Existence and time-discretization for the finite-strain Souza–Auricchio constitutive model for shape-memory alloys

被引：0
作者：
Sergio Frigeri
Ulisse Stefanelli
机构：
[1] Università di Pavia,Dipartimento di Matematica ’F. Casorati’
[2] IMATI - CNR,undefined
[3] WIAS,undefined
来源：
Continuum Mechanics and Thermodynamics | 2012年 / 24卷
关键词：
Shape-memory alloys; Finite-strain; Phase transformations in solids; Rate-independence; Existence; Time-discretization; 74C15; 74N30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We prove the global existence of solutions for a shape-memory alloys constitutive model at finite strains. The model has been presented in Evangelista et al. (Int J Numer Methods Eng 81(6):761–785, 2010) and corresponds to a suitable finite-strain version of the celebrated Souza–Auricchio model for SMAs (Auricchio and Petrini in Int J Numer Methods Eng 55:1255–1284, 2002; Souza et al. in J Mech A Solids 17:789–806, 1998). We reformulate the model in purely variational fashion under the form of a rate-independent process. Existence of suitably weak (energetic) solutions to the model is obtained by passing to the limit within a constructive time-discretization procedure.
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页码：63 / 77
页数：14
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共 104 条
  • [11] Bessoud A.-L.(1997)Shape-memory alloys: modelling and numerical simulations of the finite-strain superelastic behavior Comput. Methods Appl. Mech. Eng. 143 175194-1069
  • [12] Reali A.(2011)Magnetic shape memory alloys: three-dimensional modeling and analysis Math. Models Meth. Appl. Sci. 21 1043-317
  • [13] Stefanelli U.(2002)Non-convex potentials and microstructures in finite-strain plasticity R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 458 299-3709
  • [14] Auricchio F.(2009)A finite element model for shape memory alloys considering thermomechanical couplings at large strains Int. J. Solids Struct. 46 3694-165
  • [15] Mielke A.(2011)A rate-independent model for permanent inelastic effects in shape memory materials Netw. Heterog. Media 6 145-421
  • [16] Stefanelli U.(2009)Phenomenological 3D and 1D consistent models for shape-memory alloy materials Comput. Mech. 44 405-785
  • [17] Auricchio F.(2010)A 3D SMA constitutive model in the framework of finite strain Int. J. Numer. Methods Eng. 81 761-244
  • [18] Petrini L.(1987)Matériaux à mémoire de forme C. R. Acad. Sci. Paris Sér. II Méc. Phys. Chim. Sci. Univers Sci. Terre 304 239-849
  • [19] Auricchio F.(2003)Shape memory behaviour: modelling within continuum thermomechanics Int. J. Solids Struct. 40 827-365
  • [20] Petrini L.(2011)Existence and nonexistence for the full thermomechanical Souza–Auricchio model of shape memeory wires Math. Mech. Solids 16 349-1253
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