Modeling heat flow across material interfaces and cracks using the material point method

Abstract

Heat conduction through an object with material interfaces or cracks is influenced by heat flow across those discontinuities. This paper presents a numerical particle method for modeling such heat flow coupled to computational mechanics all within the material point method (MPM). In brief, MPM models contacts and cracks by extrapolating multiple velocity fields to a grid. To model interfacial heat flow, MPM should similarly extrapolate multiple temperature fields. Interface nodes that “see” more than one temperature field modify their heat flow to reflect interfacial physics. For example, interfaces in contact may transfer heat by perfect conduction, while separated interfaces may block heat flow or cause reduced heat flow by convection. After some validation examples, two real-world examples consider cooling an ingot within a crucible where cooling causes the ingot to lose contact with the crucible walls and thermal imaging of cracks within an opaque solid.