Finite plasticity in $$\varvec{P}^\top \! \varvec{P}$$P⊤P. Part I: constitutive model
Finite plasticity in $$\varvec{P}^\top \! \varvec{P}$$P⊤P. Part I: constitutive model
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DOI：
10.1007/s00161-016-0522-1
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发表时间：
2017
影响因子：
2.6
通讯作者：
D. Grandi;U. Stefanelli
中科院分区：
文献类型：
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作者：
D. Grandi;U. Stefanelli
用对称张量$$\varvec{P}^top\\varvec{P}$$代替经典塑性应变$$\varvec{P}$$，建立了一个有限塑性模型。这种结构是通过假设材料行为相对于中间构型的框架变换是不变的而产生的。由此得到的变分模型是低维的、对称的，并且仅基于参考构型。我们讨论了物质点水平的能量解的存在性以及时间离散化的收敛问题。通过严格的演化--收敛论证，确定了小变形模型的线性化。在第二部分中，将本构模型与平衡系统相结合，在其中我们证明了准静态演化的存在性，并确定了线性化极限(Grani和Stefan elli在2016年)。
We address a finite-plasticity model based on the symmetric tensor $$\varvec {P}^\top\!\varvec {P} $$ instead of the classical plastic strain $$\varvec {P} $$. Such a structure arises by assuming that the material behavior is invariant with respect to frame transformations of the intermediate configuration. The resulting variational model is lower dimensional, symmetric and based solely on the reference configuration. We discuss the existence of energetic solutions at the material-point level as well as the convergence of time discretizations. The linearization of the model for small deformations is ascertained via a rigorous evolution--convergence argument. The constitutive model is combined with the equilibrium system in Part II where we prove the existence of quasistatic evolutions and ascertain the linearization limit (Grandi and Stefanelli in 2016).