This study proposes a multi-field asymptotic homogenization for the analysis of thermo-piezoelectric materials with periodic microstructures. The effect of the microstructural heterogeneity is taken into account by means of periodic perturbation functions, which derive from the solution of non homogeneous recursive cell problems defined over the unit periodic cell. A strong coupling is present between the micro displacement field and the micro electric potential field, since the mechanical and the electric problems are fully coupled in the asymptotically expanded microscale field equations. The micro displacement, the electric potential, and the relative temperature fields have been related to the macroscopic quantities and to their gradients in the derived down-scaling relations. Average field equations of infinite order have been obtained and the closed form of the overall constitutive tensors has been determined for the equivalent first-order homogenized continuum. A formal solution of such equations has been derived by means of an asymptotic expansion of the macro fields. The accuracy of the proposed formulation is assessed in relation to illustrative examples of a bi-material periodic microstructure subjected to harmonic body forces, free charge densities, and heat sources, whose periodicity is much greater than the characteristic microstructural size. The good agreement obtained between the solution of the homogenized model and the finite element solution of the original heterogeneous material problem confirms the validity of the proposed formulation.
The effect of hydrostatic pressure on thermodynamic characteristics of NH$_3$CH$_2$COOH$\cdot$H$_2$PO$_3$ type ferroelectric materials
模型NH $_3$ CH $_2$ COOH $\cdot$ H $_2$ PO $_3$，考虑到有序结构元素和应变之间的压电耦合，修改$\varepsilon_i$，$\varepsilon_j$，用于调查的影响下出现的外部压力。在二粒子集团近似下，计算了机械固定和自由晶体的极化矢量分量和静态介电常数张量，以及它们的压电和热学特性。研究了静水压力对晶体相变和计算物理特性的影响。这些晶体的实验数据得到了很好的定量描述。
Vanadium-Engineered Co2NiSe4 Nanomaterial: Coupled Thermoelectric, Piezoelectric, and Electronic Optimization via DFT+U for Advanced Energy Applications
Length-scale dependent average structures, piezoelectricity enhancement and depolarization mechanisms in a non-MPB high-performance piezoelectric alloy system PbTiO3-Bi(Zr1/2Ni1/2)O3
Crafting the strain state in epitaxial thin films: A case study of CoFe2O4 films on Pb(Mg,Nb)O3-PbTiO3
无论是从基础科学的角度还是从应用的角度，都已经广泛地研究了电和磁性质的应变依赖性。通过场致极化旋转（PRO）和极化重取向（PRE）在压电单晶中的机电耦合可以在薄膜/衬底外延异质结构中提供有效应变。然而，PRO和PRE的特定途径是一个复杂的热力学过程，取决于化学组成、温度、电场和机械负荷。本文系统地研究了不同初始相和取向结构的Pb（Mg，Nb）O_3-PbTiO_3单晶的场致相变随温度的变化。不同类型的应变，挥发性/非挥发性和双轴/单轴，已被测量的宏观和原位X射线衍射技术。此外，通过磁各向异性测量研究了外延Mn掺杂CoFe 2 O 4薄膜的应变状态，其中巨磁电耦合已被证明。
Consistent machine learning for topology optimization with microstructure-dependent neural network material models
Delft University of Technology（代尔夫特理工大学）；Princeton University（普林斯顿大学）；Princeton Materials Institute (PMI), Princeton University（普林斯顿材料研究所（PMI），普林斯顿大学）；Brown University（布朗大学）
Predicting cement microstructure and mechanical properties in hydrating cement paste with a Phase-Field model
Duke University（杜克大学）；UCLouvain（天主教鲁汶大学）；ENPC, Institut Polytechnique de Paris, Univ Gustave Eiffel（法国国立路桥学校，巴黎理工学院，古斯塔夫·埃菲尔大学）；University of Montpellier（蒙彼利埃大学）
