Solid Composite Propellants (SCPs) are widely employed in the ﬁeld of propulsion due to their enduring chemical and mechanical stability during extended periods of storage, as well as their uncomplicated production and reliable performance. Unlike liquid propellants, solid propellants are self-supporting, meaning that that they function as structural materials as well asenergetic.Consequently,itisessentialtounderstandthemechanicalbehaviorofSCPsduring deﬂagration, as structural failure can have potentially catastrophic consequences. SCP failure is oftenassociatedwiththeformationandgrowthofmicromechanicaldamagesitesduetothermal and mechanical loads during burning. Thus, the ability to simulate stress propagation during the burning process is a key feature for the eﬀective design and safe use of SCPs. The ability to evaluate failure in aged propellants and of those produced using additive manufacturing is of special interest. In this work, we present an elasticity solver coupled with a thermal phase-ﬁeld model of regression of SCPs. The method implements a unique strong-form solver for ﬁnite deformation material response, featuring block structured adaptive mesh reﬁnement techniques and a multigrid solver. Two veriﬁcation results for the model are presented: ﬁrst, results for an inﬁniteplatewithapressurizedholeiscomparedtotheclassicalLamésolution;second,results for a clamped plate with a hole subjected to uniaxial tension are compared to the equivalent resultsusingthetraditionalﬁniteelement.Inbothcases,aclosematchisobserved.Next,totest the model for the application of SCPs, tension-compression tests are used to validate the model forAP/HTPBundertension.Themodelisthenusedtodeterminethemechanicalresponseofan AP/HTPB SCP during deﬂagration, driven both by thermal and mechanical loading, with both sphericalandexperimentallymeasuredmesostructures.Overall,itisdeterminedthatthemodel adequately captures the stress and strain ﬁelds, indicating the model’s viability for simulations thatlendinsightintotheinterplaybetweenmesostructure,deﬂagration,andmechanicaldamage. 1. Introduction SolidCompositePropellants(SCPs)haveplayedapivotalroleinrocketandmissilepropulsionforoveracentury. Though slightly less eﬃcient than liquid propellants, SCPs oﬀer many advantages due to their simple production and storage,self-supportandself-actuation,andoverallmechanical/chemicalstability.Akeyadvantageofthesepropellants is that their burning behavior can not be changed after ignition has started, which leads to the need for careful design [1].ThethrustgeneratedbySCPsisdirectlycorrelatedwiththetotalareaoftheburninginterfacesotheexistenceand propagation of cracks can be a major source of failure. SCPsareenergeticcompositesthatarecommonlycomposedofanoxidizer,suchasammoniumperchlorate(AP), a fuel binder, such as hydroxyl-terminated polybutadiene (HTPB), and additives such as aluminum [2–4]. SCPs are oftenstoredinenvironmentswithouttemperaturecontrol.Whiletheyaregenerallystable,theycanneverthelesssuﬀer fromthermalstrainsovertimethatcancausevoidnucleationduetodewettingprocesses[5].Theconstituentmaterials also undergo slow decomposition as they age, which can lead to degradation of the original geometry [5]. Moreover, asadditivemanufacturing(AM)ofSCPsbecomesmoreandmorefeasible,itisessentialtodeterminetheeﬀectofAM processes on mesostructure and, eventually, failure likelihood. Experimental characterization of these mechanisms is expensive and often hazardous, and to the best of the authors’ knowledge, there is no way to determine mechanical responseinsituduringdeﬂagration.Computationalsimulationsareanecessaryrecoursetoassessthebehaviorofthese <Corresponding author brunnels@iastate.edu (B. Runnels) ORCID(s):0000-0001-9914-8811 (M. Meier); 0000-0003-3043-5227 (B. Runnels) Page 1 of 13 materials, but it is very complex since these materials are heterogeneous at a microscale with signiﬁcantly diﬀerent properties, burning behavior, and stress responses. Despite the need for predictive analysis of SCP mechanics during deﬂagration, numerical modeling eﬀorts have been relatively limited. To solve the basic regression problem (sans mechanics) a