Results:

Shock dynamics equations yield solutions that agree well with numerical simulations.
In the strong-shock limit, compression dominates over shear deformation.
Mach number predictions vary based on constitutive laws: power-law (M ∝ [log(1/R)](α)), arctanh (M ∝ R(-(s-1))), and ideal gas (M ∝ R(-(s-1)/n(γ))).
Hydrostatic energy governs strong-shock behavior, while shear modulus and yield stress affect behavior away from the origin.

Conclusions:

The study provides an analytical framework for understanding converging shock waves in elastic-plastic materials.
Constitutive laws significantly dictate shock behavior, particularly in the strong-shock regime.
The elastic-plastic transition involves distinct precursor and compression regions, offering insights into material response.