Code FEmixHC
FEmixHC is a reliable and accurate general-purpose program for thermo-elastic analysis
of simple and complex structures, in medical or engineering applications. It does not require nice mesh, the
mesh can be totally distorted and multiscale. It is suitable for compressible and totally incompressible
materials, homogeneous, isotropic, anisotropic and orthotropic, and composites. It simulates without any
simplifications, homogenizations, or trick up and tuneups, or reduced integration.
Code FEmixHC is based on the new three-dimensional multifield finite element approach for analysis of isotropic,
anisotropic, orthotropic, co,posite and coated materials, in linear transient heat transfer and elastostatics. It is
derived from primal–mixed variational formulations in transient heat transfer and mechanical analysis. The finite
element configuration used is hexahedral because it is superior than tetrahedral in many aspects. The meshing is
not a problem, because the quality of the finite element mesh is irrelevant.
There is a presumption that present formulation is computationally more expensive than the standard one-field one
(e.g. displacement-based FE approach), since it requires to solve multiple unknown fields, for the same model
problem. Nevertheless, it converges faster, it reaches thermal equilibrium faster, and it is stable and reliable.
Namely, the present finite element satisfies the most difficult test of the stability, so-called Inf-Sup condition needed
to ensure the stability of the solution. In fact, dual fields heat flux and stress are of the main interest for the
engineering conclusions about the structural behavior, and here they are calculated simultaneous with the same
accuracy as primal ones.
The outcome is that users can apply heat flux and stress constraints as essential boundary conditions, and introduce
directly initial, prescribed or otherwise known strain and stress fields. Consequently, there is no need for a posteriori
heat flux and stress smoothing technique.
Resulting hexahedral finite element HC8/27 satisfies mathematical convergence requirements, like consistency and
stability, even when it is rigorously slandered, distorted or used for the totally incompressible materials. The finite
elements may differ in size up to 7 orders of magnitude. In order to minimize accuracy error and enable
introductions of displacement and stress constraints, the tensorial character of the present finite element equations
is fully respected.
Key words — Finite elements, thermo-mechanical, 3D problem, Multifield, Multiscale, Reliability, Elasticity, Geometric
invariance
Applications in cutting edge and standard model problems:
Incompressible - vascular vessels
O-ring, rubber
Fluid - solid interaction
EM - solid interaction
Melting point behavior
Bi-metals -interfacial stresses
Multiscale composite analysis with and/or without homogenization
Impact protectors
One-to-one bridging with molecular dynamic - nanoindentation
Publishing
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Mijuca D (1999) On The Main Properties Of The Primal-Mixed Finite Element Formulation, FACTA UNIVERSITATIS. 2(9) 903 - 920
UDC 518.12 532.12 539.3
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Mijuca D (2001) A New Primal-Mixed 3d Finite Element. Facta Universitatis 3(11) 167-178
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Mijuca D (2004) On Hexahedral Finite Element HC827 In Elasticity. Computational Mechanics 33(6) 466-480
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Mjuca D (2006) On Primal-Mixed formulation in Elasticity and Thermoelasticity. Monograph
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Mijuca D (2010) On A New 3D Primal-Mixed Finite Element Approach For Thermal Stress Analysis Of Multi-Layered Geometrically
Multiscale Structures. Finite Elements in Anal.
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Mijuca D et al (1997) Some Remarks On The Energy Norm And Z-Z Error Estimator. SOLID MECHANICS. VOL LXXVII 3 254-262 YU
ISBN 86-7025-263-5.
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Mijuca D et al (1998) On the efficiency of the primal-mixed finite element scheme (in 2d) Conference CST'98
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12/17/2019 10:2
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Mijuca D et al (1999) On The Main Properties Of The Primal-Mixed Finite Element Formulation. Facta Universitatis 2(9) 903 - 921
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Mijuca D et al (2005) A Novel One-To-One Multiscale Approach to Computational Mechanics of Matertals. WON Conference 180-
186.pdf
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Mijuca D et al (2006) Finite Element Simulations in Elastic and Heat Transfer Analysis. NEC Report
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Mijuca D et al (2007) A Novel Primal-Mixed Finite Element Approach For Heat Transfer In Soids. Computational Mechanics 39(4)
367-381
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Mijuca D etal (2011) On Accurate And Time Efficient Solution OF Primal Mixed Finite Element Equations In Multiscale Sold
Mechanics. International journal for Numerical Methods in Biomedical Engineering 27(1) 95-112
Recent Citations
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Cornejo, Alejandro, Mataix Vicente, Zarate Francisco. (2019) Onaate, Eugenio. Combination of an adaptive remeshing
technique with a coupled FEM-DEM approach for analysis of crack propagation problems. Computational Particle Mechanics.
