二阶抽象非线性发展包含及其在粘弹塑性中的应用

A note on the derivation of rigid-plastic models

This note is devoted to a rigorous derivation of rigid-plasticity as the limit of elasto-plasticity when the elasticity tends to infinity.

Existence of solution for a nonlinear model of thermo-visco-plasticity

We study a thermodynamically consistent model describing phenomena in a visco-plastic metal subjected to temperature changes. We complete the model with the mixed boundary condition on displacement and stress and Neumann-type condition for temperature. The main result is an existence of solution.

关于率无关耦合弹塑性损伤模型的粘塑性近似

On the visco-plastic approximation of a rate-independent coupled elastoplastic damage model

本文研究损伤与塑性传播的率无关系统，通过相同速率的粘性演化构造近似解，克服了正则性不足导致的链式法则失效问题，最终用能量-耗散平衡刻画了极限演化。

Renormalised solutions in thermo-visco-plasticity for a Norton-Hoff type model. Part I: the truncated case

We prove existence of global in time strong solutions to the truncated thermo- visco-plasticity with an inelastic constitutive function of Norton-Hoff type. This result is a starting point to obtain renoramlised solutions for the considered model without truncations. The method of our proof is based on Yosida approximation of the maximal monotone term and a passage to the limit.

Visco-Energetic solutions to some rate-independent systems in damage, delamination, and plasticity

This paper revolves around a newly introduced weak solvability concept for rate-independent systems, alternative to the notions of Energetic and Balanced Viscosity solutions. Visco-Energetic solutions have been recently obtained by passing to the time-continuous limit in a time-incremental scheme, akin to that for Energetic solutions, but perturbed by a `viscous' correction term, as in the case of Balanced Viscosity solutions. However, for Visco-Energetic solutions this viscous correction is tuned by a fixed parameter. The resulting solution notion turns out to describe a kind of evolution in …

Strain gradient visco-plasticity with dislocation densities contributing to the energy

We consider the energetic description of a visco-plastic evolution and derive an existence result. The energies are convex, but not necessarily quadratic. Our model is a strain gradient model in which the curl of the plastic strain contributes to the energy. Our existence results are based on a time-discretization, the limit procedure relies on Helmholtz decompositions and compensated compactness.

Globally stable quasistatic evolution in plasticity with softening

We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each time interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response.

Quasistatic evolution models for thin plates arising as low energy Gamma-limits of finite plasticity

In this paper we deduce by Γ-convergence some partially and fully linearized quasistatic evolution models for thin plates, in the framework of finite plasticity. Denoting by ε the thickness of the plate, we study the case where the scaling factor of the elasto- plastic energy is of order ε^ (2α-2), with α>=3. We show that solutions to the three- dimensional quasistatic evolution problems converge, as the thickness of the plate tends to zero, to a quasistatic evolution associated to a suitable reduced model depending on α.

有限应变下的准静态非关联塑性

Quasistatic nonassociative plasticity at finite strains

本文研究有限应变下非关联塑性的准静态演化问题，提出测度值能量解概念，并利用时空磨光正则化耗散项证明了解的存在性。

Relaxation of the single-slip condition in strain-gradient plasticity

We consider the variational formulation of both geometrically linear and geometrically nonlinear elasto-plasticity subject to a class of hard single-slip conditions. Such side conditions typically render the associated boundary-value problems non-convex. We show that, for a large class of non-smooth plastic distortions, a given single-slip condition (specification of Burgers vectors) can be relaxed by introducing a microstructure through a two-stage process of mollification and lamination. The relaxed model can be thought of as an aid to simulating macroscopic plastic behaviour without the nee…

From visco to perfect plasticity in thermoviscoelastic materials

We consider a thermodynamically consistent model for thermoviscoplasticity. For the related PDE system, coupling the heat equation for the absolute temperature, the momentum balance with viscosity and inertia for the displacement variable, and the flow rule for the plastic strain, we propose two weak solvability concepts, 'entropic' and 'weak energy' solutions, where the highly nonlinear heat equation is suitably formulated. Accordingly, we prove two existence results by passing to the limit in a carefully devised time discretization scheme. Furthermore, we study the asymptotic behavior of wea…

A vanishing viscosity approach to quasistatic evolution in plasticity with softening

We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the variational framework for rate-independent problems to the case of a nonconvex energy functional. We argue that, in this case, the use of global minimizers in the corresponding incremental problems is not justified from the mechanical point of view. Thus, we analize a different selection criterion for the solutions of the quasistatic evolution problem, base…

大位移与大应变欧拉框架下粘弹性动力学的时间离散

Time discretization in visco-elastodynamics at large displacements and strains in the Eulerian frame

本文将后向Euler全隐式时间离散应用于Euler框架下的大位移大应变粘弹性非线性动力学模型，考虑Kelvin-Voigt与Jeffreys流变，设计了正则化格式并证明其数值稳定性与弱解收敛性。

Well-posedness for dislocation based gradient visco-plasticity with isotropic hardening

In this work we establish the well-posedness for infinitesimal dislocation based gradient viscoplasticity with isotropic hardening for general gradient monotone plastic flows. We assume an additive split of the displacement gradient into non-symmetric elastic distortion and non-symmetric plastic distortion. The thermodynamic potential is augmented with a term taking the dislocation density tensor $\operatorname{Curl} p$ into account. The constitutive equations in the models we study are assumed to be of self-controlling type. Based on the generalized version of Korn's inequality for incompatib…

有限塑性中的一个均匀化结果

A homogenization result in finite plasticity

针对带硬化的有限应变弹塑性非均质材料储能的积分泛函，在周期微观结构假设下，通过将$\textsf{SL}(3)$视为芬斯勒流形突破塑性变形约束障碍，建立了能量在周期趋于零时的$Γ$-收敛性。

大位移下的卷积线性热粘弹性动力学的时间离散

Time discretization in convected linearized thermo-visco-elastodynamics at large displacements

本文提出了一种大位移下的卷积线性热粘弹性动力学时间离散方案，通过分析动能的凸性和熵不等式，证明了数值稳定性和收敛性。

率无关弹塑性弹簧网络模型与非局部随机场的均匀化

Homogenization of rate-independent elastoplastic spring network models with non-local random fields

该研究建立了含随机长程相互作用的弹塑性弹簧网络的离散到连续极限，证明演化解收敛于耦合分数阶非局部能量的连续模型，为纤维增强复合材料动态模拟奠定数学基础。