A　3D　peridynamic　method　involving　the　work　done　by　the　non-conservative　force　is　developed,　whose　theoretical　framework　comprises　two　parts:　the　viscoelastic　motion　equation　of　material　points　and　the　rate-dependent　fracture　criterion　of　the　bond.　For　the　description　of　motion,　a　viscoelastic　interaction　model　between　material　points　is　proposed　based　on　the　understanding　deformation　mechanism　of　concrete.　Further,　the　viscoelastic　motion　equation　is　theorized　by　applying　Hamilton＇s　principle　which　considers　the　energy　dissipation,　as　a　result,　the　viscoelastic　deformation　of　brittle　material　can　be　captured.　The　elastic　and　viscous　parameters　are　calibrated　by　the　energy　density　equivalence　between　the　developed　3D　peridynamic　method　and　the　classical　continuum　mechanics　under　the　same　deformation　condition.　For　the　control　of　strength　and　cracking,　the　dynamic　uniaxial　S　strength　criterion　is　introduced　into　the　fracture　criterion　of　the　bond　so　that　the　rate-dependent　behavior　of　strength　and　cracking　failure　can　be　reflected.　The　function　and　superiority　of　the　developed　3D　peridynamic　method　are　discussed　via　numerical　experiments.　It　is　found　that　the　developed　peridynamic　method　can　reasonably　reflect　the　influence　of　loading　rate　on　the　deformation,　strength,　and　cracking　of　brittle　material.　©　2022　Elsevier　Ltd