10.1007/s40571-019-00306-4
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Ilya Telyatnikov (2019) Modeling of deformation processes in lithospheric structures during their static interaction. THERM SCI.
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Masrat Bashir, Adnan Qayoum, Shahid Saleem (2019) Analysis of frictional heating and thermal expansion in a disc brake
using COMSOL. J Phys Conf
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Qiang Xi. Zhuo-Jia Fu, Timon Rabczuk (2019) An efficient boundary collocation scheme for transient thermal analysis in large-
size-ratio functionally graded materials under heat source load. COMPUT MECH
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Thi Huyen Cham Le, Michele D’Ottavio, Philippe Vidal, Olivier Polit (2018) Robust Displacement and Mixed CUF-Based Four-
Node and Eight-Node Quadrilateral Plate Elements. In book: Analysis and Modelling of Advanced Structures and Smart
Systems. DOI: 10.1007/978-981-10-6895-9_6
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A Sinu, Sundararajan Natarajan, K Shankar (2018) Quadratic serendipity finite elements over convex polyhedra. International
Journal for Numerical Methods in Engineering 113(1):109–129 DOI: 10.1002/nme.5605
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James Liu, Graham Harper, Nolisa Malluwawadu, Simon John Tavener (2018) Lowest-order weak Galerkin finite element
method for Stokes flow on polygonal meshes. Journal of Scientific Computing 78(3)1917–1941
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Bishnu Prasad Lamichhane,,Michael H. Meylan (2017) A new MITC finite element method for Reissner--Mindlin plate problem
based on a biorthogonal system DOI: Proceedings of the 18th Biennial Computational Techniquesand Applications
Conference.issn1445-8810 10.21914/anziamj.v58i0.11754
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Wojciech Gilewski, Marta Sitek (2017) Plate Finite Element with Physical Shape Functions: Correctness of the Formulation.
Archives of Civil Engineering 63(3). 10.1515/ace-2017-0026
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Eric Li, Z. C. He, G. R. Liu (2107) Evaluation of the stiffness matrix in static and dynamic elasticity problems. Acta Mechanica
229(1) DOI: 10.1007/s00707-017-1977-2
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Minghao Li, Dongyang Shi, Ying Dai (2016)The Brezzi–Pitkäranta stabilization scheme for the elasticity problem. Journal of
Computational and Applied Mathematics 286. DOI: 10.1016/j.cam.2015.02.024
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Kamel Meftah, , Lakhdar Sedira, Wajdi Zouari, Mabrouk HECINI, Mabrouk HECINI (2015) A multilayered 3D hexahedral finite
element with rotational. European Journal of Computational Mechanic. s DOFs. DOI: 10.1080/17797179.2015.1089462
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Miguelk Cervera, Michèle Chiumenti, Ramon Codina (2010) Mixed Stabilized Finite Element Methods in Nonlinear Solid
Mechanics. Part I: Formulation. Computer Methods in Applied Mechanics and Engineering 199(37):2559-2570. DOI:
10.1016/j.cma.2010.04.006
It can be integrated seamlessly
It can be integrated seamlessly before any advanced calculation tools for fracture, fatigue, wearing, aging or else.
The motive could be:
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mesh independent,
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HEXA mesh is made from tetra without worry about the quality of the mesh, not prone to any kind of locking
(shear, volumetric ...),
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no need for stress recovery technique,
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heat flux and stresses are primal variables as temperature and displacement and of the same accuracy,
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it allows boundary conditions per stresses for the direct transfer of initial stresses from thermal, EM, or CFD
calculations,
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it is multiscale and allows one-to-one bridging with atomistic simulations without spuriousity or need for periodic
boundary conditions.
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it gives more accurate insight into interfacial stresses.