# Inverse Design Based on Nonlinear Thermoelastic Material Models Applied to Injection Molding

## TL;DR

This paper introduces an inverse shape design method for thermoelastic bodies that determines initial shapes and temperature distributions from a known equilibrium shape, using nonlinear PDEs solved via finite element or isogeometric analysis.

## Contribution

It presents a novel inverse design approach capable of estimating initial shapes and temperature fields for thermoelastic bodies, applicable to injection molding and other fields.

## Key findings

- Successfully applied to inverse cavity design in injection molding
- Capable of prescribing initial temperature and stress fields
- Uses iterative fine-tuning for improved accuracy

## Abstract

This paper describes an inverse shape design method for thermoelastic bodies. With a known equilibrium shape as input, the focus of this paper is the determination of the corresponding initial shape of a body undergoing thermal expansion or contraction, as well as nonlinear elastic deformations. A distinguishing feature of the described method lies in its capability to approximately prescribe an initial heterogeneous temperature distribution as well as an initial stress field even though the initial shape is unknown. At the core of the method, there is a system of nonlinear partial differential equations. They are discretized and solved with the finite element method or isogeometric analysis. In order to better integrate the method with application-oriented simulations, an iterative procedure is described that allows fine-tuning of the results. The method was motivated by an inverse cavity design problem in injection molding applications. Its use in this field is specifically highlighted, but the general description is kept independent of the application to simplify its adaptation to a wider range of use cases.