?url_ver=Z39.88-2004&rft_id=arXiv%3A1701.03361&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Feprints.imtlucca.it%2F3674%2F&rft.title=Multi-field+asymptotic+homogenization+of+thermo-piezoelectric+materials+with+periodic+microstructure&rft.creator=Fantoni%2C+Francesca&rft.creator=Bacigalupo%2C+Andrea&rft.creator=Paggi%2C+Marco&rft.subject=T+Technology+(General)&rft.subject=TJ+Mechanical+engineering+and+machinery&rft.description=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%2C+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%2C+since+the+mechanical+and+the+electric+problems+are+fully+coupled+in+the+asymptotically+expanded+microscale+field+equations.+The+micro+displacement%2C+the+electric+potential%2C+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%2C+free+charge+densities%2C+and+heat+sources%2C+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.&rft.publisher=arXiv&rft.date=2017&rft.type=Working+Paper&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.rights=cc_by_nc&rft.identifier=http%3A%2F%2Feprints.imtlucca.it%2F3674%2F1%2F1701.03361.pdf&rft.identifier=++Fantoni%2C+Francesca+and+Bacigalupo%2C+Andrea+and+Paggi%2C+Marco++Multi-field+asymptotic+homogenization+of+thermo-piezoelectric+materials+with+periodic+microstructure.++Working+Paper+++arXiv+++++++(Submitted)+++&rft.relation=https%3A%2F%2Farxiv.org%2Fpdf%2F1701.03361&rft.relation=arXiv%3A1701.03361