# Numerical solution of shock and ramp compression for general material properties

## TL;DR

This paper presents a flexible numerical framework for modeling shock and ramp compression in materials with general properties, accurately capturing complex dynamic responses without detailed spatial simulations.

## Contribution

It introduces a novel, robust numerical approach that generalizes previous scalar-based solutions to handle complex material models and deformation paths.

## Key findings

- Numerical methods match analytic solutions with high accuracy.
- The approach effectively models shock interactions and phase transitions.
- Results illustrate effects of plastic work and phase changes on material temperature.

## Abstract

A general formulation was developed to represent material models for applications in dynamic loading. Numerical methods were devised to calculate response to shock and ramp compression, and ramp decompression, generalizing previous solutions for scalar equations of state. The numerical methods were found to be flexible and robust, and matched analytic results to a high accuracy. The basic ramp and shock solution methods were coupled to solve for composite deformation paths, such as shock-induced impacts, and shock interactions with a planar interface between different materials. These calculations capture much of the physics of typical material dynamics experiments, without requiring spatially-resolving simulations. Example calculations were made of loading histories in metals, illustrating the effects of plastic work on the temperatures induced in quasi-isentropic and shock-release experiments, and the effect of a phase transition.