Elasto-plasticity theory for large plastic deformation and its use for the material stiffness determination

IF 1.9 4区工程技术 Q3 MECHANICS Continuum Mechanics and Thermodynamics Pub Date : 2024-04-02 DOI:10.1007/s00161-024-01297-1

Martin Weber, Holm Altenbach

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Abstract

In this paper, we present a finite elasto-plasticity theory for large plastic deformations. For the elastic part of the model, we use the St. Venant–Kirchhoff elasticity. The plastic part is described by the isomorphy concept, the yield condition is covered by the isotropic \(J_2\) theory of (Huber in Czas Techn 22:34,1904; von Mises in Math Phys 4:582–592, 1913) and (Hencky in ZAMM 9:215–220, 1924), and the yield condition uses the principle of maximum plastic dissipation. The numeric of this theory is discussed and finally implemented in a Fortran code to use it as material law in the UMAT subroutine of the finite element program Abaqus. The material law is validated using different test calculations like tensile and shear tests as well as a large deformation simulation compared to the Abaqus internal material law. Further, we apply this material model to determine the effective material stiffness tetrad of large deformed inhomogeneous materials. For these purposes, we additionally present an automated method for determining material stiffnesses of an arbitrary material in Abaqus.

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大塑性变形的弹塑性理论及其在材料刚度测定中的应用

在本文中，我们提出了一种用于大塑性变形的有限弹塑性理论。对于模型的弹性部分，我们采用了 St.塑性部分由同态概念描述，屈服条件由（Huber 在 Czas Techn 22:34,1904; von Mises 在 Math Phys 4:582-592, 1913）和（Hencky 在 ZAMM 9:215-220, 1924）的各向同性（J_2\）理论覆盖，屈服条件使用最大塑性耗散原理。对该理论的数值化进行了讨论，并最终在 Fortran 代码中实现，将其用作有限元程序 Abaqus 的 UMAT 子程序中的材料定律。通过拉伸和剪切试验等不同的试验计算，以及与 Abaqus 内部材料定律相比的大变形模拟，对材料定律进行了验证。此外，我们还应用该材料模型来确定大变形不均匀材料的有效材料刚度四元组。为此，我们还介绍了一种在 Abaqus 中确定任意材料的材料刚度的自动化方法。

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来源期刊

Continuum Mechanics and Thermodynamics 物理-力学

CiteScore

5.30

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： This interdisciplinary journal provides a forum for presenting new ideas in continuum and quasi-continuum modeling of systems with a large number of degrees of freedom and sufficient complexity to require thermodynamic closure. Major emphasis is placed on papers attempting to bridge the gap between discrete and continuum approaches as well as micro- and macro-scales, by means of homogenization, statistical averaging and other mathematical tools aimed at the judicial elimination of small time and length scales. The journal is particularly interested in contributions focusing on a simultaneous description of complex systems at several disparate scales. Papers presenting and explaining new experimental findings are highly encouraged. The journal welcomes numerical studies aimed at understanding the physical nature of the phenomena. Potential subjects range from boiling and turbulence to plasticity and earthquakes. Studies of fluids and solids with nonlinear and non-local interactions, multiple fields and multi-scale responses, nontrivial dissipative properties and complex dynamics are expected to have a strong presence in the pages of the journal. An incomplete list of featured topics includes: active solids and liquids, nano-scale effects and molecular structure of materials, singularities in fluid and solid mechanics, polymers, elastomers and liquid crystals, rheology, cavitation and fracture, hysteresis and friction, mechanics of solid and liquid phase transformations, composite, porous and granular media, scaling in statics and dynamics, large scale processes and geomechanics, stochastic aspects of mechanics. The journal would also like to attract papers addressing the very foundations of thermodynamics and kinetics of continuum processes. Of special interest are contributions to the emerging areas of biophysics and biomechanics of cells, bones and tissues leading to new continuum and thermodynamical models.