number of methods have been proposed: these include level set methods [6, 7], coordinate-mapping [6, 8–10], and the phase ﬁeld method [11, 12] proposed recently by the authors. On the other hand, fundamental mechanics studies have focused on basic damage mechanisms such as fracture during the burn regression [13–15], isothermal damage [16], and thermally varying damage models with linear elasticity [17–19], along with the associated computational implementation [5, 20–22]. Prior studies of the thermomechanical response of SCPs during deﬂagration have been primarily in the context of discrete solid-solid and solid-gas interfaces. Speciﬁcally, Srinivasan, Matouš, Geubelle, and Jackson [23] coupled the generalized ﬁnite element method (GFEM) to the level-set method to investigate the mechanical response of an SCP consisting of spherical particles. On the other hand, a 3D investigation of thermal-elastic response couple to an EuleriancoordinatemappingmodelwasrecentlypresentedinKumarandJackson[24];extendingthemethodproposed by Kumar, Rycroft, and Jackson [9]. The thermomechanical response of an SCP described with fully implicit diﬀuse interfaces, however, remains unexplored. The problem of mechanical analysis of propellants during burn is challenging for many reasons, which we summarize here. (1) The timescale of deﬂagration is much longer than the acoustic timescale, meaning that the mechanicalresponseisquasistaticandmustbesolvedimplicitly,whereasregressionmodelsareusuallydesignedinthe contextofafully-explicitEuleriansolver.(2)Thedeﬂagrationprocessinherentlyinvolvesdrasticchangesingeometry, which is notoriously diﬃcult to capture in usual mechanics methods such as ﬁnite element. (3) The mesostructure of realisticpropellantsusuallydiﬀersconsiderablyfromidealized,packed-spheres-typestructuresoftenrequiredformost regression models. These challenges indicate that an alternative approach is needed. Inthiswork,wepresentadiﬀuseinterfacemethodforlargemechanicaldeformation.Themodelisveriﬁedagainst both theoretical and ﬁnite element results, and then used to predict mechanical response of SCPs during deﬂagration, as driven by the associated thermal and mechanical loads. This work combines the previously reported phase ﬁeld regression model [12] with a strong-form diﬀuse interface mechanics solver that was originally presented for linear elastic solids by Agrawal and Runnels [25]. It advances the previous development by combining the diﬀuse interface near-singularmechanicsformulationwithﬁnitekinematics.Therearenumerousadvantagestothisapproach.Because both methods rely on the diﬀuse interface approximation, they may be coupled together in a direct and natural way. This makes it eﬃcient and convenient to eﬀect bidirectional coupling between the deﬂagration and the mechanical response. Moreover, the use of adaptive mesh reﬁnement with a diﬀuse species ﬁeld makes it possible to simulate realistic propellants, rather than idealized structures. The remainder of the paper is structured in the following way. Section 2 provides an overview of the phase ﬁeld regression and thermal transport models, followed by a thorough presentation of the strong-form mechanics ﬁnite kinematics solver. In Section 3, a brief discussion of the computational methods is presented. Section 4 presents a selectionofresultstoverifyanddemonstratetheuseofthemodel:(i)veriﬁcationagainsttheoreticalandﬁniteelement solutions,(ii)tensionandthermalexpansiontestsin2Dand3D,(iii)thermomechanicalresponseofapackedspheres SCPduringdeﬂagration,and(iv)thermomechanicalresponseofarealisticmicrostructureduringdeﬂagration.Finally, Section 5 summarizes the ﬁndings and provides recommendations for the use and future development of the model. 2. Modeling This section provides a complete overview of the modeling methodology. The ﬁrst two sections outline, for completeness, a terse yet comprehensive overview of the previously developed regression and thermal evolution models. The third section introduces the strong-form, ﬁnite diﬀerence mechanics solver for near-singular problems. 2.1. Phase-ﬁeld modeling Thissectionreviewsthefull-feedbackphaseﬁeldregressionmodel.