Theoretical and numerical aspects of the material and spatial settings in nonlinear electro-elastostatics
Source abstract
Abstract
The formulation of the spatial and material motion problem in nonlinear electro-elastostatics is revisited in this work. A finite element discretization is realized and a numerical example is presented to demonstrate possible application of the formulation in studying the closing process of cracks.
The source flagged this abstract for review. Check formulas and completeness against the original publication.
Source: expertdata · Quality: needs review · Source record ↗
Source flags: short_text
Source flags: short_text
Research context
OpenAlex topics: Structural Health Monitoring Techniques · Ultrasonics and Acoustic Wave Propagation · Numerical methods in engineering
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (29)
Show source-provided references
1. Abendroth M, Groh U, Kuna M and Ricoeur A (2002). Finite element-computation of the electromechanical J-integral for 2-D and 3-D crack analysis. Int J Fract 114: 359–37810.1023/A:1015725725879 ↗
2. Bar-Cohen Y (2002) Electro-active polymers: current capabilities and challenges. In: Proceedings of SPIE – electroactive polymer actuators and devices10.1117/12.475159 ↗
3. Dascalu C and Maugin GA (1994). Energy-release rates and path-independent integrals in electroelastic crack propagation. Int J Eng Sci 32(5): 755–76510.1016/0020-7225(94)90058-2 ↗
4. Denzer R (2006) Computational configurational mechanics. Dissertation, Technische Universität Kaiserslautern, Germany
5. Denzer R, Barth FJ and Steinmann P (2003). Studies in elastic fracture mechanics based on the material force method. Int J Numer Methods Eng 58: 1817–183510.1002/nme.834 ↗
6. Epstein M and Maugin GA (1990). Inhomogeneities, Eshelby’s tensor and J-integral in electroelasticity. In: Hsieh, RKT (eds) Mechanical modelling of new electromagnetic materials, pp 253–258. Elsevier, Amsterdam
7. Epstein M and Maugin GA (1991). Energy-momentum tensor and J-integral in electrodeformable bodies. Int J Appl Electromagn Mater 2: 141–145
8. Huang Y-N and Batra RC (1996). Energy-momentum tensors in nonsimple elastic dielectrics. J Elasticity 42: 275–28110.1007/BF00041793 ↗
9. Kalpakides VK and Agiasofitou EK (2002). On material equations in second gradient electroelasticity. J Elasticity 67: 205–22710.1023/A:1024926609083 ↗
10. Kienzler R and Herrmann G (2000). Mechanics in material space with applications to defect and fracture mechanics. Springer, Berlin Heidelberg New York
11. Kuhl E and Steinmann P (2004). Computational modeling of healing: an application of the material force method. Biomech Model 2: 187–203
12. Liebe T, Denzer R and Steinmann P (2003). Application of the material force method to isotropic continuum damage. Comput Mech 30: 171–18410.1007/s00466-002-0377-0 ↗
13. Maugin GA (1993) Material inhomogeneities in elasticity. Chapman and Hall10.1007/978-1-4899-4481-8 ↗
14. Maugin GA and Epstein M (1991). The electroelastic energy-momentum tensor. Proc Roy Soc London A 433: 299–31210.1098/rspa.1991.0049 ↗
15. McMeeking RM and Landis CM (2005). Electrostatic forces and stored energy for deformable dielectric materials. ASME J Appl Mech 72: 581–59010.1115/1.1940661 ↗
16. Pak YE (1990). Crack extension force in a piezoelectric material. ASME J Appl Mech 57: 647–65310.1115/1.2897071 ↗
17. Pak YE and Herrmann G (1986a). Conservation laws and the material momentum tensor for the elastic dielectric. Int J Eng Sci 24: 1365–137410.1016/0020-7225(86)90065-0 ↗
18. Pak YE and Herrmann G (1986b). Crack extension force in a dielectric medium. Int J Eng Sci 24: 1375–138810.1016/0020-7225(86)90066-2 ↗
19. Qi H, Fang D and Yao Z (2001). Analysis of electric boundary condition effects on crack propagation in piezoelectric ceramics. Acta Mech Sinica 17(1): 59–7010.1007/BF02487770 ↗
20. Steinmann P (2000). Application of material forces to hyperelastostatic fracture mechanics. I. Continuum mechanical setting. Int J Solids Struct 37: 7371–739110.1016/S0020-7683(00)00203-1 ↗
21. Steinmann P (2002a). On spatial and material setting of hyperelastodynamics. Acta Mech 156: 193–21810.1007/BF01176756 ↗
22. Steinmann P (2002b). On spatial and material setting of thermo-hyperelastodynamics. J Elasticity 66: 109–15710.1023/A:1021233322132 ↗
23. Steinmann P (2002c). On spatial and material settings of hyperelastostatic crystal defects. J Mech Phys Solids 50: 1743–176610.1016/S0022-5096(01)00135-1 ↗
24. Steinmann P (2005). On potential energy shifts in hyperelastic energy-momentum tensors. Technische Mechanik 25(3–4): 174–181
25. Steinmann P, Ackermann D and Barth FJ (2001). Application of material forces to hyperelastostatic fracture mechanics. II. Computational setting. Int J Solids Struct 38: 5509–552610.1016/S0020-7683(00)00381-4 ↗
26. Trimarco C (2007). Material electromagnetic fields and material forces. Arch Appl Mech 77(2–3): 177–18410.1007/s00419-006-0056-2 ↗
27. Vu DK, Steinmann P (2007) Nonlinear electro- and magneto-elastostatics: material and spatial settings. Int J Solids Struct (accepted)10.1016/j.ijsolstr.2007.05.017 ↗
28. Vu DK, Steinmann P and Possart G (2007). Numerical modelling of non-linear electroelasticity. Int J Numer Methods Eng 70: 685–70410.1002/nme.1902 ↗
29. Wang XD and Jiang LY (2003). The effective electroelastic property of piezoelectric media with parallel dielectric cracks. Int J Solids Struct 40: 5287–530310.1016/S0020-7683(03)00285-3 ↗