On the formulation of evolutive laws and complementarity conditions for non-smooth elastoplastic materials

IF 1.9 4区工程技术 Q3 MECHANICS

Continuum Mechanics and Thermodynamics Pub Date : 2025-01-03 DOI:10.1007/s00161-024-01341-0

Fabio De Angelis

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Abstract

In the present work a formulation of evolutive laws and complementarity conditions in non-smooth elastoplasticity is discussed. The treatment addresses the problem of non-smooth elastoplasticity which is represented by functions characterized by singularities and defined by non-smooth yielding limit conditions and non-differentiable functions. The mathematical theory of subdifferential calculus is properly advocated to provide the suitable mathematical framework in order to treat non-differentiable functions and non-smooth problems. Extended expressions of evolutive laws and complementarity conditions in non-smooth elastoplasticity are illustrated within the adopted generalized mathematical treatment. Relations between the presented mathematical formulations and the expressions in classical elastoplasticity are pointed out and discussed. The proposed treatment has significant advantages since it provides a geometrical framework to the maximum dissipation principle for non-smooth problems in elastoplasticity. Furtherly, the proposed treatment gives insights in the interpretation of the adopted geometrical framework for different types of evolutive laws for new materials and solids such as for instance in some types of new metamaterials with non-smooth constitutive behavior. In addition, the present formulation is also useful in the design of metamaterials, such as pantographic ones, where the plasticity of the pivots is relevant.

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非光滑弹塑性材料演化规律及互补条件的表述

本文讨论了非光滑弹塑性的演化规律和互补条件。该方法解决了用奇异函数表示的非光滑弹塑性问题，该问题由非光滑屈服极限条件和不可微函数定义。适当地提倡子微分的数学理论，为处理不可微函数和非光滑问题提供合适的数学框架。在采用的广义数学处理中，给出了非光滑弹塑性演化规律和互补条件的扩展表达式。指出并讨论了所提出的数学公式与经典弹塑性公式之间的关系。该方法为弹塑性非光滑问题的最大耗散原理提供了一个几何框架，具有显著的优越性。此外，所提出的处理方法为新材料和固体的不同类型演化规律所采用的几何框架的解释提供了见解，例如在某些类型的具有非光滑本构行为的新超材料中。此外，本公式也可用于设计超材料，如受电弓材料，其中轴的可塑性是相关的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.